Augustin C Tibère-Inglesse

Sean D Mcguire

Pierre Mariotto

Christophe O Laux

Validation cases for recombining nitrogen and air plasmas

We report on Raman scattering and emission spectroscopy measurements in recombining atmospheric pressure plasmas of air and nitrogen. An inductively coupled plasma torch is used to create an equilibrium plasma, which is then forced to rapidly recombine by flowing through a water-cooled tube. For all conditions, temperature measurements are performed using Optical Emission Spectroscopy (OES) and Raman scattering at the exit of tubes of varying lengths. The density of atomic nitrogen is also determined. Evidence of strong chemical nonequilibrium is found in a number of cases. For these cases, we observe that the rotational temperatures measured with OES differ from those measured with Raman scattering, and that the atomic nitrogen density is elevated with respect to equilibrium. A power balance analysis confirms that a large fraction of gas enthalpy is stored in the non-recombined nitrogen atoms. For cases where the plasma remains in equilibrium, we performed numerical simulations using the Eilmer3 CFD code. Eilmer3 does not predict the measured drop in gas temperature measured using Raman and emission spectroscopy. Prior efforts by the CFD community have also failed to correctly predict this temperature drop. The results presented in this paper are therefore intended as validation test-cases for CFD simulations.

I. Introduction

During atmospheric entry, a capsule enters the atmosphere of a planet (Earth, Mars…) at a velocity that can exceed 10 km/s. The strong shockwave that forms in front of the capsule heats the gas to temperatures that can exceed 10,000K. The high temperature of the gas leads to ionization, molecular dissociation, excitation and intense gas radiation. The study of the radiative and convective heat transfer of such a plasma is critical for the design of the heat shield (or thermal protection system, TPS) of the capsule. For high entry velocities, these heatshields are carbon-based and represent a significant constraint for the mission, particularly in regard to their weight. The heat flux to the forebody of the capsule has been the primary focus of past research and is now relatively well understood [START_REF] Gnoffo | Planetary-Entry Gas Dynamics[END_REF] [START_REF] Johnston | Influence of Coupled Radiation and Ablation on the Aerothermodynamic Environment of Planetary Entry Vehicles[END_REF]. However, predictions of the heat flux to the afterbody surface suffer from large uncertainties. This is due mainly to two factors. The first is the presence of significant quantities of carbon in the plasma, introduced via the ablative heat shield in the front of the capsule. The carbon sublimates from the forebody heat shield and recombines in the flow, forming molecules such as CN and CO that emit and absorb radiation in the afterbody region. This is currently the focus of some studies (see for example Refs. [START_REF] Loehle | Ablation Radiation Coupling Investigation in Earth Re-entry Using Plasma Wind Tunnel Experiments[END_REF] [4] [START_REF] Mcguire | Infrared spectroscopic measurements of carbon monoxide within a high temperature ablative boundary layer[END_REF]). The second phenomenon is the hydrodynamic expansion of the plasma into the afterbody region. This expansion rapidly cools the plasma, forces plasma recombination and a departure from chemical equilibrium. This chemical nonequilibrium and the resulting radiation are not accurately modeled at the moment. Earlier experiments conducted at Stanford University in atmospheric pressure recombining nitrogen plasmas showed that certain transitions emit up to 30 times more than the corresponding equilibrium radiation [START_REF] Laux | lonizational Nonequilibrium Induced by Neutral Chemistry in Air Plasmas[END_REF] [START_REF] Laux | State-to-state modeling of a recombining nitrogen plasma experiment[END_REF]. CFD simulations were also performed to reproduce the measured atomic N recombination and gas cooling but, as shown in Figure 1, were not in agreement with the measurements [START_REF] Candler | Numerical Simulation of a Nonequilibrium Nitrogen Plasma Experiment[END_REF] [START_REF] Nagulapally | Numerical Simulation of Nonequilibrium Nitrogen and Air Plasma Experiments[END_REF]. The experiments were conducted with a water-cooled tube mounted at the exit of an atmospheric pressure plasma torch facility. The CFD calculations predicted that the gas temperature decreases by about 400K between the tube entrance and exit for a tube length of 15 cm. These predictions differ dramatically from the measurements, which show a temperature drop of more than 2400K. [START_REF] Nagulapally | Numerical Simulation of Nonequilibrium Nitrogen and Air Plasma Experiments[END_REF] The combined effect of these two phenomena, namely the introduction of carbon into the flow and the recombination phenomena, leads to large uncertainties on the heat flux to the afterbody surface. For earth reentry, simulations performed by Johnston et al [START_REF] Johnston | Influence of Coupled Radiation and Ablation on the Aerothermodynamic Environment of Planetary Entry Vehicles[END_REF] [START_REF] Johnston | Features of Afterbody Radiative Heating for Earth Entry[END_REF] show that uncertainties on the radiative heat flux to the afterbody can be up to 100% for velocities around 14 km/s. The velocity in the case of a real Mars reentry scenario could be higher, particularly for a Mars reentry mission [START_REF] Johnston | Shock Layer Radiation Modeling and Uncertainty for Mars entry[END_REF] and this would increase the uncertainty resulting from these phenomena.

Figure 1: CFD simulations vs experimental results for several CFD simulations. Figures taken from Ref.

The heat flux per unit area to the afterbody surface is lower than on the forebody: for example, for the Stardust reentry, the total heat flux on the afterbody is about 20 W/cm² as compared to 100 W/cm² [START_REF] Johnston | Features of Afterbody Radiative Heating for Earth Entry[END_REF] on the forebody. However, the afterbody surface represents approximately 2/3 of the total area, and therefore significant heating may occur on the afterbody. Uncertainties on these afterbody heat fluxes can therefore cause an overestimation of the TPS shield due to design margins. This, in turn, leads to a significant cost increase and added weight.

These considerations can affect the feasibility of a mission. A fundamental study of the mechanisms governing the plasma dynamics in the afterbody of a spacecraft is therefore needed in order to reduce these uncertainties.

In this paper, we revisit the previous experiments conducted by Laux, Gessman et al [START_REF] Laux | lonizational Nonequilibrium Induced by Neutral Chemistry in Air Plasmas[END_REF] [7] [START_REF] Gessman | Experimental study of kinetic mechanisms of recombining atmospheric pressure air plasmas[END_REF] at Stanford University. To that end, we have now implemented a Raman scattering diagnostic to complement emission spectroscopy measurements. Whereas emission spectroscopy gives access to excited states, Raman scattering gives access to the ground state. These techniques are thus complementary. We used our 50-kW plasma torch at the EM2C laboratory to supply a high enthalpy plasma, at conditions reproducing those of the Stanford experiments. The plasma is then cooled in a water-cooled tube to force rapid recombination. If cooling is sufficiently fast, a nonequilibrium plasma is produced at the exit of the tube. We use emission and Raman spectroscopy to study the temperature, chemical composition, and resulting radiation from the plasma. These experiments provide simple test cases of recombining plasmas to validate CFD codes: in particular, they provide validation cases for the chemical kinetics mechanisms used in the CFD codes. We performed experiments for a variety of conditions, ranging from equilibrium to nonequilibrium cases, to assess the impact of the chemical kinetics on the plasma properties.

II. Experimental setup

The plasma torch facility is a TAFA Model 66 inductively coupled plasma (ICP) torch powered by a 120-kVA radio frequency LEPEL Model T-50-3 power supply. The power supply operates at 4 MHz and can supply a maximum of 12 kV DC and 7.5 A to the oscillator plates. Details of the plasma torch facility are provided in previous publications [START_REF] Macdonald | Measurements of air plasma/ablator interactions in an inductively coupled plasma torch[END_REF] [7] [START_REF] Laux | Optical diagnostics and radiative emission of air plasmas[END_REF]. The plasma produced within the torch exits through a 1-cm diameter nozzle at a speed of approximately 600 m/s. The plasmas studied here are comprised of 90 or 60 slpm of N2 or air premixed with 50 slpm of argon to provide stable operating conditions for the torch. A water-cooled tube made of brass is mounted on top of the plasma torch. The length of the tube is modular, here up to 25 cm. Emission and Raman measurements are performed at the entrance and exit of the modular tube. Instead of creating a strong expansion as with a reentering capsule, the plasma is forced to recombine by imposing rapid cooling via the cold wall (maintained at approximately 300 K considering the relatively high thermal conductivity of brass). This setup is therefore intended as a simplified experimental model of a real atmospheric entry scenario. Details of the experimental setup are presented in figure 2. Both Raman scattering and emission spectroscopy measurements were performed for several conditions. Optical emission spectroscopy (see setup in figure 3) is used to measure emission from vibrational bands of the first negative system of N2 + and of the first and second positive systems of N2. When atomic lines are visible, the plasma temperature is measured using absolute emission of several lines of different species, using the procedure detailed in [START_REF] Laux | Optical diagnostics and radiative emission of air plasmas[END_REF]. It is important to note that the use of emission from atomic lines to measure temperature relies on the assumption of equilibrium, which has only been verified to be valid at the entrance of the water-cooled tube and needs to be verified at the exit of the tube. However, where presented, these measurements were found to be consistent with other measurements of temperature, namely using Raman scattering. If no atomic lines are detectable, the temperature is measured using emission spectroscopy of N2 + rotational lines using the procedure detailed in [START_REF] Laux | Rotational temperature measurements in air and nitrogen plasmas using the first negative system of N2 +[END_REF]. The measured molecular spectra are compared with theoretical ones generated using the radiation code SPECAIR [START_REF] Specair | Software Package, Ver. 3.0[END_REF] assuming the measured equilibrium temperature and the known pressure (1 atm). N2 first positive emission is studied in detail. Here also, the SPECAIR radiation code is used to analyze it. For equilibrium cases, this first positive emission is found to be in good agreement with equilibrium calculations at the measured temperature, providing additional confirmation of the gas temperature for these cases. However, there are a number of cases where the first positive emission cannot be modeled under an assumption of equilibrium. For these cases, a secondary measure of temperature is necessary (e.g. N2 + emission or N2 Raman scattering). It is then possible to adjust the population of all emitting vibrational levels of the N2 B electronic state in SPECAIR [START_REF] Laux | Optical diagnostics of atmospheric pressure air plasmas[END_REF] for this transition. This is done using an overpopulation factor for each vibrational level, defined as

𝜌 𝜈 = 𝑛 𝜈 (𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑) 𝑛 𝜈 (𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚)
where nv is the population density of vibrational level v. The equilibrium value is determined using the temperature obtained via either Raman scattering or N2 + emission.

Figure 3: Experimental setup used for emission spectroscopy

All spectra measured using emission spectroscopy are calibrated from pixel counts to absolute emission intensity using an Optronics Laboratories tungsten lamp (model OL550). All spectra are Abel-inverted to obtain the spatially resolved local plasma emission.

To provide an independent confirmation of the gas temperature measured using OES, vibrational Raman scattering measurements have been performed. These yield information on the ground state levels of N2. Given that the bulk of the gas will be in the ground state, these Raman measurements are more representative of the gas temperature. The experimental setup for Raman spectroscopy is presented in Figure 4 and the detailed measurement procedure is given in Ref [START_REF] Mcguire | Ultraviolet Raman spectroscopy of N2 in a recombining atmospheric pressure plasma[END_REF]. Measurements are performed in the UV region of the spectrum. A frequency-doubled Continuum dye laser was used to generate a 10-ns, 30-mJ ultraviolet pulse at 281 nm. Rhodamine 590 dye was used to form a 562-nm laser beam that was then frequency-doubled to produce the final output beam at 281 nm. While the quadrupled output of a Nd:YAG laser at 266 nm may have sufficed for the measurements, the ability to tune the dye laser offered the ability to avoid potential laser-induced interferences in the UV. The wavelength used for these measurements, namely 281 nm, represents a tradeoff between avoiding laser-induced interferences and maximizing laser power. This Raman technique is sensitive to both the rotational and vibrational temperatures of the N2 ground state. The results suggest that both temperatures are in equilibrium, so only one temperature will be given in the results section. Moreover, rotational relaxation at atmospheric pressure is very fast and so we assume that rotational and translational temperatures are equal. Additional Rayleigh scattering measurements of density support this assumption [START_REF] Mcguire | Ultraviolet Raman spectroscopy of N2 in a recombining atmospheric pressure plasma[END_REF]. Ultimately, the fluid dynamics and plasma kinetics within the water-cooled tube are coupled. However, in an effort to decouple these effects, experiments were performed for a variety of conditions presented in Table 1. The conditions range from laminar to turbulent regimes and from chemical equilibrium to nonequilibrium. The chemical conditions (equilibrium or nonequilibrium) are estimated based on the results of Gessman et al. [START_REF] Gessman | An experimental investigation of the effects of chemical ionizational nonequilibrium in recombining atmospheric pressure air plasmas[END_REF] and will be verified in the Results section. Note that the measurements for the case 'Pure air' are taken from the paper by Gessman et al [START_REF] Gessman | An experimental investigation of the effects of chemical ionizational nonequilibrium in recombining atmospheric pressure air plasmas[END_REF]. We repeated these experiments and obtained the same results, which are therefore not presented here. For all other cases, the reported results are from the measurements presented in this paper. In the first part of this article, we give an overview of the experiments performed in air/argon or nitrogen/argon mixtures. For each test condition, we provide the temperature profiles measured using both emission and Raman spectroscopy, the emission spectra of the nitrogen first positive system, and the power balance. While the Air/Ar mixture remains in equilibrium, the N2/Ar mixture is found to be in chemical nonequilibrium at the exit of the tube. For equilibrium cases using the Air/Ar mixture, the underlying dynamics are governed primarily by the Air/Ar flow regime. Both laminar and turbulent cases are examined. For nonequilibrium cases using the N2/Ar mixture, both hydrodynamics and chemical kinetic effects are important. The nonequilibrium vibrational distributions within the N2B electronic state were measured and used to infer the density of unrecombined atomic nitrogen [START_REF] Laux | State-to-state modeling of a recombining nitrogen plasma experiment[END_REF]. In the second part of this paper, we will discuss simulations done using the CFD code Eilmer3 [START_REF] Gollan | About the formulation, verification and validation of the hypersonic flow solver Eilmer[END_REF].

Mass flow rate

II)

Experimental study of Air/Ar and N2/Ar plasmas a. Air/Ar

The basic operating conditions for these test cases are presented in Table 1. The gas is air (1.9 g/s) mixed with argon (1.5 g/s). Three tube lengths were investigated: 0 cm (inlet of the tube), 10 and 15 cm. The radial temperature profiles were measured with both Raman scattering and OES. As can be seen in Fig. 5, the two methods are in agreement. For the emission spectroscopy measurements, several atomic lines (Argon at 738, 750, 751 and 763 nm, Nitrogen at 742, 744, 746 nm) were used, and all yielded the same temperature within experimental uncertainty. Therefore, only the temperature profile obtained from the oxygen triplet at 777 nm is presented in the figure. The relatively high uncertainty bars for the Raman measurements at 0 cm are due to the low signal-to-noise ratio, because of the low densities associated with high temperatures, and because nitrogen is highly dissociated at these temperatures. Finally, note that the Raman scattering measurements give both the rotational and vibrational temperatures of N2 ground state. Because the rotational and vibrational temperatures were found to be equal, only one temperature is presented here.

Overall, the Raman and emission spectroscopy closely match, which indicates that the flow remains close to LTE at all positions. The centerline temperature drop is about 2400 K. Emission spectra of the N2 first positive transition were recorded between 550 to 800 nm. These spectra are also calibrated in absolute intensity and are Abel-inverted to produce local volumetric emission. In Figure 6, we compare the Abel-inverted spectrum at the plasma centerline (r = 0 cm) and exit of the 15 cm tube, with the spectrum computed with SPECAIR, assuming equilibrium at the centerline temperature presented in Figure 5 (4660 K). The spectra are in good agreement with one another, with the exception of a small discrepancy between 600 and 625 nm. This agreement confirms the assumption of equilibrium. Similar results are observed for all Abelinverted spectra at other radial positions, both at the exit of the 10 and 15 cm test-sections.

In addition to the emission and Raman measurements, we also performed a power balance. For this, the difference in water temperature at the inlet and outlet of the tube was measured. The gas enthalpy was also estimated from the measured temperature profiles at the inlet and outlet of the tube. The power balance, assuming equilibrium conditions, is then:

Δ𝑃 𝑔𝑎𝑠 (𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚) = [∫ 𝜌 𝑔𝑎𝑠 𝑉 𝑔𝑎𝑠 ℎ 𝑔𝑎𝑠 2𝜋𝑟𝑑𝑟 𝑟=5 𝑚𝑚 𝑟=0 𝑚𝑚 ] 𝑜𝑢𝑡𝑙𝑒𝑡 -[∫ 𝜌 𝑔𝑎𝑠 𝑉 𝑔𝑎𝑠 ℎ 𝑔𝑎𝑠 2𝜋𝑟𝑑𝑟 𝑟=5 𝑚𝑚 𝑟=0 𝑚𝑚 ] 𝑖𝑛𝑙𝑒𝑡
where 𝑉 𝑔𝑎𝑠 represents the gas velocity, 𝜌 𝑔𝑎𝑠 the mass density, and ℎ 𝑔𝑎𝑠 the specific enthalpy. The thermodynamic properties of the plasma were calculated using the CEA code [START_REF] Mcbride | Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications II. User's Manual and Program Description[END_REF] at the measured temperatures. Note that the velocity is estimated by matching the mass flow rate and assuming a radial velocity profile selfsimilar to that of the measured temperature: this is justified by the fact that the Prandtl number is close to unity. The uncertainty on the velocity determined with this procedure is estimated to be 30%.

The calorimetric power balance on the water that traverses the water-cooled tube gives the power removed at the wall and is equal to:

Δ𝑃 𝑤𝑎𝑡𝑒𝑟 = 𝑚̇𝑤 𝑎𝑡𝑒𝑟 𝑐 𝑝 𝑤𝑎𝑡𝑒𝑟 (𝑇 𝑤𝑜 -𝑇 𝑤𝑖 )
where 𝑚̇𝑤 𝑎𝑡𝑒𝑟 is the measured water mass flow rate, and 𝑇 𝑤𝑖 and 𝑇 𝑤𝑜 are the temperatures of the water at the inlet and the outlet of the cooling tube, respectively.

Assuming equilibrium conditions for the plasma, the power balance reads:

Δ𝑃 𝑤𝑎𝑡𝑒𝑟 = Δ𝑃 𝑔𝑎𝑠 (𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚)
The results for Δ𝑃 𝑤𝑎𝑡𝑒𝑟 and Δ𝑃 𝑔𝑎𝑠 (𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚) are presented in figure 7. At 10 cm, both approaches give the same results to within their respective uncertainty. This supplies additional evidence for the equilibrium assumption. At 15 cm we see a difference between the two lines which may be indicative of a departure from equilibrium. A suspected reason for this discrepancy is an overpopulation of atomic nitrogen near the wall. This is observed to be a very strong effect in the N2/Ar experiments (presented in section II.b). Unrecombined atomic N can account for a large amount of enthalpy. This hypothesis will be investigated more in the following nitrogen cases. Nonetheless, the relatively good agreement between the two curves here gives us confidence in the fact that the plasma is at least close to equilibrium. Also, this equilibrium case serves as a validation of our Raman measurements because both the Raman and emission spectroscopy measurements are in agreement with one another. Finally, note that we estimated the radiative losses using SPECAIR through the tube outlet and found them negligible (< 10W).

b. N2/Ar: low mass flow rate For this case, 1.2 g/s of nitrogen and 1.5 g/s of Argon were injected into the plasma torch. Three axial positions were studied: 0, 10 and 15 cm. Radial temperature profiles were measured at these three locations using Raman and emission spectroscopy. At 0 and 10 cm, the temperature measured using OES was obtained from the absolute intensity of five atomic lines, namely the nitrogen lines at 742, 744 and 746 nm and the argon lines at 751 and 763 nm. All five lines give similar results and therefore only one will be presented (nitrogen at 746 nm here). The temperature at 15 cm is measured using OES of N2 + rotational lines as no atomic lines were visible. Note that at 0 and 10 cm, therefore, the temperature measured using OES corresponds to the electronic temperature of atomic species whereas, at 15 cm, it corresponds to the rotational temperature of N2 + B. For the Raman measurements, the rotational and vibrational temperatures were found to be equal and, therefore, we only give one temperature here. Results are shown in figure 8. At 0 and 10 cm, the temperature measured with both Raman and emission spectroscopy are in agreement with another. At 15 cm, the temperature measured with Raman is slightly lower than the temperature measured with emission spectroscopy. At the exit of the 15-cm tube, we also measured N2 first positive emission between 500 and 800 nm. We compared the measured spectrum with spectra computed using SPECAIR, using the temperatures measured with Raman and emission spectroscopy. Results are shown in figure 9. All measured spectra are Abel-inverted and we present here the centerline spectra. It is clear from figure 9 that the measured spectrum is very different from the spectra computed assuming LTE at the temperatures obtained from emission spectroscopy (T = 5000 K) and Raman spectroscopy (T = 4600 K). These differences indicate that the plasma is not in equilibrium. We also note that the measured total radiated power between 550 and 800 nm is twice higher than the radiation predicted assuming LTE at the temperature measured via emission spectroscopy, and 10 times higher if we consider LTE at the temperature measured using Raman spectroscopy. Vibrational level of N 2 B

To quantify the degree of departure from equilibrium within the vibrational levels of the N2 B state, we used the radiation code SPECAIR and altered the population of the individual vibrational levels of N2B in order to reproduce the experimental spectrum. The experimental spectrum was reconstructed by introducing overpopulation factors for the various contributing vibrational levels and using an optimization algorithm to minimize the difference between computed and experimental spectra. The results of the measured population distribution and the corresponding spectra are presented in figure 10. Here, the rotational temperature is assumed to be the temperature measured using Raman scattering, which is likely to be more representative of the gas temperature. The good agreement between the spectrum computed using SPECAIR (assuming the nonequilibrium vibrational population distribution shown in Figure 10b) and the experimental one gives us confidence in our measurements of the N2B vibrational level overpopulation factors. Note that the distribution of vibrational levels of N2B does not follow a Boltzmann distribution: such a distribution would correspond to a straight line in Figure 10b. It is therefore not possible to characterize this distribution using a single temperature. Furthermore, the total density of all vibrational levels, which yields the density in the N2B state electronic state, is highly overpopulated with respect to its equilibrium value. To reproduce this overpopulation in CFD simulations, a vibrationally specific model must be used.

This same procedure was repeated to determine the temperature profiles and vibrational distributions in the N2B electronic state at all radial positions. Figure 10 presents these results at the center location (r=0 mm). Figure 11 shows results at other radial locations. For these, we used the temperature obtained by Raman scattering. The population of the N2B vibrational levels remains relatively constant over the first 2 mm radius at the exit of the 15-cm tube. This is consistent with the relatively flat temperature profile for a tube length of 15 cm over the same range (Figure 8). This result suggests that a 1D numerical model may be sufficient for reproducing these population distributions. From these data, it is possible to determine the atomic nitrogen density as a function of radial position as shown in Figure 12. The theory beyond this analysis is explained in Ref. [START_REF] Laux | State-to-state modeling of a recombining nitrogen plasma experiment[END_REF]: the vibrational level v=13 of N2 B is a spontaneously predissociating state, in partial local thermodynamic equilibrium with ground state nitrogen atoms (N 4 S):

𝑁 2 (𝐵, 𝑣 = 13) ↔ 𝑁( 𝑆 4 ) + 𝑁( 𝑆 4 )

The overpopulation of atomic nitrogen can then be expressed as a function of the measured overpopulation, ρ N 2 ,𝐵,𝑣=13 , of vibrational level v=13 of N2B, via the following equation: The measured atomic nitrogen density is well above its equilibrium value at 15 cm. This suggests that atomic nitrogen is partly frozen in the tube. Furthermore, a significant amount of enthalpy is stored in the unrecombined N. This is an important consideration for the power balance. Considering the density measured in figure 12, the enthalpy stored in unrecombined nitrogen atoms is given by the following relation:

𝜌 𝑁 = √ ρ N 2 ,𝐵,𝑣=13 0
Δ𝐻 𝑐ℎ𝑒𝑚 = (𝑛 𝑁 -𝑛 𝑁 * )𝐸 𝑑𝑖𝑠𝑠 𝑁 2
where 𝑛 𝑁 is the measured number density of N, 𝑛 𝑁 * is the equilibrium density of N, and 𝐸 𝑑𝑖𝑠𝑠 𝑁 2 the energy of dissociation of N2. This enthalpy must then be divided by the residence time of the gas in the tube to obtain a power:

Δ𝑃 𝑐ℎ𝑒𝑚 = ∫ Δ𝐻 𝑐ℎ𝑒𝑚 τ residence 𝑑𝑟 𝑟=𝑅 𝑟=0 = ∫ Δ𝐻 𝑐ℎ𝑒𝑚 𝑥 𝑉 𝑔𝑎𝑠 (𝑥, 𝑟) 𝑑𝑟 𝑟=𝑅 𝑟=0
where x is the length of the tube (10 or 15 cm) and 𝑉 𝑔𝑎𝑠 represents the mean velocity of the gas at the axial position x. Note that the velocity has not been measured directly and is therefore estimated as discussed in Section IIa.

The power balance presented in IIa now becomes:

Δ𝑃 𝑤𝑎𝑡𝑒𝑟 = Δ𝑃 𝑔𝑎𝑠 (𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚) -Δ𝑃 𝑐ℎ𝑒𝑚𝑖𝑠𝑡𝑟𝑦
where Pchemistry represents the power stored in chemical and internal modes. We find that the dominant part of this power is contained in unrecombined atomic N. The chemical energy stored in the overpopulated vibrational levels of N2 B and N2 C, measured using emission spectroscopy, was also considered but was found to be negligible in comparison. Figure 13 shows the results obtained for the power measurements. For the N2/Ar plasma, the good agreement between the black and the blue curves suggests that the unrecombined N accounts for the missing energy. This energy balance gives us confidence in our temperature measurements. It also shows the importance of accounting for chemical nonequilibrium in the power balance. Evidently, this chemical effect is as important as the heat transfer to the water-cooled tube walls. An accurate kinetic model is therefore mandatory to correctly predict the drop in temperature using a CFD code.

c. N2/Ar: high mass flow rate

For this case we have reproduced the condition of Gessman et al [START_REF] Gessman | Experimental study of kinetic mechanisms of recombining atmospheric pressure air plasmas[END_REF]. 1.9 g/s of nitrogen was mixed with 1.5 g/s of argon. The mass flow rates are equal to those presented in section IIb for the Air/Ar plasma: air injection was simply replaced with nitrogen injection. The plasma was studied at 0, 10 and 15 cm. Figure 14 shows the radial temperature profiles measured using both Raman and emission spectroscopy. At 0 cm, both Raman and emission spectroscopy give the same temperature measurement. However, at 10 and 15 cm, the temperature measured using Raman scattering is significantly lower than the temperature measured using emission spectroscopy. This was observed to a lesser extent in the previous case (nitrogen/argon at low mass flowrate). Recall that the temperatures measured using OES and Raman scattering were in good agreement for the Air/Ar case. This previous agreement gives us confidence in the temperatures presented here and implies that the difference is not an artifact of the measurement. This difference between the two measurements therefore implies a strong nonequilibrium between the temperature of excited states of nitrogen and the temperature of the ground state. At 15 cm, the temperature measured by emission spectroscopy corresponds to the rotational temperature of the N2 + B state. This discrepancy will be discussed at the end of this section.

These observations suggest that our emission measurements may not provide a representative estimate of the bulk gas temperature. The Raman measurements show that the bulk gas temperature is much lower. Referring back to Figure 1, we find that the temperature decrease in the the 15-cm tube is more pronounced than in the experiments of Gessman et al. [START_REF] Gessman | Experimental study of kinetic mechanisms of recombining atmospheric pressure air plasmas[END_REF]. Furthermore, the measured temperature decrease is much larger than what is predicted by the CFD codes for this high flowrate nitrogen/argon plasma.

As before, we measured the N2 first positive emission spectrum between 500 and 800 nm at 15 cm, and we compared it with LTE spectra computed with SPECAIR at the temperature measured by Raman or emission spectroscopy. All spectra are Abel-inverted. First, the centerline spectra are presented. The results are shown in Figure 15. There is again a clear discrepancy between the measured and the computed spectra assuming equilibrium at the temperatures measured with emission and Raman spectroscopy. The difference is significantly higher for the temperature measured with Raman spectroscopy. These results imply a nonequilibrium vibrational distribution within the N2B state. As before, we altered the population of N2B vibrational levels using overpopulations factor and the optimization algorithm. The final result, showing the experimental spectrum and the computed nonequilibrium spectrum, are in good agreement. Note that we assumed a Boltzmann distribution for the rotational levels of N2B at the temperature measured with Raman spectroscopy. We also assumed that the rotational temperature is the same for each vibrational level. The influence of the rotational temperature on the results is discussed in Appendix A. The N2B vibrational levels are highly overpopulated, much more than for the low mass flow rate N2/Ar case. This is to be expected given that the higher gas velocity in the high mass flowrate case results in a reduction in the gas residence time in the tube, leaving less time for the recombining plasma to equilibrate. Furthermore, the increase in Reynolds number implies a turbulent flow which increases the heat transfer to the wall.

The overpopulation factors at several radial positions are shown in Figure 17. At each radial position, the vibrational levels of N2B are overpopulated. Note that the absolute density of N2B does not change significantly with the radial position despite the decrease of temperature with radial position. This leads to an increase of the overpopulation of N2B. The atomic N density was determined using the method presented in Section IIb. These measurements were performed at 10 and 15 cm. The results are presented in Figure 18. The density of atomic nitrogen is significantly above its equilibrium value at 10 cm and does not change substantially between 10 and 15 cm, suggesting that the population of N is not only frozen radially as discussed before, but also effectively frozen with axial distance beyond 10 cm. The atomic nitrogen density was also measured by Gessman et al at the center of the tube [START_REF] Gessman | An experimental investigation of the effects of chemical ionizational nonequilibrium in recombining atmospheric pressure air plasmas[END_REF]. They measured a density of (1.62±0.3) ⋅ 10 17 cm 3 . This is to be compared with our measurement of (1.02±0.06) ⋅ 10 17 cm 3 .

A power balance analysis was performed using the same methodology as presented in Section IIb. The results are presented in Figure 19. The good agreement between the black and the blue curves suggests, as before, that the unrecombined N accounts for the missing power. Note that all the calculations were done using the temperature measured via Raman spectroscopy. The chemical power stored in the overpopulated vibrational levels of N2 B (measured in Figure 16) and N2 C, measured using emission spectroscopy, were also considered.

Here again, this power is negligible in comparison with the power stored in the unrecombined N. This power balance gives us confidence in the fact that the temperature of the gas is indeed the temperature measured using Raman.

Although our measurements are self-consistent, they do not yield insight into the actual mechanism causing the rapid drop in temperature observed for all test cases: nitrogen/argon, air/argon and pure air plasmas. We examine this question with CFD models in the next section.

Discussion about N2 + (B) rotational temperature

For both N2/plasma cases, the temperature measured with OES at the exit of the 15-cm tube corresponds to the rotational temperature of N2 + (B). This rotational temperature is higher than the temperature measured using Raman spectroscopy. Previous work suggested that, for recombining flows, the rotational temperature of N2 + may not be in equilibrium with the translational temperature [START_REF] Studer | Raman scattering,measurements within a flat plate boundary layer in an,inductively coupled plasma wind tunnel[END_REF]. Additional studies in shock tubes [START_REF] Fujita | Experimental Investigation of Air Radiation from Behind a Strong Shock Wave[END_REF] [23] also showed that the vibrational and rotational temperatures of the N2 + first negative system could be significantly different from the gas temperature. These studies noted a similar trend in the N2 second positive system. In addition, using the N2 + first negative system Venable et al [START_REF] Venable | Observations of departures from equilibrium in a nitrogen arc[END_REF] measured higher temperatures than the gas temperature. Devoto et al [START_REF] Devoto | Air transport coefficients from electric arc measurements[END_REF] noted a difference between the temperature using only the bandhead of the N2 + first negative system and that measured using all lines of this system. Both Venable and Devoto suggested that the population of high rotational levels of N2 + (B) were not in equilibrium with the low lying rotational levels. Their assumptions were based on Griem's work [START_REF] Griem | Principles of Plasma Spectroscopy[END_REF] according to which such conditions can occur when the collisional-radiative relaxation time of a given state of an ion becomes lower than the thermalization time of electrons. This can occur for example when a steep gradient of temperature exists.

We have studied the reaction kinetics of N2 + (B) in order to compare its production timescale with the R-T relaxation timescale. We will focus of the N2/Ar plasma case presented in IIc) at the exit of a 15-cm tube. The R-T relaxation time can be obtained from Parker [START_REF] Parker | Rotational and Vibrational Relaxation in Diatomic Gases[END_REF] and is approximately 8 ns at 3200K. Given that the plasma is in steady-state at the exit of the tube, the production time of N2 + (B) is equal to its depletion time. The main reaction for removal of N2 + (B) comes from collisional quenching with N2 (Valk et al [START_REF] Valk | Measurement of collisional quenching rate of nitrogen states N2(C 3 Πu, v = 0) and N2 + (B 2 Σg + ,v=0)[END_REF]):

R1: 𝑁 2 + (𝐵) + 𝑁 2 → 𝑁 2 + (𝑋) + 𝑁 2
In our case, this gives a quenching time around 2 ns, which is smaller than the R-T rotational time. Therefore, N2 + (B) is depleted before its rotational distribution can equilibrate with the gas temperature.

Given that the plasma is in steady-state at the exit of the water-cooled tube, the timescale for the production of N2 + (B) must be equal to the timescale for the recombination N2 + (B), i.e. about 2 ns. The mechanism for the fast production of N2 + (B) is not understood at present. We review below several possible mechanisms, including direct production of N2 + (B) or excitation of N2 + (X) [START_REF] Linss | Two N2 + (B 2 Σu + ) populations with different Boltzmann distribution of the rotational levels found in different types of N2/Ar discharges-improved estimation of the neutral gas temperature[END_REF].

We first investigate the production of N2 + (X). Three main reactions are considered, with reactions rates taken from the given references: Only reaction R4 is fast enough (~2 ns) compared to the R-T relaxation time. Sonnenfroh et al [START_REF] Sonnenfroh | A laser-induced fluorescence study of product rotational state distributions in the charge transfer reaction: Ar + ( 2 P3/2) + N2→Ar + N2 + (X) at 0.28 and 0.40 eV[END_REF] experimentally observed that the R4 reaction produced N2 + at rotational temperatures higher than that of the reactants. This could explain the high measured rotational temperature of N2 The R7 rate was assumed to be similar to that excitation of N2(X) by collisions with metastable argon atoms. R7 and R8 are the fastest reactions (~10 µs) but are still much slower than R-T relaxation. Note that high vibrational levels of N2(X) can be populated via reactions with argon metastable atoms [START_REF] Touzeau | Vibrational excitation of N2(C) and N2(B) by metastable argon atoms and the determination of the branching ratio[END_REF]. This could decrease the characteristic time of R8 by an order of magnitude.

N2 + (B) can also be produced directly via:

R9: 𝑁 2 (𝑋) + 𝑒 -→ 𝑁 2 + (𝐵) + 2𝑒 - [38]
R10:

𝑁 + + 𝑁 + 𝑀 → 𝑁 2 + (𝐵) + 𝑀 [37]
R10 is the fastest method for the creation of N2 + (B) (~1 µs) but is still slow compared to its recombination time and the R-T relaxation time.

Clearly, other reactions are probably at play to produce N2 + (B) at time scales of less than 2 ns. These reactions are likely two-body reactions, but at present their rates are not known. Among possibilities, we could mention:

R11: 𝑁 2 + (𝑋, 𝑣 > 12) + 𝑁 2 → 𝑁 2 + (𝐵) + 𝑁 2
In conclusion, being under steady state conditions assures us than the rate of production of N2 + (B) should be equal to its recombination rate. The time scale of this process, due to collisional quenching, is about 2 ns, which is smaller than the R-T relaxation time (~8 ns). It is therefore likely that N2 + (B) is produced at high rotational temperature and does not have time to thermalize before it reacts. This would explain the higher measured rotational temperature of N2 + (B) at the exit of a 15-cm tube for the b) and c) case.

II) CFD modeling of an equilibrium air

As seen in the previous sections, the recombining air mixture investigated was found to remain at or close to equilibrium. As a first step, we focus on modeling only an equilibrium case of a pure air plasma. This is the simplest to test CFD models.

The data for this test case is taken from Gessman et al [START_REF] Gessman | An experimental investigation of the effects of chemical ionizational nonequilibrium in recombining atmospheric pressure air plasmas[END_REF]. For this case, the measured spectra corresponded well with spectra calculated assuming equilibrium conditions. The Reynolds number is about 1900 and the flow is therefore assumed laminar (Re < 2300).

The CFD simulations presented here were performed with the Eilmer3 code, a finite-volume Navier-Stokes flow solver [START_REF] Gollan | About the formulation, verification and validation of the hypersonic flow solver Eilmer[END_REF] implemented on block-structured grids and developed at the Centre for Hypersonics at the University of Queensland. The computational domain corresponds to a 1-cm diameter tube that is 25 cm in length. The flow is assumed axisymmetric and a 2D simulation is performed. For the outlet boundary condition, the pressure is fixed at atmospheric pressure. As an alternate boundary condition at the tube exit, the presence of a reservoir was investigated but gave similar results. For the inlet boundary condition, the temperature profile is specified by extrapolating the measured temperature out to the wall diameter where the temperature is fixed at 300 K. The velocity profile is assumed to be self-similar to the temperature profile as mentioned before. The velocity profile is also constrained to satisfy the experimental mass flow rate. At the wall, we impose a boundary condition using ghost cells with a fixed temperature of 300 K along the tube wall. The heat flux is calculated using Fourier's law between the ghost cell and the last cell in the plasma. The flow is laminar, and therefore no turbulence models are used. The gas is assumed to be at equilibrium everywhere in the tube, consistent with the conclusions of the measurements of Ref. [START_REF] Gessman | An experimental investigation of the effects of chemical ionizational nonequilibrium in recombining atmospheric pressure air plasmas[END_REF]. The thermophysical properties (viscosity, thermal conductivity, density…) of the plasma are calculated using the NASA CEA code [START_REF] Mcbride | Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications II. User's Manual and Program Description[END_REF] to generate a database of the transport properties as a function of temperature. Comparisons between our simulations and the experiments of Gessman et al are presented in figure 20. For this laminar equilibrium case, Fig. 20 shows that the numerical predictions differ from the measurements. The slight change of the slope in the temperature profile near the wall is due to the presence of a local minimum in the equilibrium heat capacity around 4000 K calculated by CEA. This corresponds to the temperature interval in between oxygen and nitrogen dissociation. To examine the sensitivity of the predictions to the rate of heat transfer at the wall, we artificially increased the heat flux to the wall by a factor of 10, which is equivalent to multiplying the local thermal conductivity of the first cell (used in the Fourier's law) by 10. The temperature in the boundary cell close to the wall remains very close to the wall temperature. Thus, it appears that the cause for the discrepancy is an underprediction of radial heat transfer within the gas.

To confirm that assumption, we performed a parametric study on the thermal conductivity of the plasma. We added a conductivity varying exponentially with the temperature to model a possible radiative conductivity. The radiative conductivity of an air plasma may be estimated using the Rosseland approximation built in SPECAIR. The Rosseland approximation leads to the following radiative conductivity for a semitransparent medium:

𝜆 𝑅 (𝑇) = 4𝜋 3 𝑛 2 ∫ 1 𝑘 𝜆 𝑑 𝑑𝑇 𝐿°𝜆(𝑇)𝑑𝜆 ∞ 0
where n is index of refraction, 𝐿°𝜆 the radiance of the black-body from Planck's law, and k is the spectral absorption coefficient [START_REF] Taine | Transferts thermiques: Introduction aux transferts thermiques[END_REF]. It assumes that the plasma is optically thick. Note that, for our conditions, the plasma is not optically thick over all wavelengths. In the regions where the plasma is optically thin, k is very small, which causes the conductivity integral to diverge. Therefore, a choice must be made regarding the range of wavelengths used in the integral. There are no well-defined and physically meaningful criteria for selecting this range and, furthermore, a small modification in this choice can have a large impact on the resulting conductivity. Thus the Rosseland conductivity is ill-defined here. With these limitations in mind, we took as a starting reference point the radiative conductivity of an argon plasma reported in [START_REF] Owano | Electron-ion three-body recombination coefficient of argon[END_REF]. To obtain reasonable agreement between the Eilmer3 model and the measurements, the radiative conductivity must be 300 times higher than this reference value. The conductivities taken for this calculation are shown in figure 21 and the results in figure 22. Note that the equilibrium conductivity calculated using CEA corresponds to the sum of both the thermal and the reactive conductivities. For both cases, the results between experiments and numerical simulations are in good agreement at 15 and 20 cm with the assumed radiative conductivity. Even so, there remains a discrepancy at 25 cm. This could come from effects due to turbulence. The Reynolds number of 1900 is estimated based on the conditions at 0 cm.

However, its value increases as the temperature decreases along the tube. At 25 cm, the Reynolds number is about 2600, which may indicate the presence of turbulence, and could help explain the observation that the drop in temperature between 20 and 25 cm is much higher than that between 15 cm and 20 cm.

Given the discrepancy between theoretical predictions and experimental measurements for this simple equilibrium case, a comparison with the more complexed nonequilibrium N2/Ar test cases was not performed. Nevertheless, the results obtained for the pure air case suggest that radiation transport may play an important role. In future work, we intend to model this by coupling the fluid code with radiation transport.

III) Conclusions

Experiments have been conducted in a plasma torch facility to study equilibrium and nonequilibrium recombining plasmas of nitrogen/argon and air/argon mixtures. These experiments supply data that can be used to validate CFD and kinetic codes for recombining nitrogen and air plasmas. We have attempted to decouple this problem into two physical effectshydrodynamic phenomena and chemical kinetic phenomenaby presenting data where the plasma remains in equilibrium and should be modeled using a comparatively simple hydrodynamic code, and cases where the plasma is strongly out of equilibrium and requires a detailed chemical kinetic model to be coupled to a fluid code.

We experimentally studied cases in chemical equilibrium (Air/Ar) and in chemical nonequilibrium (N2/Ar). The Air/Ar plasma case served to validate our temperature measurements using Raman spectroscopy because these agreed with the emission spectroscopy measurements. For the case of an N2/Ar plasma, the Raman measurements yielded a much lower temperature than the emission spectroscopy measurements. Similar phenomena were observed by other authors [START_REF] Bruggeman | Gas temperature determination from rotational lines in nonequilibrium plasmas: a review[END_REF] and potential explanations were given. Furthermore, strong evidence of chemical nonequilibrium was found in the emission spectroscopy measurements. Both N2/Ar cases gave similar results although the high flow rate case was farther out of equilibrium than the low mass flow rate case.

Based on the temperature measured using Raman spectroscopy, we were able to calculate overpopulation factors for the N2B state in order to describe the observed nonequilibrium. The absolute density of atomic N was also inferred from the first positive emission of N2. Finally, a simple energy balance showed that a large portion of enthalpy remains in the unrecombined atomic nitrogen. This case is therefore useful to test QSS kinetic models such as that previously implemented in Ref. [START_REF] Laux | State-to-state modeling of a recombining nitrogen plasma experiment[END_REF].

The CFD model Eilmer3 was used to simulate the temperature drop for an equilibrium case. This fluid code underpredicts the measured temperature drop in the tube. For this case, the discrepancy between CFD and experiments cannot be explained by chemical kinetics as the plasma remains in equilibrium. Given our CFD predictions and experimental results, it appears that the reason for the discrepancy is due to an inability to model the radial heat transfer within the gas.

These recombining plasmas raise many interesting issues for the CFD community to resolve. The experiments were done using a simple configuration and, therefore, present a relatively seemingly simple test case for the modeling of nonequilibrium recombining air and nitrogen flows. Yet, as shown in the paper, challenges remain to correctly simulate these test cases. These issues are currently the object of our continued investigations.

Figure 2 :

 2 Figure 2: Water-cooled test-section mounted at the exit of the plasma torch

Figure 4 :

 4 Figure 4: Experimental setup for Raman UV scattering measurements. A periscope consisting of two quartz prisms allows to adjust the height and direction of the laser beam. The 90° image rotator serves to horizontally align the laser beam with the spectrometer entrance slit.

Figure 5 :

 5 Figure 5: Temperature profiles measured with Raman scattering and OES at 0, 10 and 15 cm for the Air/Ar plasma.

Figure 6 :

 6 Figure 6: Comparison between centerline experimental and computed spectra at the 15 cm-tube exit. The black curve represents the calibrated Abel-inverted measured spectrum and the red one the spectrum computed with SPECAIR assuming equilibrium at the temperature measured with Raman and emission spectroscopy.

Figure 7 :

 7 Figure 7: Power measurements using two different approaches. Blue: measured power removed by water cooling. Red: Power change between the exit and the inlet of the tube assuming equilibrium throughout the tube.

Figure 8 :

 8 Figure 8: Temperature profiles measured with Raman and emission spectroscopy at 0, 10 and 15 cm for the N2/Ar plasma at low mass flowrate. The red line represents the temperature measured using emission spectroscopy and the blue one the temperature measured using Raman spectroscopy

Figure 9 :

 9 Figure 9: Comparison between the measured spectrum and SPECAIR LTE computations at the temperatures measured with Raman spectroscopy (red line) and with emission spectroscopy (green line) at 15 cm for the N2/Ar plasma at low mass flowrate.

Figure 10 .

 10 Figure 10. (a) Measured and computed spectra at the exit of the 15-cm tube for the N2/Ar case at low mass flowrate. (b) Vibrational population distribution of N2B taken for SPECAIR nonequilibrium calculations.

Figure 11 :

 11 Figure 11: Radial profiles of the absolute density of vibrational levels of N2B at the exit of the 15-cm tube. N2/Ar plasma at low mass flowrate.

Figure 12 :

 12 Figure 12: radial population distribution of atomic nitrogen atoms at 0 and 15 cm, measured and calculated assuming LTE at the temperature measured using Raman spectroscopy. N2/Ar plasma at low mass flowrate.

Figure 13 :

 13 Figure 13: Power balance measurements for the N2/Ar plasma (low mass flowrate), using two different approaches. Blue: measured power removed by water cooling. Red: Power change between the outlet and the inlet of the tube assuming equilibrium throughout the tube. Green: power stored into unrecombined N atoms using the measured overpopulation factors. Black (red minus green curve): total power removed from the gas.

Figure 14 :

 14 Figure 14: Temperature profiles measured using both Raman and emission spectroscopy at 0, 10 and 15 cm. N2/Ar plasma at high mass flowrate.

Figure 15 :

 15 Figure 15: calibrated measured spectra and the corresponding computed spectra using SPECAIR, assuming equilibrium at the exit of the 15 cm tube. The measured spectra are Abel-inverted and only the emission of the 0.5 mm thick center slab is plotted.

Figure 16 :

 16 Figure 16: (a) Measured and computed spectra at the exit of the 15-cm tube for the N2/Ar case at high mass flowrate. (b) Vibrational population distribution of N2B taken for SPECAIR nonequilibrium calculations. To improve the fit, we added as a parameter of our optimization the overpopulation of N2 + (A 2 Σg + ) corresponding to the transition N2 + Meinel.

Figure 17 :

 17 Figure 17: Population of vibrational levels of N2B at different radial positions at the exit of a 15-cm tube exit. N2/Ar plasma case at high flow rate.

Figure 18 :

 18 Figure 18: radial population distribution of atomic nitrogen at 0, 10 and 15 cm, measured and calculated assuming an equilibrium population at the temperature measured using Raman spectroscopy. N2/Ar plasma case at high flow rate.

Figure 19 :

 19 Figure 19: Power measurements using two approaches for the N2/Ar plasma (high flowrate).

Figure 20 :

 20 Figure 20: Comparison of measured and simulated (Eilmer3) temperature profiles at 0, 15, 20 and 25 cm for the pure air plasma.

Figure 21 :Figure 22 :

 2122 Figure 21: Thermal conductivity taken for our simulations as a function of the temperature

Table 1 : Measured mass flow rates and expected conditions for the different plasma cases studied. The plasma torch cannot be operated with pure N2 and thus the N2/Ar mixture is necessary for studying nitrogen kinetics. The Air/Ar mixture was chosen for comparison with the N2/Ar 2 case, keeping the same mass flow rate, hence aerodynamic regime, in order to isolate the effects related to chemical kinetics. Note that the turbulent energy of the flow was not measured. The labels 'laminar' and 'turbulent' are based on the Reynolds number estimates.

 1

			Estimated Reynolds number	Chemical
			based on the tube diameter	conditions
	Pure air	𝑚̇𝐴 𝑖𝑟 = 1.9 g/s	~1900 (laminar)	Equilibrium
	Air/Ar	𝑚̇𝐴 𝑖𝑟 = 1.9 g/s 𝑚̇𝐴 𝑟 = 1.5 g/s	~3600 (turbulent)	Equilibrium
	N2/Ar 1	𝑚̇𝑁 2 = 1.2 g/s 𝑚̇𝐴 𝑟 = 1.5 g/s	~2700 (slightly turbulent)	Nonequilibrium
	N2/Ar 2	𝑚̇𝑁 2 = 1.9 g/s 𝑚̇𝐴 𝑟 = 1.5 g/s	~3600 (turbulent)	Nonequilibrium

Acknowledgments

This work has been supported by Ariane Group, under a CIFRE Ph.D. grant (number 42701092/20160218/JSE), with Dr. Laurent Visconti as Technical Monitor. We would like to thank Professors Peter Jacobs and Rowan Gollan (University of Queensland) for their help with the Eilmer3 code.

Appendix A: Influence of rotational temperature of N2B on the computed spectra For N2/Ar plasmas, in figures 12 and 18, we plotted the computed spectrum using SPECAIR assuming a nonequilibrium vibrational distribution. The rotational temperature was assumed to be equal to the temperature measured using Raman spectroscopy. However, recall that emission measurements of the rotational temperature of N2 + B were higher than the Raman temperature. Given this, it is not clear what rotational temperature to use for the simulation of the first positive emission of N2. This issue will be discussed in this appendix.

For this analysis, we focus on the N2/Ar plasma test case presented in section IIc (high flow rate). The measured spectrum was not sufficiently resolved in wavelength to directly measure the rotational lines of N2B and infer a rotational temperature. Thus we conducted a parametric study on the N2B rotational temperature. In our optimization algorithm, we then altered the population of the N2B vibrational levels. Because the final distribution is not Boltzmann, the measured population of any given vibrational state was defined relative to its equilibrium value at the chosen rotational temperature. This was done through the use of the overpopulation factor. In the results presented in section II, the rotational temperature was fixed to the temperature measured using Raman spectroscopy as this was felt to be more representative of the bulk gas temperature. We will now change the rotational from 2500 K to 5500 K and, for each temperature, determine the corresponding overpopulation factors. Note that we assume that all vibrational levels of N2B have the same rotational temperature in this study because the measured spectrum is not sufficiently resolved in wavelength to have an accurate result and it will add many degrees of freedom to the fitting algorithm. We compare the total relative error between the measured spectrum and the one resulting from our algorithm for each rotational temperature. Note the presence of a local minimum around 4000 K. This may indicate that the rotational temperature of N2B is closer to this temperature. We have also plotted on figure A.2 the resulting spectrum from our algorithm for several rotational temperatures, as well as the experimental spectrum. Note that the temperature of 4000 K gives a better agreement with experiments, particularly in the region where the emission is lower. Beyond this analysis, we have no justification for fixing the rotational temperature to 4000 K. It was for this reason that the Raman temperature measurement was used for the analysis. Additional measurements are necessary to resolve this problem: high resolution measurements of the first positive system would be very valuable to that end. We can still note that based on this analysis, the rotational temperature of N2B is likely to be higher than the temperature measured with Raman spectroscopy, as is the rotational temperature of N2 + B measured with emission spectroscopy.

As a final note, figure A.3 shows the absolute population of the vibrational levels of N2B resulting from our algorithm for various rotational temperature inputs. As expected, the absolute population of the vibrational levels of N2B is not significantly dependent of the rotational temperature.