Speaker
Description
Plasma wind tunnels are fundamental assets when designing Thermal Protection Systems (TPS) for re-entry capsules or the demise process of Space Debris (SD) subjected to uncontrolled atmospheric re-entry. In ground, thermal and momentum variables such as enthalpy, pressure and velocity must be accurately measured to reproduce the aerothermochemical environment of the hypersonic flow experienced during the atmospheric re-entry. However, the harsh testing environment due to the extremely high temperatures, makes a direct measure of such quantities extremely challenging.
The von Karman Institute Plasmatron, a leading Inductively Coupled Plasma (ICP) wind tunnel, is extensively used for testing thermal protection systems (TPS) and studying the demise of space debris. The facility can operate in supersonic and subsonic conditions, but only the latter are here considered. Even though re-entry trajectories occur at hypersonic speeds, experiments in subsonic regime are crucial for TPS and space debris studies. These tests replicate the aerothermochemical environment of the stagnation region near the boundary layer, as described by the Local Heat Transfer Simulation (LHTS) methodology. The LHTS guarantees that, under the assumption of Local Thermochemical Equilibrium (LTE) at the boundary layer edge, the chemical non-equilibrium boundary layer, and consequently the total heat flux at the wall, in the ground and flight are the same if the total enthalpy, total pressure and the velocity gradient are matched. The velocity gradient, mostly linked with the geometry of the samples/flying body, is determined through numerical computations. The pressure is assumed constant and equal to the measured static pressure of the chamber ($p_{c}$) being the plasma flow in a low subsonic regime. The enthalpy is estimated using rebuilding procedures or semi-empirical formulation.
In the last few years, experimental campaigns at VKI highlighted OES as a powerful tool to extract thermodynamic quantities such as enthalpy and temperature. Extracting such variables involves several steps and assumptions that will be reviewed in the following. This work aims to extend the application of OES to a broad range of testing conditions covering the majority of VKI Plasmatron envelope, in subsonic regime and considering an air mixture, and consolidate the procedure highlighting some corrections. Results, in terms of temperature profiles, will be compared with those of CFD computations simulating the flow of the facility.
Enthalpy is computed through equilibrium computation, $h=f(T_{OES},p_{s} \approx p_{c})$ with $T_{OES}$ the temperature from the OES. Retrieving $T_{OES}$ involves multiple steps that can be summarized as follows: i) filter the raw data from the experimental noise and background, ii) calibrate the system in absolute intensity, iii) retrieve the local emission ($\varepsilon$) through the Abel inversion transform assuming axisymmetry of the jet and negligible absorption effects. iv) Temperatures are then extracted and compared employing two different procedures. The first approach considers the electromagnetic radiation emitted by an atomic species, and it relies on the
isotropic volumetric emission intensity equation
\begin{equation}
\varepsilon_{u l}=\frac{E_u-E_l}{4 \pi} \mathcal{A}{u l} n_i(p, T) g_u \frac{e^{-E_u /\left(k{\mathrm{B}} T\right)}}{Q_{\mathrm{int}, i}(T)},
\end{equation}
\noindent that can be inverted and solved for the temperature, with the left-hand side evaluated experimentally. In this work, we will consider only the transition of the atomic oxygen at $\approx$ 777nm, with the corresponding temperature $T_{O777}$. Attention is directed towards validating the approach with synthetic spectra. We simulate the local emission of the VKI Plasmatron using the NASA spectral model ($\textit{NEQAIR}$). For a fixed value of $p_c$, the database is generated for a set of temperatures assuming LTE (translational, rotational, vibrational and electronic temperatures are set equal, and the number density of the species of interest follows a Boltzmann distribution), for air mixture of 11 species (e-, N+, O+, NO+, N2+, O2+, N, O, NO, N2, O2). The synthetic database is then convolved with the Instrumental Line Shape (ILS) function providing an estimate of the left-hand side of the equation. For $p_c$ = 50mbar and temperatures ranging from 5500 to 7900K, results show discrepancies between 160 and 260K. The reason lies in the typical ILS function of the set-up approximated by the square root of a Voigt function with a Full Width Half Maximum of 0.53nm. The second approach retrieves the temperature by fitting the experimental spectra with the simulated counterpart. The estimated temperature, $T_{SF_{\lambda_1-\lambda_2}}$, result from an optimization procedure minimizing the residual
\begin{equation}
\mathcal{R}(T_{SF_{\lambda_1-\lambda_2}})=\sum_p \left[\varepsilon^\text{synth}\left(\lambda_p,T\right)-\varepsilon^\text{meas}\left(\lambda_p\right)\right]^2 / \left[\varepsilon^\text{meas}\left(\lambda_p\right)\right]^2,
\end{equation}
\noindent with $\lambda_1$-$\lambda_2$ denoting the boundaries of the spectral range considered, and $\lambda_p$ the discrete wavelength. Two separate ranges are considered : 710-875nm and 340-430nm. The former is dominated by the atomic transition of O and N, the latter by some of the molecular rovibronic bands of CN and N2+ and N2. Although the concentration of CN (CO2 disocciates and atoms of C and N recombines) is in the order of particles per million (ppm), small variations may significantly impact the temperature estimation being CN a strong radiator. Four different databases are considered with different concentrations of CO2: 0, 50, 100 and 410ppm.
An experimental campaign is carried out at four different electrical power of the VKI Plasmatron facility, $\text{P}_{el}$ = 175, 200, 250 and 275kW, and $p_c$ = 50mbar. Plasma emissions are recorded from the lateral side at 335mm and 385mm along the jet-centerline from the torch exit section. Results show an excellent agreement between $T_{O777}$, corrected to take into account the effect of the ILS, and the spectral fitting in 710-875nm, $T_{SF_{710-875}}$, with a maximum discrepancy below 50K. Results in the 340-430nm range show 100ppm being the concentration minimizing the residual in all conditions. Temperature differences between $T_{SF_{340-430}}$ and $T_{O777}$ range from 60 and 130K for the low and mid power and up to 350K at the highest condition, due to possible thermal non-equilibrium effect. Overall, the good agreement between the temperatures validate the assumption of LTE, at least for temperatures lower than 7300K. Results can be therefore compared with numerical simulation of the temperature profile of the in-house CoolFluid-ICP solver that simulates the flow field of the facility under the assumption of LTE and axisymmetric steady flow. Results show that an efficient of $\eta= \frac{\text{P}^{num}_{el}}{\text{P}^{exp}_{el}}$ $\approx$ 44$\%$ exists between the numerical and experimental $\text{P}_{el}$ even though further investigations, both from a numerical and experimental perspective, are necessary. By the time of the conference, the objective is to extend the analysis to multiple testing conditions (e.g, $p_s$ = 15, 30, 75, 100, 200mbar), covering the majority of the VKI Plasmatron envelope in subsonic regime.
Summary
This work focuses on characterizing the free stream plasma jet of the VKI Plasmatron through optical emission spectroscopy. The objective is to explore most of the testing envelope in subsonic regime conditions
