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Measuring electron number densities in hypersonic plasma flows is crucial for understanding aerothermodynamic phenomena, where traditional fluid dynamics principles no longer apply due to high speeds. The gas around the vehicle becomes hot enough to cause dissociation and ionisation of molecules, creating a chemically reacting flow [1]. The aerothermodynamic phenomena include chemical reactions, thermodynamic non-equilibrium, plasma formation, strong shock waves, and viscous interactions, which influence the communication blackout during re-entry along with aerodynamic heating, and material degradation [2], [3]. Ground testing facilities, such as the T6 Stalker Tunnel at the University of Oxford, provide a means to investigate ionisation rates, equilibrium ionisation percentages, and electron number densities under controlled conditions [4]. Both intrusive and non-intrusive diagnostic techniques can be employed to measure these parameters in hypersonic flows. Non-intrusive methods, such as microwave interferometry and spectroscopic techniques, offer the advantage of not disturbing the flow field [3]. However, intrusive measurements, particularly Langmuir probes, remain widely used in plasma facilities due to their simplicity, reliability, and ability to provide localised measurements [2], [5]. Their use in impulse facilities has been limited due to implementation and analysis restrictions. This work seeks to demonstrate the functionality of the probes in hypersonic facilities.
Langmuir probes, particularly triple probes, first demonstrated by Chen and Sekiguchi in 1964 [6], use three electrodes, with two forming a constant voltage circuit and the other floating at the plasma potential. These probes are employed in plasma facilities to measure electron number densities in highly ionised plasmas [7]. Goekce [5] previously attempted to use Langmuir probes in hypersonic plasma flows, but the results were challenging and the conclusions were limited. This highlights the complexity of adapting this diagnostic technique to the transient and high-enthalpy conditions characteristic of impulse facilities, further underscoring the innovative nature of the present research.
For the first time, electron number densities are measured in the University of Oxford's T6 Stalker tunnel. Intrusive measurements using Langmuir probes have been performed, and non-intrusive measurements using a Michelson interferometer, are planned. This work presents the Langmuir probe measurement results obtained so far. The objectives of the experiments are twofold: (i) to assess the operational efficacy of the Langmuir probes and validate their performance, and (ii) to quantify electron number densities behind shock waves across a spectrum of hypersonic flow conditions, specifically for shock speeds ranging from 4 to 7 km/s and freestream pressures between 13 and 133 Pa within the T6 Stalker Tunnel.
Benchtop tests, replicating the cabling and instrumentation layout within the tunnel, revealed a battery response time of 1.5 μs, with the overall system response time measured at 3 μs. These response times are deemed sufficiently rapid, given the described test times of 20 μs in [5]. The results of all benchtop tests demonstrated the Langmuir probes' proper functionality, confirming their readiness for experiments in the T6 Stalker Tunnel. The experiments in T6 acquired data in synthetic air, using the flush-mounted Langmuir probes, and operated in the aluminium shock tube mode (AST). A pair of rake-mounted Langmuir probes were positioned below the shock tube centreline at the dump tank exit, with concurrent Pitot pressure measurements for freestream pressure and test time characterisation. The probes were powered by a battery system operating at 9V.
Preliminary results from both Langmuir probes suggest repeatable current measurements and current-voltage (I-V) characterisation. Further testing and analysis are required to establish the consistency and reliability of the measurements. The calculated electron number density in the equilibrium region on the probe surface lies in the range of 1014/cm3. The expected electron number density in the given regime however is expected to be in the range between 1017/cm3 and 1018/cm3 [8], which lies in the post-shock equilibrium. The obtained electron number density measurements correspond to the secondary shocked gas near the probe surface, rather than the primary post-shock flow. This measured density differs from the predicted values by two orders of magnitude. This discrepancy likely arises from the presence of a non-equilibrium region between the primary post-shock flow and the probe surface. In this region, the gas undergoes additional processing due to the probe's presence, altering its properties. Further investigation into this phenomenon and its effects on electron number density measurements will be focused on in subsequent stages of this research.
To date, a solid foundation to work towards fulfilling the aims of this study could be established. The Langmuir probes are operational and generating data in the T6 Stalker Tunnel. Further experiments will provide more data with which the accuracy and functionality of the Langmuir probes can be evaluated further. These investigations will also investigate the reasoning why the observed order of magnitude is smaller than the expected order of magnitude in electron number density.
References
[1] Anderson, J. D. (2006). Hypersonic and High-Temperature Gas Dynamics, Second Edition. AIAA Education Series.
[2] Dunn, M. G., and Lordi, J. A., “Measurement of Electron Temperature and Number Density in Shock-Tunnel Flows. Part I: Development of Free-Molecular Langmuir Probes,” AIAA Journal, Vol. 7, No. 8, 1969, pp. 1458–1465. https:doi.org/10.2514/3.5415
[3] Yamada, G., Kawazoe, H., and Obayashi, S., “Electron density measurements behind a hypersonic shock wave in argon,” Journal of Fluid Science and Technology, Vol. 11, No. 1, 2016, p. JFST0005. https://doi.org/10.1299/jfst.2016jfst0005
[4] Collen, P., Doherty, L. J., Subiah, S. D., and McGilvray, M., “Development and commissioning of the T6 Stalker Tunnel,” Experiments in Fluids, Vol. 62, 2021, p. 225. https://doi.org/10.1007/s00348-021-03298-1
[5] Goekce, S., “Development of Langmuir Probes for Hypersonic Plasma Flow Diagnostics,” Master’s thesis, University of Queensland, 2009
[6] Chen, S. L., and Sekiguchi, T., “Instantaneous Direct-Display System of Plasma Parameters by Means of Triple Probe,” Journal of Applied Physics, Vol. 36, No. 8, 1965, pp. 2363–2375. https://doi.org/10.1063/1.1714492.
[7] Lindner, J. et al, “Langmuir analysis of electron beam induced plasma in environmental TEM”, Ultramicroscopy, Vol. 243, 2023, 113629.
[8] Iain D. Boyd; Modelling of associative ionization reactions in hypersonic rarefied flows. Physics of Fluids, 1 September 2007; 19 (9): 096102. https://doi.org/10.1063/1.2771662
Summary
Measuring electron number densities in hypersonic plasma flows is crucial for understanding aerothermodynamic phenomena, where traditional fluid dynamics principles no longer apply due to high speeds. The gas around the vehicle becomes hot enough to cause dissociation and ionisation of molecules, creating a chemically reacting flow [1]. The aerothermodynamic phenomena include chemical reactions, thermodynamic non-equilibrium, plasma formation, strong shock waves, and viscous interactions, which influence the communication blackout during re-entry along with aerodynamic heating, and material degradation [2], [3]. Ground testing facilities, such as the T6 Stalker Tunnel at the University of Oxford, provide a means to investigate ionisation rates, equilibrium ionisation percentages, and electron number densities under controlled conditions [4]. Both intrusive and non-intrusive diagnostic techniques can be employed to measure these parameters in hypersonic flows. Non-intrusive methods, such as microwave interferometry and spectroscopic techniques, offer the advantage of not disturbing the flow field [3]. However, intrusive measurements, particularly Langmuir probes, remain widely used in plasma facilities due to their simplicity, reliability, and ability to provide localised measurements [2], [5]. Their use in impulse facilities has been limited due to implementation and analysis restrictions. This work seeks to demonstrate the functionality of the probes in hypersonic facilities.
