Speaker
Description
Background of the study
A few years ago, the HES-SO team completed an ESA/OSIP project which indicated that our 1 kW pulsed microwave sulphur lamp can produce plasmas exhibiting significant similarities to weakly ionised molecular hypersonic plasmas encountered during the intense heat phase of shuttle atmospheric entry [1]. In particular, the wall temperature of the bulb reaches values close to the level measured on the thermal protection system of the STS-2 Shuttle [2]. The plasma itself exhibits a similarity due to a phenomenon called plasma ball formation (PBF), which our team discovered around ten years ago, by tuning the pulse parameters. We showed that the PBF is produced by an acoustic spherical resonance [3]. In addition, we obtained two independent proofs showing that, as with hypersonic molecular plasmas, the dissociation of heavy particles in the PBF is governed by pure vibrational mechanisms. However, dissociation in conventional electrical discharges is primarily induced by direct electron impact, posing challenges for inductively coupled facilities. Reducing compromises in terrestrial hypersonic installations results in an ongoing increase in costs. In this regard, the PBF-based technique we are developing could be a cost-effective addition to existing methods. This study focuses on one of its metrological objectives: measuring surface accommodation coefficients.
As stated in reference [4], the plasma pulses within the bulb increase its internal energy by populating high vibration levels. This results in a distribution of states that significantly deviates from the Boltzmann distribution. Consequently, compared to the local thermodynamic equilibrium (LTE) case, an additional heat transfer rate is released onto the bulb wall due to the surface catalytic effect on vibrational relaxation and recombination processes. These two characteristics are present in plasmas produced by an atmospheric hypersonic shock wave. The PBF accentuates the vibrational overexcitation and creates a three-component dissipative structure within the bulb that exhibits similarity to structures observed during atmospheric re-entry [4]:
- Partially dissociated plasma - Shock wave
- Peripheral gas around the PBF - Shock layer
- Bulb wall - Vehicle wall
This analysis led us to propose using the PBF to measure relevant physical properties, with the aim of broadening the scope of cost-effective CFD software. CFD codes are the primary numerical simulation technique used to model hypersonic flows at lower altitudes within the continuum and near-continuum regimes (Knudsen number, Kn, < 0.1), thanks to their high computational efficiency [5]. However, CFD breaks down if Kn >> 0.1. In this case, one must switch to methods that solve the Boltzmann equation, that can be solved by approximations such as state-to-state chemical kinetic approaches [6]. The accuracy of classical CFD decreases as non-equilibrium effects increase. While new machine-learning-augmented closures are being developed to extend its validity, there is still a lack of measured datasets [7]. Since the upgraded PBF facility allows for significant cost reductions, the proposed approach will enable large-scale data collection to train machine learning models once it is automated.
Methodology
The metrology principle utilises the non-equilibrium plasma plume of the PBF process. This plume meets the bulb wall via convective flow around the plasma ball. The wall temperature on the external surface of the bulb $T_w$ is calculated using CFD analysis of this convection flow, considering the heat transferred to the environment. The results are compared to measurement achieved with an infra-red camera. To match the measured value, an additional surface heat source term $\dot q_w$ is applied to the wall.
To determine the surface accommodation coefficient resulting from the catalytic effect of the wall ($\alpha$), we introduce a phenomenological law to describe the energy exchange between the flow and the surface, as set out in [8]:
\begin{equation}
\alpha \approx \frac{(P-\Phi)/S_b-\dot q_r}{(P-\Phi)/S_b-\dot{q_w}}
\end{equation}
where $P$ the absorbed microwave power, $\Phi$ is the emitted optical flux, $S_b$ the internal area of the bulb, and $\dot{q_r}$ represents the rate of heat transfer due to the elastic collisions of molecules with the wall (i.e. excluding surface chemical interactions). This can therefore be determined by CFD analysis.
Our work is based on the Navier–Stokes Multi-Block (NSMB) software tool, with the aim of upgrading it to include surface accommodation. This code is used for thermal, structural and fluid analyses, with a particular focus on supersonic and hypersonic flows [9, 10]. The convection flow is calculated within the Boussinesq approximation. The applied boundary conditions are:
- At the plasma boundary, the surface temperature is 3,354 K, as determined by thermodynamic modelling in a previous project [1] using measurements achieved with the standard 1 kW microwave sulphur lamp [11] and the spherical resonance frequency of our pulsed lamp [3];
- At the external wall of the bulb: radiation to ambient at 295 K (free convection is < 8% of the input power). The output of the calculation is the Dirichlet condition $T = T_w$.
- The no-slip boundary condition is applied to the interface between the gas and quartz bulbs.
- The medium is pure $S_2$ vapour: molecular dissociation of the gas surrounding the plasma ball does not come into consideration, since the luminescence there is much lower than that of the plasma ball itself.
Results
CFD simulations were carried out for a range of values of the additional surface heat source term ($\dot q_w$). This term is plotted as a function of the average bulb temperature $T_w$, as shown in the figure below. The objective is to identify a fit that yields the $\dot{q_w}$ value corresponding to the measured $T_w$, value (1290 K). The best fit is a power function, and the values of its two parameters, as well as the determination coefficient, which is very close to 1, are shown in the plot. The value obtained for $\dot{q_w}$ is 104 $kW/m^2$.
Figure 1. The additional surface heat source term ($\dot{q_w}$) as a function of the average bulb temperature ($T_w$).
Conclusion
The power released on the bulb wall due to surface accommodation is half of the input power, $ S_b \;\dot{q_w} = 0.51 \, P $, confirming the importance of non-LTE effects. The value obtained for $\dot{q_w}$ is remarkably similar in magnitude to that calculated by Shinn et al. using STS-2 shuttle flight data. The load near the nose ranges from 100 to 500 $kW/m^2$ (see Figure 3 in Reference 2). This therefore confirms the value of developing a low-cost, PBF-based method to complement existing hypersonic plasma simulation techniques. The next steps involve stabilising the PBF in a static bulb and producing it with atmospheric gases, such as $N_2$, $O_2$ and $CO_2$.
The authors would like to thank SEFRI, the Swiss federal government's specialised agency, for supporting our work through funding (contract SBFI-633.4-2025-2028/HEIG-VD AerothermGTF/2).
References
[1] Courret G and Nikkola P, Study on the role of the pycnoclinic acoustic force in hypersonic flight conditions, Technical ESA RFP/3-17148/21/NL/GLC/ov, HES-SO / HEIG-VD, Yverdon-les-Bains, Switzerland, Final report, November 2022
[2] Shinn, J., J. Moss, and A. Simmonds. "Viscous-shock-layer heating analysis for the shuttle windward-symmetry plane with surface finite catalytic recombination rates." 3rd Joint Thermophysics, Fluids, Plasma and Heat Transfer Conference. 1982. https://doi.org/10.2514/6.1982-842
[3] G. Courret, P. Nikkola, S. Wasterlain, O. Gudozhnik, M. Girardin, J. Braun, S. Gavin, M. Croci, and P. W. Egolf, "On the plasma confinement by acoustic resonance", The European Physical Journal D, 71(8):1–24, 2017
[4] Courret, G., & Nikkola, P. (2022). Plasma ball formation: an experimental technique to test radiative models in non-equilibrium plasmas. In Proceedings of the 9th International Workshop on Radiation of High Temperature Gases for Space Missions, 12-16 septembre 2022, Santa Maria, Portugal.
[5] Zhang, Wenqing, et al. "A review of the mathematical modeling of equilibrium and nonequilibrium hypersonic flows." Advances in Aerodynamics 4.1 (2022): 38.
[6] Colonna, G., Armenise, I., Bruno, D., & Capitelli, M. (2006). Reduction of state-to-state kinetics to macroscopic models in hypersonic flows. Journal of thermophysics and heat transfer, 20(3), 477-486.
[7] Nair, Ashish S., et al. "Physics-based machine learning closures and wall models for hypersonic transition-continuum boundary layer predictions." Physical Review Fluids 11.3 (2026): 033402.
[8] Brun, R. (2009). Introduction to reactive gas dynamics. Oxford University Press.
[9] Truong, Dinh Hung, et al. "Unsteady CFD simulations for Active Flow Control on a High-lift Wing-Flap system." GDR «Flow Separation Control», Poitiers, France, Videoconference meeting. 2021.
[10] Vos, Jan B., et al. "Aerodynamic investigations of a vertical landing launcher configuration by means of computational fluid dynamics and wind tunnel tests." AIAA Scitech 2022 Forum. 2022.
[11] Johnston, C. W., J. Jonkers, and J. J. A. M. Van Der Mullen. "Operational trends in the temperature of a high-pressure microwave powered sulfur lamp." Journal of Physics D: Applied Physics 35.20 (2002): 2578-2585.
Summary
A novel metrological approach based on Plasma Ball Formation (PBF) is proposed to determine surface accommodation coefficients in molecular hypersonic plasmas. The PBF, generated in a pulsed microwave sulphur lamp, produces strongly non-equilibrium conditions that exhibit several similarities with atmospheric entry plasmas. These include vibrational overexcitation and catalytic wall effects. CFD simulations performed with the NSMB solver are combined with infrared wall-temperature measurements to quantify an additional catalytic heat flux at the bulb wall. A correlation has been established between wall temperature and catalytic heat flux, providing a practical method of estimating surface accommodation coefficients. The next steps involve stabilising the PBF in a static bulb and producing it using atmospheric gases such as $N_2$, $O_2$ and $CO_2$. If this is successful, this low-cost laboratory technique could facilitate the generation of large experimental relevant datasets for validating CFD models and developing machine learning–assisted closures in non-equilibrium aerothermodynamics.