11th International Workshop on Radiation of High Temperature Gases for Space Missions

21 Sept 2026, 08:15 → 25 Sept 2026, 17:00 Europe/London

The Angevin Castle (Mola Di Bari)

Louis Walpot (ESA/TEC-MPA)

The workshop is organized by the Working Group “Radiation of High Temperature Gas” (RHTG) managed by ESA, through the ESA Technology Directorate. The local organization for this event is managed by Institute for Plasma Science and Technology (ISTP) CNR, Bari section and Department of Mechanics, Mathematics and Management, Polytechnic University of Bari (Italy).

The Workshop is devoted to promoting a dialogue on the state of the art and recent advances for simulation/modelling and experimental techniques of hypersonic radiating gas flows for the determination of radiative heat fluxes encountered during atmospheric entry. The workshop provides the opportunity to explore related areas of research to face the challenges of future space flight.

• Non-equilibrium chemical kinetics
• Hypersonic flows
• Plasma radiative emission and absorption
• Experimental facilities and experimental techniques
• Experimental and numerical modelling improvements of radiative heat transfer: refinement, verification, validation and comparison for space object re-entry simulation tools
• Test cases proposed for validation

 

Registrations and Abstract submission will be open on Sunday, February 15 2026. There is no workshop fee.  

v3_RHTG-11_Abstract-Contributon_Formatting_Guide_md.pdf

Monday 21 September

08:30 → 09:00 REGISTRATION

09:00 → 09:30 Opening

09:30 → 10:30 Radiation modeling and simulation: Monday morning 1

Convener: Brett Cruden (AMA Inc/NASA Ames)

09:30 Dragonfly Aerothermal Design and DrEAM Instrumentation Approaching Aeroshell Assembly

NASA Ames and Langley are partnering with DLR to propose a comprehensive instrumentation suite known as the Dragonfly Entry Aerosciences Measurements (DrEAM). DrEAM will provide key aerothermodynamic data and performance analysis for Dragonfly’s forebody and backshell Thermal Protection System (TPS), and also includes a DLR-provided Data Acquisition System (DAS). Titan’s atmosphere predominantly consists of nitrogen (~98% by mole) with small amounts of methane (~2% by mole). CN is a strong radiator and is found in nonequilibrium concentrations for Titan entry, the modeling of which has proven to be a difficult task. The DrEAM instrumentation suite will significantly advance the state-of-the-art not only by documenting the environment and performance of Dragonfly’s entry system but also by making key measurements in Titan’s atmosphere for the first time, thus providing new benchmark data applicable to entry science more generally.

Aerodynamic and aerothermal environments and TPS response will be measured using sensors similar to the Mars Entry, Descent, and Landing Instrumentation 2 (MEDLI2) Instrumented Sensor Plug (MISP) and the COMbined Aerothermal and Radiometer Sensor (COMARS) suite, with the latter supplied by DLR. For MEDLI2, MISP used embedded thermocouples (TCs) to directly measure in-depth temperature of the TPS at several locations, which can also be used to infer surface environments via inverse analysis. For DrEAM, the MISP style plugs will be known as Dragonfly Sensors for Aero-Thermal Reconstruction (DragSTR) plugs. Atmospheric density measurements and capsule aerodynamic data will be obtained through the onboard Inertial Measurement Unit (IMU), supplemented by hypersonic pressure transducers similar to those used by the MEDLI Mars Entry Atmospheric Data System (MEADS). The DrEAM pres-sure sensors will be known as Dragonfly Atmospheric Flight Transducers (DrAFT) On Schiaparelli, the COMARS suite included three total surface mounted heat flux sensors, three pressure sensors, six narrowband radiometers (provided by CNES) and one broadband radiometer. For DrEAM, a similar sensor package will be used with all sensors provided by DLR which is called COmbined Sensor System for Titan Atmosphere (COSSTA), see Fig. 1 showing the C3 being calibration at NASA Ames.

Figure 1: Angular characterization of the COSSTA sensors using the Laser Driven Light Source

The presentation will detail the various sensors to be included at each location around the aeroshell as well as provide a status on the current design, do-no-harm testing and flight hardware delivery.

Aerothermal analysis for the Dragonfly mission involves predicting the coupled convective and radiative heating environments the aeroshell will experience during entry into Titan’s dense, nitrogen‑methane atmosphere. This work integrates high‑fidelity CFD and nonequilibrium radiation modeling, drawing on assessments of turbulence behavior, roughness effects, wall‑temperature sensitivities, and species contributions such as $C_2N_2$, to characterize the flow field and heating across the forebody, shoulder, and aftbody regions. Iterative margin development, informed by wind‑tunnel comparisons, shock‑tube bias analysis, and parametric uncertainty studies, ensures that thermal protection system (TPS) sizing accounts for model uncertainty and mission risk. The resulting environments and status leading into aeroshell fabrication will be discussed.

Brief Presenter Biography:

Dr Brandis is a senior research scientist employed in the aerothermodynamics branch at NASA Ames. He is the DrEAM lead investigator, Dragonfly aerothermal lead and PI for NASA’s Entry Systems Modeling project.

References

[1.] A. Gülhan. et al. “Aerothermal Measurements from the
ExoMars Schiaparelli Capsule Entry,” Journal of Spacecraft and Rockets, 2018. https://doi.org/10.2514/1.A34228

Speaker: Dr Aaron Brandis (NASA Ames Research Center)

figure_194_01.png

10:00 Coupled Flow-Radiation Sensitivity and Uncertainty Analysis of the Dragonfly Capsule

Background

NASA’s Dragonfly mission, which aims to deliver a rotorcraft to Saturn’s moon Titan, must withstand extreme
convective and radiative heating during its entry into the moon’s dense nitrogen-methane atmosphere. Because of strongly radiating species, particularly the cyanogen (CN) radical, the forebody radiative heating can be as much as 50% of the total heat flux, necessitating the inclusion of radiation analysis when modeling the heating
of the probe during its entry.
Engineering predictions of the heat flux to the spacecraft surface – both the forebody and afterbody – are subject to uncertainty resulting from unknown freestream methane content of Titan’s atmosphere, as well as uncertainties in the parameters used to model chemical kinetics, radiative emission, and solid conduction in the
heat shield. These uncertainties carry major implications for the entry system reliability and so must be quantified.
Furthermore, there is an interest in evaluating whether the uncertainty in Titan’s atmospheric freestream methane content can be reduced through afterbody radiometer measurements of the Red and Violet bands of CN – the main transitions driving radiative heating – that will be gathered during entry; however, whether this can be accomplished given the uncertainty in predicting these bands is unknown.

Methodology
Flow simulations are performed with US3D, a computational fluid dynamics (CFD) solver developed at the University
of Minnesota. Radiation calculations are performed using the Multi-Fidelity Radiation Package (MURP),
which is coupled to US3D using the PreCICE library. Within each US3D calculation, the grid is tailored –
typically 2–4 times – in order to minimize numerical errors originating from poor alignment of cell faces with
the bow shock. Coupling between US3D and MURP can be either one-way, with data flowing from US3D into
MURP only once, at the end of the calculation, or two-way, in which US3D and MURP actively exchange data
with one another throughout the calculation. Two-way coupling enables the US3D flowfield to respond to the flux of radiated power into or out of each cell. Sensitivity and uncertainty quantification for the radiative environment requires propagating a large set of
uncertain chemical-kinetic and CN electronic-excitation rate coefficients, together with the freestream methane
content, through the flow–radiation model. Because a single high-fidelity (HF) US3D–MURP evaluation costs on the order of tens of CPU-hours, direct propagation over the hundreds of samples needed for variance-based sensitivity analysis is computationally prohibitive. To retain HF accuracy at a tractable cost, a bi-fidelity (BF)
surrogate is constructed. For an initial analysis, the focus is on defining QoIs on the surface of the vehicle.
For the purpose of CH4 inference, the QoIs are defined as the CNred and CNviolet. The BF method chosen is interpolative decomposition (ID)1 due to the correlation obtained between the LF and HF models. A dense low-fidelity (LF) ensemble is generated with a Lagrangian streamline solver employing a one-dimensional tangentslab radiative transfer approximation2, which runs in minutes per sample and broadly covers the uncertain input space. A pivoted QR factorization of the LF ensemble identifies a small set of maximally informative skeleton samples and an associated interpolation matrix; the US3D–MURP model is then evaluated only at these skeleton samples, and the full HF dataset is reconstructed by applying the LF-derived interpolation weights to the sparse HF evaluations. Because the LF and HF radiance fields are strongly correlated and the data singular values decay rapidly, the HF CNred and CNviolet profiles are recovered to within roughly one percent in the Frobenius norm using only a handful of HF simulations, reducing the cost of the analysis by approximately two orders of
magnitude relative to a full HF ensemble. This surrogate forms the backbone of the present study and underlies the global, variance-based (Sobol) sensitivity analysis of the CNred and CNviolet band radiances and their ratio along the vehicle surface.

Building on the cost reduction demonstrated for the radiative quantities, the study extends to a reliability
analysis of the forebody heat shield, whose quantity of interest is the bondline temperature: an interior quantity,
defined at the interface between the thermal protection system (TPS) and the underlying structure, whose exceedance of a critical threshold would compromise the integrity of the heat shield and the survival of the payload. In contrast to the CNred and CNviolet radiances, which are surface observables, the bondline temperature is obtained by supplying the surface convective (US3D) and radiative (MURP) heating distributions to a solid thermal solver, from which a Sobol analysis identifies the kinetic, excitation, and composition parameters that
most strongly drive its variability, and a reliability assessment evaluates the heat shield against its thermal design
margin. Because the underlying coupled, mesh-refined flow–radiation simulations are as expensive as those in the radiative analysis, the same low-/high-fidelity paradigm is a natural candidate for keeping this analysis tractable, with the uncoupled US3D heating solution on a coarser forebody mesh serving as the LF model and the coupled,
refined solution as the HF model.

Results

Before proceeding with sample generation, differences in forebody radiative heating between one- and two-way
coupling are evaluated first. Results from ten sample points evaluated at the maximum convective heating trajectory point reveal a difference of approximately 1% between the radiative heating obtained from the two-way
vs. one-way US3D–MURP coupling. As a result, the first 200 high-fidelity samples are generated using one-way
radiation coupling.
Bi-fidelity surrogates constructed from the interpolative decomposition reproduce high-fidelity CNred and
CNviolet radiance profiles to within approximately 1% of the high-fidelity result using only a handful of targeted
high-fidelity evaluations, at roughly two orders of magnitude lower computational cost than a full high-fidelity ensemble. Global sensitivity analysis confirms that freestream methane concentration is the dominant driver of variability in the CNred/CNviolet radiance ratio at both trajectory points considered, providing quantitative justification for using this ratio as a single-parameter diagnostic of methane abundance. Spatially resolved Bayesian inversion shows that methane identifiability is strongest in the near-afterbody at peak radiative heating, and is comparatively weaker and more spatially confined at peak convective heating, where CN emission is less intense.
When uncertainty in the CN electronic excitation rate coefficients is additionally propagated, the region over which methane remains identifiable contracts substantially, indicating that excitation-rate uncertainty is a
first-order factor limiting the diagnostic value of afterbody radiometer measurements and should be prioritized
in future efforts to reduce Titan atmospheric composition uncertainty.

Results

Before proceeding with sample generation, differences in forebody radiative heating between one- and two-way coupling are evaluated first. Results from ten sample points evaluated at the maximum convective heating trajectory point reveal a difference of approximately 1% between the radiative heating obtained from the two-way vs. one-way US3D–MURP coupling. As a result, the first 200 high-fidelity samples are generated using one-way
radiation coupling.
Bi-fidelity surrogates constructed from the interpolative decomposition reproduce high-fidelity CNred and
CNviolet radiance profiles to within approximately 1% of the high-fidelity result using only a handful of targeted
high-fidelity evaluations, at roughly two orders of magnitude lower computational cost than a full high-fidelity
ensemble. Global sensitivity analysis confirms that freestream methane concentration is the dominant driver of
variability in the CNred/CNviolet radiance ratio at both trajectory points considered, providing quantitative justification
for using this ratio as a single-parameter diagnostic of methane abundance. Spatially resolved Bayesian
inversion shows that methane identifiability is strongest in the near-afterbody at peak radiative heating, and is comparatively weaker and more spatially confined at peak convective heating, where CN emission is less intense.
When uncertainty in the CN electronic excitation rate coefficients is additionally propagated, the region over which methane remains identifiable contracts substantially, indicating that excitation-rate uncertainty is a first-order factor limiting the diagnostic value of afterbody radiometer measurements and should be prioritized
in future efforts to reduce Titan atmospheric composition uncertainty.

Conclusion

Uncertainty quantification efforts relating to the Dragonfly mission’s entry into Titan’s atmosphere were summarized, with particular emphasis on the feasibility of inferring the freestream methane concentration and on quantifying the reliability of the forebody heat shield. Freestream methane identifiability is shown to be strongly affected by both the radiometer placement and the degree of uncertainty in rate coefficients used to model CN electronic excitation. Further results from the forebody reliability study will be given in the presentation.

References
[1] H. Cheng et al. “On the Compression of Low Rank Matrices”. In: SIAM Journal on Scientific Computing 26.4 (2005), pp. 1389–1404. doi: 10.1137/030602678; J. Hampton et al. “Practical error bounds for a non-intrusive bi-fidelity approach to parametric/
stochastic model reduction”. In: Journal of Computational Physics 368 (2018), pp. 315–332. doi:10.1016/j.jcp.2018.04.015

[2] S. Boccelli et al. “Lagrangian diffusive reactor for detailed thermochemical computations of plasma flows”. In: Plasma Sources
Science and Technology 28.6 (2019), p. 065002.

Speaker: Timothy Aiken (University of Colorado)

Aiken, Gaymann, Sands, et al. - Coupled Flow-Radiation SA_UQ of Dragonfly.pdf

10:30 → 11:00 Coffee Break at the Palazzo Roberti Courtyard

Piazza XX Settembre, 60-62, 70042 Mola di Bari BA
https://maps.app.goo.gl/hwoVgZsAzCMpJNwZ6

11:00 → 12:00 Radiation modeling and simulation: Monday morning 2

Convener: Brett Cruden (AMA Inc/NASA Ames)

11:00 The Physics of Asymptotic High-Speed Flow Regimes I: Thermodynamics and Kinetics

What are the asymptotic limits of high-speed flows? Many years ago, it was postulated that post-shock temperatures would eventually reach a cap postulated to be around 20,000K, as increasing shock speeds would lead to endothermic processes offsetting the additional energy processed through the shock. These include, the excitation of a plethora of higher energy levels known to exist near dissociation and ionization thresholds for the flow species, dissociation and ionization reactions, and finally radiation which would lead to additional energy bleeding away from the shock layer.

The first part of this work discusses different updates to kinetic and thermodynamic models for air, capable of modeling the physical-chemical properties of plasmas at such high temperatures and ionization levels. We will point out additional theoretical hurdles in defining thermodynamic properties at extremely high temeratures, and the implications on the principle of detailed balance.

Radiative effects, modeled in a loose coupling, are discussed in a separate part II presentation.

Speaker: Mario Lino da Silva (Instituto de Plasmas e Fusão Nuclear - Instituto Superior Tecnico)

11:30 The Physics of Asymptotic High-Speed Flow Regimes II: Radiative Heat Transfer

We present a loosely coupled radiative transfer analysis for superorbital Earth entry, targeting the strongly radiating shock layers encountered at entry velocities in the 18-25 km/s range characteristic of sample-return and high-energy return trajectories. At such velocities the post-shock gas reaches temperatures at which radiative heating becomes a leading contributor to the total wall heat flux, comparable to or exceeding the convective component. A self-consistent treatment of the radiation field is therefore required to predict the aerothermal environment and to inform the sizing of thermal protection systems.

The present work consists in the implementation of a loosely coupled radiative transfer capability within the SPARK framework. The flowfield is first converged with the SPARK Navier-Stokes solver, either assuming local thermodynamic equilibrium or using the two-temperature ($T/T_{ev}$) nonequilibrium model. The resulting thermodynamic state is passed to the SPARK Line-by-Line radiation module, which returns a divergence-of-flux source term that is fed back into the energy equation. Two distinct models are used to evaluate the radiative source term. In the first, the shock layer gas is assumed to be optically thin, meaning that none of the radiated energy is reabsorbed. In the second model, the flux divergence is computed by solving the radiative transfer equation line-by-line under the tangent slab approximation. In both cases an attempt is made to exploit the $T^4$ scaling of radiative emission for both increasing stability of the simulations, and improve the predictive capacity of the models while minimizing the necessary amount of radiative property computations.

This work was supported by the FCT - Fundação para a Ciência e Tecnologia, I.P., under projects UID/50010/2025 (\url{https://doi.org/10.54499/UID/50010/2025}), UID/PRR/50010/2025 (\url{https://doi.org/10.54499/UID/PRR/50010/2025}), UID/PRR2/50010/2025 (\url{https://doi.org/10.54499/UID/PRR2/50010/2025}) and LA/P/0061/2020 (\url{https://doi.org/10.54499/LA/P/0061/2020}).

Speaker: Tiago Garrão

12:00 → 14:00 Lunch Break

Participants are asked to arrange their own lunch and return 10 minutes prior to the start of the session

14:00 → 15:30 ablative-radiative TPS and Meteors: Monday afternoon 1

14:00 Optical emission spectroscopy for laser-heated graphite in expansion tube

I. Introduction　
Ablation experiments have traditionally been conducted using plasma wind tunnels. Plasma wind tunnels can generate high-temperature flows for relatively long durations and are suitable for measuring recession rates and internal temperature histories of ablative materials. However, because the test gas is generated as a plasma flow, its degree of dissociation can be higher than that in actual re-entry environments, which limits the reproduction of chemical species. To reproduce flow conditions closer to actual atmospheric re-entry environments, heating experiments in hypersonic impulse facilities have attracted increasing attention. Zander et al. [1] conducted experiments at a surface temperature of 2400 K by electrically heating graphite using a DC power supply. Their results showed that CN formation near the surface increased with increasing surface temperature. Chang et al. [2] proposed another approach in which a test model was preheated in an arcjet facility and subsequently exposed to an expansion-tube flow. This method can reproduce a realistic internal temperature gradient by arcjet heating and has the advantage of being applicable to various model materials and geometries. Murray [3] performed electrically heated carbon–carbon composite ablation experiments in the Hypersonic Shock Tunnel at Sandia National Laboratories. Spallation from the C/C surface was observed, and the measured particle velocities ranged from 50 to 2000 m/s, with a mode of approximately 300–340 m/s. TDLAS measurements of CO indicated that the CO number density increased as the surface temperature was raised from 1900 K to 2200 K.
In this study, a graphite test model was preheated using a 4 kW continuous-wave laser before being exposed to an expansion-tube flow. Laser heating has been widely used in ablation studies, and its effectiveness has already been demonstrated. After laser preheating, the graphite model was tested in an expansion tube, and optical emission spectroscopy focused on the CN violet band was conducted to investigate changes in chemical species emission caused by an increase in surface temperature.

II. Experimental Setup
A Test Model
IG-11 grade isotropic graphite manufactured by Toyo Tanso Co., Ltd. was used as the test material. This graphite is manufactured by cold isostatic pressing (CIP) and has a purity of 99.96%, a density of 1770 kg/m³, and an emissivity of 0.80. The test model had a cylindrical shape with a diameter of 20 mm.
B Expansion Tube, CW laser and Rotating Sting
The experiments were conducted using the MX-6 free-piston expansion tube at Tokyo Metropolitan University. The reservoir pressure was set to 1 MPa. The driver gas was helium at 50 kPa, the driven gas was air at 120 Pa, and the acceleration tube was filled with air at 20 Pa. Under these conditions, the shock velocity was approximately 7.4 km/s, the Pitot pressure was approximately 200 kPa, and the test time was approximately 50 μs. JPT 4 kW continuous-wave fiber laser was used for preheating. The central wavelength of the laser was 1080 nm. The laser beam was collimated to a diameter of 20 mm using optics attached to the laser head. Because the beam profile was centrally peaked, the effective beam diameter was approximately 9.5 mm.
In laser preheating, uniform irradiation of the model surface is important for obtaining a nearly uniform surface temperature distribution. To achieve this, a specially designed rotating sting was used to rotate the test model about the centerline of the expansion tube. Although the laser irradiated the model from above, rotation enabled heating of the lower part of the model as well, resulting in a more uniform circumferential temperature distribution.

C Optical Emission Spectroscopy and Surface Temperature Measurement
Optical emission spectroscopy was performed with a focus on the CN violet band as an indicator of changes in surface-temperature-dependent species emission. An Andor Kymera 193i Czerny–Turner spectrograph and an Andor DH334T-18H-13-8SW ICCD camera were used. The surface temperature was measured using a FLIR T860 infrared camera. Although the upper temperature limit of the camera is 2100℃, the measurable temperature range was extended to above 3000℃ by using an infrared neutral-density filter. The infrared camera and neutral-density filter system was calibrated using a CHINO-S14 blackbody furnace at JAXA over the temperature range of 800℃ to 1400℃.

III. Results
The graphite test model was heated using a laser output power of 4 kW. The surface temperature reached 1500 K after 4.3 s, 2000 K after 8.5 s, and 2400 K after 15 s. The temperature distribution on the model surface was approximately within ±5%. Optical emission spectroscopy showed an increase in CN emission intensity as the surface temperature increased.

IV. Conclusion
A new ablation experiment combining laser preheating with an expansion tube was conducted. The graphite test model was successfully heated up to a maximum surface temperature of 2400 K. The increase in surface temperature enhanced the CN emission intensity, showing qualitative agreement with previous studies. These results indicate that laser preheating combined with an expansion tube is a promising approach for reproducing ablation phenomena under conditions closer to actual atmospheric re-entry environments.

References
1. F. Zander, R. G. Morgan, U. Sheikh, D. R. Buttsworth, P. R. Teakle, “Hot-Wall Reentry Testing in Hypersonic Impulse Facilities”, AIAA JOURNAL, Vol. 51, No. 2, February 2013, pp. 476-484.
2. Eric Won Keun Chang, Omar Valeinis, Joseph Steer, Matthew McGilvray, Tobias Hermann, Thomas E. Schwartzentruber, Berk Gur, Rui Fu, Alexandre Martin, “Operational Prediction of Arcjet Model Preheating within Expansion Tube Facility”, AIAA SciTech 2026 Forum, 12-16 January 2026, 2026-0459.
3. John S. Murray, Chris Murzyn, Erin Mussoni, Justin L. Wagner, “Carbon-Carbon Ablation Experiments in the Sandia Hypersonic Shock Tunnel”, AIAA SciTech 2026 Forum, 12-16 January 2026, 2026-461.

Speaker: Hiroki Hirano (Tokyo Metropolitan University)

14:30 Spectroscopic Measurements for Low-Density Ablator in Expansion Tube with Gas Injection

Background of the Study
Recent studies in non-equilibrium thermochemical CFD suggest that boundary conditions involving the ejection of reactive ablation gases from the wall can increase chemical heating near the wall at moderate mass fluxes, potentially leading to an increase in heat flux [1]. Furthermore, under high-speed conditions such as hyper-orbital reentry and entry into the atmospheres of outer planets, shock layer radiation becomes prominent in addition to convective heating [2]; therefore, the ablation gas reaction zone may contribute to wall heating as a near-wall gas phase layer accompanied by emission, absorption, and re-radiation. Therefore, in future low-density TPS designs, it is necessary to clarify whether the ejection of ablation gas simply shields the wall surface or increases wall heating through interaction with the high-temperature main flow.
However, in actual ablation tests, the composition, mass flux, and timing of pyrolytic gas generation are simultaneously determined as a result of the material’s internal response; thus, it is difficult to independently isolate the effects of the reaction, luminescence, and radiation fields generated in the gas phase [3]. Furthermore, while arc jet tests are excellent for material evaluation, the main flow pressure and dissociation state differ from those in the actual environment, making it difficult to simultaneously reproduce the gas-phase reaction field that becomes a problem during high-speed reentry at speeds of the order of 10 km/s [3].
Therefore, this study aims to establish a framework for evaluating the effects of ablation gas outflow on the near-wall gas phase by combining thermochemical non-equilibrium CFD with optical measurements, using a known gas outflow isolated from material response.
Methodology
In this study, we focus on a porous carbon leading edge placed in a hypersonic, high-enthalpy flow and simulate ablation gas release by applying a controlled gas outflow from the wall surface. By isolating the outflow conditions from the internal material response, we systematically investigate the effects of gas species, outflow intensity, and outflow timing on the near-wall gas phase.
The experiments were conducted using the MX6 free-piston expansion wave tube at Tokyo Metropolitan University [4]. A high-porosity porous carbon material was placed on the front surface of the test specimen, and gas was introduced from an external supply system via a plenum inside the model. By synchronizing wind tunnel operation with the gas injection system, the start time of gas injection relative to the arrival time of the main flow is controlled. The effects of the supply system pressure, the pressure inside the model, and the main flow conditions are verified, and the luminescence field near the wall is simultaneously acquired. The obtained luminescence distribution is compared with the injection layer structure and the distribution of major chemical species predicted by non-equilibrium thermochemical CFD and used to interpret changes in the near-wall gas phase.
In the numerical analysis, we employed non-equilibrium thermochemical CFD based on the compressible Navier–Stokes equations, introducing outlet boundary conditions that specify the mass flux and gas composition in the direction normal to the wall. In the future, we plan to evaluate the relationship between reactive zone formation and changes in the radiation field in stages by extending the study to reactive model gases and more detailed optical measurements.
Results
An evaluation of the supply system response in a stationary field confirmed that the rise in discharge pressure is strongly influenced by the gas species and the piping and plenum systems. In particular, while the rise in supply pressure and internal model pressure was relatively rapid for lighter gases, gases with higher molecular weights required a longer time to establish pressure. These results indicate that, in order to establish blowout within the short test duration of an expansion wave tube, it is necessary to consider the valve opening lead time, piping volume, and the influence of the internal plenum of the model for each gas species.
In the expansion wave tube tests, conditions with different blowout start times were compared. Under conditions where a shock wave velocity close to the non-blowout threshold could be maintained, there was a tendency for the blowout pressure not to stabilize sufficiently within the test duration. On the other hand, under conditions where blowout overlapped with the test duration, changes appeared in the light emission distribution near the wall, while an effect on the mainstream shock wave velocity was also confirmed. This indicates that, in short-duration, high-enthalpy flow, simultaneously satisfying the conditions for blowout establishment and non-interference with the mainstream is a key constraint in this problem.
Furthermore, under certain blowout conditions, a tendency was observed for the light emission intensity near the porous wall to decrease compared to non-blowout conditions. In thermochemical non-equilibrium CFD simulations as well, a tendency for the oxygen atom distribution near the wall to change due to gas ejection was observed, suggesting a qualitative consistency with the changes in the luminescence field observed experimentally. These results suggest that the near-wall gas layer formed by controlled gas ejection alters the distribution of chemical species and the luminescence field in high-enthalpy flow.
Conclusion
In this study, focusing on the ablation gas blowout problem in low-density TPS, we established a numerical and experimental framework for evaluating near-wall reactions and luminescence fields using a known gas blowout decoupled from the internal material response. We confirmed the response of the outflow supply system, its influence on the main flow in the expansion wave tube, and changes in the luminescence field near the wall. By combining these findings with an interpretation of the near-wall gas layer structure obtained via thermochemical non-equilibrium CFD, we demonstrated the potential for outflow to alter the near-wall gas phase in a high-enthalpy flow.This method is characterized by its ability to independently address the effects of gas composition, mass flux, and ejection timing—factors that are difficult to separate in plasma wind tunnel tests using actual ablators.
In the future, we will improve the compatibility between the blowout conditions and the main flow conditions, and by expanding the use of reactive simulated ablation gas and optical measurements, we will evaluate the formation of the heat-generating zone, chemical reactions, and changes in the luminescence and radiation fields in stages. Through this, we aim to clarify the competition between the blowout shielding effect and the increase in heating mediated by chemical reactions and radiation in low-density TPS.
References
[1] Maxime Lalande, Nicolas Dellinger, Ysolde Prévereaud, and Nathalie Bartoli, “Assessment of Air-Pyrolysis Gas Reactions on the Wall Heat Flux During Atmospheric Re-Entry,” International Journal of Heat and Mass Transfer, Volume 256, Article 127984, 2026. DOI: 10.1016/j.ijheatmasstransfer.2025.127984.
[2] Aaron M. Brandis, Christopher O. Johnston, Brett A. Cruden, and Dinesh K. Prabhu, “Equilibrium Radiative Heating from 9.5 to 15.5 km/s for Earth Atmospheric Entry,” Journal of Thermophysics and Heat Transfer, Volume 31, Issue 1, pages 178–192, 2017. DOI: 10.2514/1.T4878.
[3] Bernd Helber, Alessandro Turchi, James B. Scoggins, Annick Hubin, and Thierry E. Magin, “Experimental Investigation of Ablation and Pyrolysis Processes of Carbon-Phenolic Ablators in Atmospheric Entry Plasmas,” International Journal of Heat and Mass Transfer, Volume 100, pages 810–824, 2016. DOI: 10.1016/j.ijheatmasstransfer.2016.04.072.
[4] Yosuke Kurosaka and Kohei Shimamura, “Microwave Radar Diagnostics of Piston Motion in a Free-Piston-Driven Expansion Tube,” Shock Waves, Volume 34, pages 465–474, 2024. DOI: 10.1007/s00193-024-01194-1.

Speaker: Taichi Kumazaki (Tokyo Metropolitan University)

15:00 Influence of Gas Surface Interactions Modeling on Radiative Heat Transfer for Hypersonic Atmospheric Entry

Workshop topic: Ablative-Radiative TPS and Meteors

Background of the study

During high-speed atmospheric entry the shock-heated gas emits and absorbs strongly, and radiative heating becomes a significant (at the highest speeds dominant) contribution to the heat load on the vehicle's thermal protection system (TPS). At lunar-return velocities (around 11 km/s) the radiative flux is already comparable to convective heating near peak heating, and for sample-return and interplanetary trajectories in the 12–20 km/s range it becomes the leading term. Reliable prediction of this radiative environment is therefore central to the design and sizing of entry heat shields [1, 2].

Most modern heat shields use carbon-fiber/phenolic ablators, the Phenolic Impregnated Carbon Ablator (PICA) being the most representative. These materials protect the vehicle by ablating, through oxidation, nitridation and sublimation of the carbon fibers, and pyrolysis of the phenolic matrix, injecting CO, atomic carbon, CN and hydrogen-bearing species into the boundary layer [3, 4]. There, these products reduce convective heating, but they also introduce strong additional radiating systems and modify both the emission and the absorption of the shock layer [5]. The radiative and the ablative environments are thus two-way coupled: shock-layer radiation drives the wall temperature and hence the ablation rate, while the ablation products reshape the radiative field that reaches the wall. Predicting the radiative heat flux on an ablating heat shield therefore requires simulations that couple the flowfield, the surface chemistry and the radiative transport in a self-consistent way. The objective of this study is to quantify this coupling between ablative gas-surface chemistry and radiation across a range of high-speed Earth-entry conditions.

Methodology

The study relies on a high-fidelity framework coupling three computational tools. The finite-volume CFD solver HEGEL [6] integrates the two-temperature, thermochemical-nonequilibrium Navier-Stokes equations for an air-carbon-phenolic mixture on an axisymmetric body; the thermochemical library PLATO [7] supplies the closure models (chemical kinetics, transport properties and gas-surface fluxes); and the radiation transport solver MURP [8] integrates the radiative transfer equation for a non-gray, absorbing and emitting medium, returning both the volumetric radiative source term fed back to the flow energy balance and the wall-incident radiative flux. HEGEL and MURP are coupled explicitly and advanced until a steady-state coupled solution is reached.

Gas-surface interactions are described with a zero-dimensional surface model that evaluates all surface processes from the local wall state, adopted here as an intermediate-fidelity step toward fully coupled material simulations. The model combines state-of-the-art finite-rate air-carbon chemistry, carbon sublimation, and a steady-state pyrolysis closure that injects the hydrogen-bearing pyrolysis gas into the boundary layer; a spatially resolved surface recession rate follows directly from the surface mass balance. Radiation is computed line-by-line from quasi-steady-state electronic populations, accounting for bound-bound, bound-free and free-free transitions of N, O and C and for the principal diatomic systems (N$_2$, O$_2$, NO, CN, CO, C$_2$, N$_2^+$); the radiating systems of the pyrolysis-gas species are also included when ablation is active. A reduced-order spectral grouping strategy reproduces the line-by-line solution to within about 5% using only 100 spectral groups, making the coupled simulations affordable [9].

The framework is applied to a 60° sphere-cone capsule entering Earth's atmosphere. To isolate the role of the surface chemistry on the radiative environment, three wall treatments are compared: a fully catalytic, ablation-free wall used as a bounding reference; the baseline air-carbon ablation model; and an extended ablation model that adds carbon sublimation and phenolic-matrix pyrolysis.

Results

A coupled CFD-radiation simulation at an entry velocity of 10 km/s establishes the baseline. Relative to the catalytic wall, surface ablation injects CO, atomic carbon and minor amounts of CN into the boundary layer and softens the near-wall temperature gradient, lowering the stagnation-point convective heat flux ($\approx$ 1500 to 1300 W/cm$^2$) and the radiative-equilibrium wall temperature ($\approx$ 4200 to 3800 K). Despite this cooler boundary layer, the wall-incident radiative flux is consistently higher for the ablating wall: it rises from 112 to 143 W/cm$^2$ at the stagnation point (+27%), with the ablative-to-catalytic ratio reaching about 1.7 further downstream. This increase is driven by strong emission from carbon-bearing species (atomic carbon and the CN Violet system), combined with reduced boundary-layer absorption from the weaker N$_2$/O$_2$ recombination at the ablating surface.

These results show that the choice of surface chemistry model has a first-order, counterintuitive effect on the radiative heating: a treatment that lowers convective heating can simultaneously raise the radiative flux. They also indicate that the coupling should strengthen with entry velocity, since the hotter walls reached at higher speeds intensify carbon sublimation and pyrolysis-gas injection.

Conclusion

The baseline results establish that ablative gas-surface chemistry and shock-layer radiation are tightly two-way coupled in high-speed Earth entry, and that the fidelity of the surface chemistry model is a first-order driver of the predicted radiative heating rather than a second-order correction. The full contribution will extend the analysis to entry velocities of 12, 15 and 20 km/s, representative of sample-return and interplanetary conditions, and present a systematic three-way comparison of the catalytic, baseline air-carbon, and extended ablation walls, quantifying how carbon sublimation and pyrolysis-gas injection reshape the boundary-layer radiation and the wall heat-flux and recession-rate distributions.

Beyond the present study, the zero-dimensional surface closure is intended as a stepping stone toward fully coupled CFD-radiation-material simulations, in which in-depth conduction, pyrolysis-gas transport and the resulting heat-shield shape change are resolved. Extending the framework along representative entry trajectories would then enable time-accurate predictions of the radiative environment of ablating heat shields, with direct relevance to TPS design and to the modelling of meteoric entry.

Speaker: Alessandro Meini (UCI)

RHTG_2026_abstract.pdf

15:30 → 16:00 Coffee Break at the Palazzo Roberti Courtyard

Piazza XX Settembre, 60-62, 70042 Mola di Bari BA
https://maps.app.goo.gl/hwoVgZsAzCMpJNwZ6

16:00 → 17:30 State to state and Collisional Radiative Modelling: Monday afternoon 2

Convener: Marco Panesi (University of California, Irvine)

16:00 Nonequilibrium kinetics and radiation of high-temperature N$_2$/CH$_4$ plasmas

This work aims to improve the prediction of CN electronic state populations in high temperature $\text{N}_2/\text{CH}_4$ plasmas, an essential prerequisite for robust radiative flux modeling during Titan entry [1], [2], [3]. We develop a comprehensive collisional radiative (CR) model that tracks all relevant global species as well as the ground state $\text{CN}(X^2\Sigma^+)$ and the first four excited states: $\text{CN}(A^2\Pi)$, $\text{CN}(B^2\Sigma^+)$, $\text{CN}(a^4\Sigma^+)$, and $\text{CN}(D^2\Pi)$. The global species reactions of the CR model are based on the modified mechanism of Gökçen [4], [5]. The reactions involving CN excited states include heavy particle/electron-impact dissociation, heavy particle/electron-impact excitation, and spontaneous emission. The corresponding rate coefficients are taken from Ref. [4], while adding processes that were not included in the initial set.

The CR model predictions are compared against two independent data sets:
(i) absorption/emission measurements of the CN red ($A-X$) and violet ($B-X$) bands in a recombination plasma experiment, and
(ii) emission measurements of the same bands in a dissociating plasma obtained with the Low Density Shock Tube (LDST) of NASA Ames Research Center [6], [7].
The model is coupled to a one dimensional space marcher (1D SM) for comparison with LDST measurements.

The recombination experiment consists of generating a plasma using an inductively coupled plasma (ICP) torch that subsequently recombines in a water cooled tube. Initial CR model predictions of $\text{CN}(X^2\Sigma^+)$, $\text{CN}(A^2\Pi)$ and $\text{CN}(B^2\Sigma^+)$ number densities underpredict the measurements by up to a factor five at 37.5-cm tube length. A kinetic analysis, combined with One At a Time and Sobol' sensitivity studies revealed that the $\text{N}_2$ recombination reaction is by far the dominant source of variance of the densities of CN electronic states. The next-most important contributor to the total variance is the recombination reaction into $\text{CN}(A^2\Pi)$. CN electronic states densities are also sensitive to the exchange reaction $\text{CN}(A^2\Pi) + \text{N} \leftrightarrow \text{N}_2 + \text{C}$, along with the heavy particle excitation/deexcitation reactions between the three electronic states. Guided by these insights, we perform a quasi Monte Carlo (QMC) optimization of the rate coefficients corresponding to the reactions identified by the sensitivity analysis within their respective uncertainty domains. This analysis showed that good agreement with the measured CN densities in the recombination tube can only be achieved if we increase the $\text{CN}(A^2\Pi)$ recombination rate coefficient by a factor of at least 200. A separate QMC study performed on one LDST dataset showed that reducing the $\text{CN}(A^2\Pi) \leftrightarrow \text{CN}(B^2\Sigma^+)$ heavy particle excitation rate by at least a factor 30 brings the LDST predictions within 20% of experiment.

Finally, a global QMC optimization that respects both experiments is performed. Based on this analysis, we recommend a final set of modifications to the reaction rate coefficients of the baseline model that allows for reasonable agreement with both datasets. Good agreement can only be obtained if the $\text{CN}(A^2\Pi)$ recombination/dissociation rate ($\text{C} + \text{N} + \text{M} \leftrightarrow \text{CN}(A^2\Pi) + \text{M}$) is allowed to be different for the LDST and recombination experiments, indicating that the chemical pathways – dissociation in the case of LDST and recombination for the recombination experiment – are not the same for these two experiments.

[1] A. M. Brandis, R. G. Morgan, and T. J. McIntyre, “Analysis of Nonequilibrium CN Radiation Encountered During Titan Atmospheric Entry,” Journal of Thermophysics and Heat Transfer, vol. 25, no. 4, pp. 493–499, Oct. 2011, doi: 10.2514/1.50966.
[2] T. E. Magin, L. Caillault, A. Bourdon, and C. O. Laux, “Nonequilibrium radiative heat flux modeling for the Huygens entry probe,” J. Geophys. Res., vol. 111, no. E7, p. 2005JE002616, Jul. 2006, doi: 10.1029/2005JE002616.
[3] M. Wright, “The Dragonfly Entry and Descent System”.
[4] C. O. Johnston, T. K. West, and A. M. Brandis, “Features of Afterbody Radiative Heating for Titan Entry,” in AIAA Aviation 2019 Forum, Dallas, Texas: American Institute of Aeronautics and Astronautics, Jun. 2019. doi: 10.2514/6.2019-3010.
[5] T. Gökçen, “N2-CH4-Ar Chemical Kinetic Model for Simulations of Atmospheric Entry to Titan,” Journal of Thermophysics and Heat Transfer, 2007.
[6] A. Fagnani, A. M. Brandis, and B. A. Cruden, “Characterization of Titan Entry Radiative Heating in the Low Density Electric Arc Shock Tube,” in AIAA SCITECH 2025 Forum, in AIAA SciTech Forum. American Institute of Aeronautics and Astronautics, Jan. 2025. doi: 10.2514/6.2025-0448.
[7] A. Fagnani, D. L. Drescher, J. W. Streicher, R. Hanson, A. M. Brandis, and B. A. Cruden, “Assessment of CN Non-Boltzmann Kinetics Against Low Density Shock Tube Data,” in AIAA SCITECH 2026 Forum, Orlando, FL: American Institute of Aeronautics and Astronautics, Jan. 2026. doi: 10.2514/6.2026-1677.

Speaker: Cyrine Merhaben (EM2C Laboratory, CentraleSupélec, Université Paris Sacaly)

16:30 State-to-state kinetics of pure reacting CO mixture: shock tube case

The characterization of carbon monoxide thermochemistry is critical for aero-thermodynamic modeling of Mars and Venus atmospheric entry, where CO, resulting from carbon dioxide dissociation, is a predominant species in the high-enthalpy shock layer [1].

Accurate predictions of the shock layer properties rely on the fidelity of the underlying kinetic models. To this aim, the experimental campaign conducted by Cruden \textit{et al.} [2] at the NASA Ames EAST facility characterized incident shock waves in pure CO (0.25 Torr, 3.4 - 9.5 km/s) using emission and absorption spectroscopy to determine temperature relaxation profiles behind the shock front. A key outcome of their analysis demonstrated that current kinetic parameters from the literature fail to uniformly predict CO dissociation rates across the entire velocity spectra, matching the experimental data only within restricted bounds. This discrepancy highlights the need to improve the modeling of CO dissociation and C$_2$ exchange pathways.

Based on these premises, the present work aims to numerically reproduce the EAST experiments with the code GPKin [3] applied to 1D shock tube calculation by implementing a state-to-state kinetic model for pure CO focusing on the CO dissociation [4-8], energy transfer vibration-translation (VT) and vibration-vibration (VV) processes [9-11].

Temperature profiles are here compared with literature experimental results [2]. Moreover, species mole fractions and CO vibrational distributions predicted by the numerical solver are here shown and discussed.

References

[1] P. A. Gnoffo, Planetary-Entry Gas Dynamics, Annual Review of Fluid Mechanics, 31 (1999) 459; 10.1146/annurev.fluid.31.1.459.
[2] B. A. Cruden, A. M. Brandis, and M. E. MacDonald,Characterization of CO Thermochemistry in Incident Shockwaves, 2018 Joint Thermophysics and Heat Transfer Conference, AIAA AVIATION Forum, American Institute of Aeronautics and Astronautics (2018); 10.2514/6.2018-3768.
[3] G. Colonna, M. Capitelli and L. D. Pietanza, Self-consistent kinetics, in Plasma Modeling (Second Edition) Methods and applications, ch. 9 ed. G. Colonna and A. D'Angola (IOP Series in Plasma Physics); 10.1088/978-0-7503-3559-1ch9
[4] J. P. Appleton, M. Steinberg, and D. J. Liquornik, Shock-Tube Study of Carbon Monoxide Dissociation Using Vacuum-Ultraviolet Absorption, The Journal of Chemical Physics, 52, 5, 2205 (1970); 10.1063/1.1673286.
[5] C. O. Johnston and A. M. Brandis,Modeling of nonequilibrium CO Fourth-Positive and CN Violet emission in CO$_2$–N$_2$ gases, Journal of Quantitative Spectroscopy and Radiative Transfer, 149, 303 (2014); 10.1016/j.jqsrt.2014.08.012.
[6] C. Park, J. T. Howe, R. L. Jaffe, and G. V. Candler, Review of Chemical-Kinetic Problems of Future NASA Missions, II: Mars Entries, Journal of Thermophysics and Heat Transfer, 8, 1 (1994); 10.2514/3.496.
[7] C. Park,Rate Parameters for Electronic Excitation of Diatomic Molecules II. Heavy Particle-Impact Processes, 46th AIAA Aerospace Sciences Meeting and Exhibit, AIAA 2008-1446, American Institute of Aeronautics and Astronautics, Reno, NV, USA (2008); 10.2514/6.2008-1446.
[8] R. L. Macdonald, A. Munafò, C. O. Johnston, and M. Panesi, Nonequilibrium radiation and dissociation of CO molecules in shock-heated flows, Physical Review Fluids, 1, 4, 043403 (2016); 10.1103/PhysRevFluids.1.043403.
[9] C. Gorse, M. Cacciatore, and M. Capitelli, Shock Processes in Non-Equilibrium Carbon Monoxide Plasmas. I. Vibrational Kinetics and Dissociation Rates, Chemical Physics 85 (1984) 165-176; 10.1016/0301-0104(84)85030-2
[10] Q. Hong, L. Storchi, C. Bolelli, J. Li, Q. Sun, and J. Li, Quantum-Classical Rate Coefficients of Vibrational Energy Transfer in Carbon Monoxide Based on Highly Accurate Potential Energy Surface, The Journal of Chemical Physics, 138, 7, 074304 (2013); 10.1063/1.4798661.
[11] M. Cacciatore and G. D. Billing,Semi-Classical Calculation of VV and VT Rate Coefficients in CO, Chemical Physics 58 (1981): 395-407.

Speaker: Emmanuel Scalera (CNR)

image.png

17:00 A simplified approach to atom and molecule thermodynamic functions

Determination of thermodynamic properties of the species in a plasma is a relevant aspect in the aerothermodynamics, also in non-equilibrium conditions, to calculate the contribution to internal levels to the system enthapy and to the equilibrium constants of relevant reactions [1]. The most accurate approach is to perform the Boltzmann summation on the entire level spectrum, truncated to avoid the divergence of the partition function [2, 3]. This calculation is very time consuming, needing the evaluation of a number of exponentials of the order ranging from many hundreds to hundreds of thousands.

The paper presents the general theory to calculate thermodynamic properties of atomic and molecular species lumping all the levels in a small number of groups, each one characterised by a statistical weight and energy, and applying the Boltzmann statistics [4,5].

For atomic species the method is based on the Taylor series of the exponential function [Colonna] and it has shown that the convergence properties strongly depend on the variance of the level distribution [4]. This approach gives very good accuracy for many atoms such as nitrogen, oxygen and hydrogen [4,5]. However, difficulties arise when the method is applied to atoms with electrons in the angular momentum quantum number $\ell\ge 2$. Therefore, a multi-group strategy has been implemented to improve the accuracy of the second order approximation and to account for the dependence of the number of levels included in the calculation of the thermodynamic properties [6]. The multi-group approach has been applied to Cu, Cu$^{+}$ and Cu$^{+2}$, validating the method by comparison between the multi-group and the exact calculation.

The idea has been adapted to the diatomic molecules [7] considering that a given number of ro-vibrational levels can be approximated with the truncated harmonic oscillator and rigid rotor. All the other levels can be lumped in a multi-group structure as in the case of atomic species. It is difficult to determine where is the upper limit of the levels approximated by the harmonic oscillator and rigid rotor. For this reason, a best fitting procedure has been implemented to find the coefficients of the approximate expression.

The method adopted for diatomic molecules has been extended to polyatomic molecules [7], taking into account that there are different vibrational modes and 2-3 rotational axes.

The proposed approach has been demonstrated to be accurate in a wide range of temperature, limiting the calculation of the thermodynamic properties to a small number of exponentials. Moreover, the lumping level approach allows to include the ionisation lowering in the atomic partition function, very relevant when electron density grows.

References

[1] J. D. Anderson, Hypersonic and High Temperature Gas Dynamics, American Institute of Aeronautics and Astronautics, 2006; 10.1007/978-3-319-05200-7
[2] D. Landau and E. Lifshitz, Statistical Physics, Pergamon Press, Oxford, 1986;10.1515/9783110648485-015
[3] M. Capitelli, G. Colonna, and A. D’Angola, Fundamental Aspects of Plasma Chemical Physics: Thermodynamics, in Springer Series on Atomic, Optical, and Plasma Physics, volume 66. Springer Science \& Business Media, 2011; 10.1007/978-1-4419-8182-0
[4] G. Colonna and M. Capitelli, A few level approach for the electronic partition function of atomic systems, Spectrochimica Acta Part B: Atomic Spectroscopy, 64 (2009) 863-873; 10.1016/j.sab.2009.07.002
[5] G. D’Ammando, G. Colonna, and M. Capitelli, A simplified approach to calculate atomic partition functions in plasmas, Physics of Plasmas, 20 (2013) 032108; 10.1063/1.4794286
[6] G. Colonna, L. Bruyas, A simplified approach to calculate thermodynamic properties of metal atoms, in preparation;
[7] G. Colonna, A. D’Angola, and A. Laricchiuta, Thermodynamic and transport properties of complex plasmas, in Plasma Modeling (Second Edition) Methods and applications, ch- 21 IOP Publishing Bristol, UK, 2022; 10.1088/978-0-7503-3559-1ch21

Speaker: Gianpiero Colonna (CNR-ISTP Bari)

Tuesday 22 September

09:00 → 10:30 Plasma facilities, simulations and diagnostics: Tuesday morning 1

09:00 Experimental Measurements of Non-Equilibrium Flow Relaxation for Uranus Entry using Vacuum-Ultraviolet and Visible Spectroscopy

The ice giants, Uranus and Neptune, are the least explored planets in our solar system. Voyager 2 conducted a brief flyby of Uranus in 1986, before reaching Neptune, but the visit provided incomplete data and left many phenomena unexplained. As such, a larger-scale return mission, named the Uranus Orbiter and Probe (UOP), was designed to perform a multi-year orbit and deploy a probe into the planet’s atmosphere. The UOP mission was classified as the highest-priority flagship mission in the 2023-2032 Planetary Science and Astrobiology Decadal Survey, ideally launching in the early 2030s, so it is vital to better understand the entry environment. Current models of the flow chemistry demonstrate great uncertainties for a number of reasons, so their development is crucial.

As the Uranian atmosphere is composed mostly of hydrogen, alongside helium and trace species, unreliable hydrogen dissociation rates limit computational models. Additionally, the extreme entry velocity of approximately 22.3 km/s is challenging to reproduce, so there are few facilities capable of experimental simulations. In such simulations, vacuum-ultraviolet (VUV) spectroscopy is required for the analysis of molecular hydrogen behaviour, which is a highly complex system to operate successfully, especially in impulse facilities. These factors have prevented the accurate quantification of the non-equilibrium flow relaxation that would occur in the shock layer during UOP probe entry. The rate of dissociation and potential recombination of hydrogen contributes significantly to the total heat flux impacting the probe’s heat shield, so it must be considered for design optimisation [1]. Spectroscopy enables the analysis of this behaviour, particularly in the VUV region, as the presence of molecular hydrogen is measurable through its radiative emissions.

Various studies have reported that hydrogen emits radiation at negligible or very low intensity under Uranus entry conditions. The Electric Arc Shock Tube (EAST) at NASA Ames Research Center was used for Uranus and Saturn entry simulations, but the post-shock relaxation of hydrogen could only be analysed for Saturn entry, given limitations in exposure time for a moving shock [2]. However, giant planet entry experiments in the Oxford T6 Stalker Tunnel demonstrated that hydrogen emissions may be detectable in an expansion tube, in which a model enables the analysis of a stationary shock. Longer exposure times could be used, increasing the signal of less-intense features. As the facility was not equipped with VUV spectroscopy at the time, only H-alpha could be measured, but no molecular bands [3].

The X2 expansion tube at the University of Queensland (UQ) is capable of replicating Uranus entry conditions through the Stalker Substitution method. While current driver conditions limit the freestream velocity to roughly 20 km/s, the target post-shock temperature can be achieved, allowing the replication of flow chemistry. By increasing the composition of helium in the test gas, to act as an inert diluent, the specific heat of the mixture is reduced, producing a higher post-shock temperature with a lower velocity. In recent X2 experiments, three peak-velocity Uranus entry conditions were tested with varying test gas compositions, while spectral measurements were taken in the VUV, ultraviolet (UV) and visible wavelength regions. These conditions were designed to replicate the post-shock properties of the 34.5 s trajectory point proposed by Palmer et al., developed using the TRAJ program [1]. James et al. utilised PITOT3 to determine that the equilibrium post-shock temperature at this trajectory point was achievable in X2 with an approximate 40%He/60%H2 mixture, while the frozen post-shock temperature requires an approximate 60%He/40%H2 mixture [4]. As such, the test gas compositions tested in the current study were 45%He/55%H2, 50%He/50%H2 and 55%He/45%H2.

Various instrumentation was used to ascertain the test times of each condition, ensuring accurate spectral measurements of the hydrogen/helium shock layer. This included two high-speed cameras, one with an H-alpha bandpass filter to detect the region of steady hydrogen flow. Additionally, a visible photodiode and three pitot probes beneath the model supported the test time evaluation. Flow contamination was found to increase the intensity of hydrogen spectral emissions and shift the test time, so great effort was made in the pre-shot procedure to minimise it. Methods included several passes of acetone and isopropyl alcohol in the shock tube, acceleration tube and nozzle, the maintenance of a low vacuum in the facility at all times excluding turnarounds, and immediate firing after filling the shock tube. A cleaned fused silica window was used to maximise transmission in the UV and visible regions, and a single-use, alumina-polished magnesium fluoride window was installed before each shot for maximum transmission in the VUV region.

The 50%He/50%H2 and 55%He/45%H2 test conditions resulted in similar spectral measurements, and approximate shot repeatability was obtained. The Lyman-band of molecular hydrogen was observed in the VUV region and spanned at least half of the shock layer, indicating a slow dissociation and mostly non-equilibrium flow. Recombination was not clearly detected at the model edge. Negligible contamination was emitted in this region, despite atomic nitrogen lines being previously observed, suggesting that air contamination in the shock tube was successfully minimised. The atomic hydrogen features were generally much weaker, where the Lyman-alpha and H-beta lines were not measurable at all. The H-alpha line was detected in the visible region, but it was low in intensity. As the wavelengths measured with the visible spectrometer ranged from approximately 635nm to 915nm, many contaminants could be observed, emitting at a similar intensity relative to H-alpha.

In contrast, the 45%He/55%H2 condition resulted in a slightly brighter Lyman band in the VUV region, and it appeared to exhibit recombination at the model edge, as shown in Fig. 1. As this condition contained less inert diluent, it reached a lower post-shock temperature and hence a greater post-shock density, likely causing such phenomena. The radiative emissions in the UV and visible regions displayed similar patterns, where the spectra observed were similar to the preceding conditions but with a slightly greater intensity.

Figure 1. Integrated radiance from 140-165nm, comparing Lyman-alpha molecular hydrogen band emissions from 50% helium Uranus entry condition and 55% helium Uranus entry condition.

The results indicate a clear capability for measuring hydrogen relaxation in Uranus entry simulations using the X2 expansion tube, as the molecular Lyman band is detectable and quantifiable in the VUV region. However, further analysis is required to determine the appropriate test gas substitution that yields the expected post-shock temperature. As the relaxation behaviour was not consistent between all conditions, it cannot be concluded which condition best represented the proposed peak-velocity Uranus entry trajectory point. Spectral fitting will be implemented to derive the post-shock temperatures, furthering the analysis.

References

[1] Grant Palmer, Dinesh Prabhu, and Brett A. Cruden: Aeroheating Uncertainties in Uranus and Saturn Entries by the Monte Carlo Method. Journal of Spacecraft and Rockets 51.3, 801-814 (2014).
[2] Brett A. Cruden and David W. Bogdanoff: Shock Radiation Tests for Saturn and Uranus Entry Probes. Journal of Spacecraft and Rockets 54.6, 1246-1257 (2017).
[3] Joseph Steer et al.: Commissioning of Upgrades to T6 to Study Giant Planet Entry. Journal of Spacecraft and Rockets 61.6, 1545-1562 (2024).
[4] C. M. James et al.: Simulating Gas Giant Atmospheric Entry Using Helium and Neon Test Gas Substitutions. Journal of Spacecraft and Rockets 56.3, 725-743 (2019).

Speaker: Daisy-May Joslyn (The University of Queensland)

DJoslyn_RHTG11_abstract.pdf

figure_203_01.png

10:00 New 8-Color, Spectrally-Resolved, Pathlength-Amplified Absorption Spectroscopy Measurements of Air-Argon-XenonPlasmas Behind Reflected Shock Waves

Background

The validation of new collisional-radiative models for the excitation and ionization of air requires quantitative measurements of the different excited and ionized species present in re-entry and hypersonic-relevant flows. Such measurements behind shock waves have been difficult, owing to the rapid timescales of the formation and decomposition of excited atoms, molecules, and ions, as well as their low concentrations. Previous works have shown that using recently developed pathlength amplification technology for reflected shock tubes, such measurements are possible for some key excited states of oxygen and nitrogen, as well as electron number density from the Stark shift and broadening of a high-lying argon state, a common bath gas used in reflected shock tube experiments. These early experiments identified large discrepancies between existing collisional-radiative models and experimental measurements of O and N excited states on the order of 3x, while the Ar excited state populations were well-predicted. Models likewise overpredicted the late-time electron number densities by a factor of 2. Unfortunately, these measurements captured only a small fraction of the important excited atomic states present in such flows and entirely neglected the molecular excited states.
This work presents new measurements of three excited states of O, three excited states of N, two excited states of Ar, NO(A), N2(A), N2+(X), six states of Xe including the first excited state, along with multiple measurements of the translational temperature, electron number density, and electron temperature across multiple mixtures of O2/N2/Ar/Xe. Up to ten of these species were measured simultaneously, with measurements depending on the mixture and temperature regime.

Methodology

Pathlength-amplified, spectrally-resolved laser absorption spectroscopy enabled the capture of time histories in each shock tube experiment, with vibrationally-frozen post-reflected-shock temperatures ranging from 8500 K to 15000 K in O2/N2/Ar, 8500 K to 25000 K in O2/N2/Xe, and up to 50000 K in pure xenon. Pressures varied between 0.03 atm and 2 atm, with the vast majority of experiments conducted below 0.5 atm. Eight different lasers were deployed simultaneously in each experiment, capturing different regions of the NIR spectrum. Six of these lasers operated over a narrow range of 1-2 cm-1 allowing for the detailed capture of absorption lineshapes for both atomic and molecular lines, all while sampling at rates between 500 kHz and 1 MHz. A seventh laser system, a MEMS VCSEL centered at 1060 nm produced by Thorlabs allowed for the sampling of the entire 1 – 1.1 um region, capturing 900 cm-1 of spectra at up to 400 kHz. An eighth and final laser system, a tunable Coherent Chameleon laser, produced broadband laser light at 811 nm which was spectrally resolved using a 3-meter spectrometer to capture the first excited state of argon. All lasers passed through a Stanford reflected shock tube 5 mm away from the endwall, minimizing non-ideal shock tube effects encountered at high temperatures.
Results
Time histories were successfully collected in over 120 experiments, a subset of which will be presented. NO(A) measurements showed the rapid evolution of the number density in time, capturing the rise, peak, and decay of the population. N2(A) was observed to have a similar rise time in air mixtures where both NO(A) and N2(A) were present, forming much faster than in N2-Ar mixtures. N2(A) was always observed with a much slower decay than the NO(A) population, likely due to the much more rapid dissociation of NO than N2. N2+ exhibited a very slow formation and removal time, lasting much longer than either NO(A) or N2(A). Neighboring atomic states were observed to be in near-equilibrium with each other, with high-lying and strongly radiating states being relatively depleted over low-lying states with no strong radiation pathways. Electrons were observed to form on the atomic excitation timescale.

Conclusion
This new expansive dataset will enable the validation and improvement of collisional-radiative models for the excitation and ionization of air through a collaboration with the University of Colorado Boulder.

Speaker: Devin Merrell (Stanford University)

RHTG_abstract.pdf

10:30 → 11:00 Coffee Break at the Palazzo Roberti Courtyard

Piazza XX Settembre, 60-62, 70042 Mola di Bari BA
https://maps.app.goo.gl/hwoVgZsAzCMpJNwZ6

11:00 → 12:00 Plasma facilities, simulations and diagnostics: Tuesday morning 2

11:00 Measuring the surface accommodation of molecular hypersonic plasmas

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.

Speaker: Gilles Courret (HEIG-VD)

figure_4.png

11:30 A generalized gas–surface interaction boundary condition unifying finite-rate surface chemistry and catalytic recombination in CFD++

Background of the study

During atmospheric entry, the interaction of the dissociated, thermochemically non-equilibrium boundary-layer gas with the vehicle surface strongly influences the wall composition, the surface heat flux, and both the convective and radiative heating experienced by the thermal protection system (TPS). Surface catalycity governs the recombination of atomic species such as $N$ and $O$ and, in the fully catalytic limit, can increase the wall heat flux several-fold relative to a non-catalytic surface. Historically, computational tools have treated gas–surface interaction (GSI) with two largely disjoint families of models: phenomenological catalytic-wall models based on specified reaction efficiencies (the $\gamma$ model, or specified-reaction-efficiency1, SRE, models), and detailed finite-rate surface chemistry (FRSC) models that resolve adsorption, desorption, Eley–Rideal and Langmuir–Hinshelwood steps, sublimation and ablation. In many production solvers these families are implemented independently, and even inconsistently across different wall boundary conditions (isothermal, adiabatic, radiative-equilibrium), leading to duplicated logic, divergent physics between wall types, and no clean pathway from a simple catalytic wall to a fully finite-rate mechanism. The present work removes this artificial separation by developing a single, general boundary-condition model that treats catalytic recombination and finite-rate surface chemistry as limiting cases of one unified formulation, implemented in the CFD++ solver [1].

Methodology

Both model families are recast within a common surface mass balance (SMB) framework following Marschall and MacLean [2,3]. At the gas–solid interface the wall composition is obtained by balancing the diffusive and convective species fluxes against the net surface chemical production:

\begin{equation}
\mathbf{J}_i\cdot\mathbf{n} + \rho v\, y_i = \dot{w}_i, \qquad \rho v = \sum_i \dot{w}_i = \dot{m} \tag{1}
\end{equation}

where $\mathbf{J}_i$ is the (corrected Fickian) diffusion flux, $y_i$ the wall mass fraction, $v$ the blowing velocity set by the net mass rate $\dot{m}$, and $\dot{w}_i$ the surface source term. Adsorbed (surface-phase) species are closed by their own coverage balance together with a site-conservation constraint, while bulk-phase species account for ablation and deposition. The gas mass fractions (or partial densities), surface coverages, and blowing velocity are solved simultaneously with a fully coupled Newton method using analytically derived Jacobians.

The unification relies on expressing every GSI process as a reaction contributing to the species chemistry source term $\dot{w}_i$. The FRSC model involves reactions using the mass-action law, whereas the catalytic reactions based on the SRE model use a rate model based on the first-order Knudsen–Langmuir flux, with an optional Motz–Wise correction. Because both reaction types contribute to $\dot{w}_i$ through the same net-stoichiometry operator, surface mechanisms of arbitrary complexity are handled by a single solver invoked identically from every wall boundary condition. The SRE model is thereby recovered as the macroscopic, steady-state limit of the finite-rate adsorption and recombination kinetics. A further contribution is a generalized evaluation of the backward-rate coefficients, in which the equilibrium constants are reconstructed by combining gas-phase thermodynamic properties with adsorption and sublimation rate data. This removes the need for the (generally unavailable) thermodynamic data of surface- and bulk-phase species and eliminates reaction-specific hard-coded expressions, so that arbitrary reaction types can be treated within the same framework. The formulation also supports partially ionized boundary layers: ion–wall recombination reactions of the form $X^+ + e^- \rightarrow X$ are solved together with the neutral surface chemistry, while the electron mass fraction is obtained from a charge quasi-neutrality condition rather than from a separate wall balance.

Results

The non-equilibrium reactive boundary-condition framework has been verified on a graphite sphere-cone model in a high-enthalpy (about $27$ MJ/kg) arc-jet air flow, reproducing the stagnation heat flux and pressure and the coupled surface response, with the predicted heating lying between the non-catalytic and fully catalytic limits. The unified catalytic capability is verified against the legacy SRE model walls: for homonuclear recombination ($2N \rightarrow N_2$, $2O \rightarrow O_2$) the SMB solver reproduces the reaction-limited Knudsen–Langmuir flux to Newton-solver tolerance, and the generalized backward-rate formulation recovers the same equilibrium as the original Zhluktov–Abe treatment [4] while extending it to arbitrary reaction types. Representative entry-relevant catalytic and multi-reaction cases will be presented to demonstrate the consistency and generality of the model across the different wall boundary-condition types and its impact on the predicted near-wall composition and surface heating.

Conclusion

A single generalized boundary-condition model has been developed that unifies phenomenological catalytic recombination and detailed finite-rate surface chemistry within one surface mass balance formulation, solved by a coupled Newton method with analytical Jacobians in CFD++. By expressing the SRE catalytic model as a limiting reaction type of the finite-rate framework, and by generalizing the backward-rate computation to avoid surface- and bulk-phase thermodynamic data, the model delivers consistent, extensible, and thermodynamically sound GSI predictions across all wall boundary conditions. The framework also broadens the catalytic modeling capability already available in CFD++: whereas the earlier catalytic wall was designed around a predefined set of recombination reactions, the unified formulation allows surface mechanisms to be specified freely, and it further improves the consistency of the species-diffusion treatment at the wall. This unified surface treatment enables the accurate prediction of near-wall composition and surface heating in non-equilibrium entry environments, and provides a modular basis for incorporating new catalytic and ablative mechanisms. The framework has furthermore been designed with future coupling to a material-response code in mind.

References

[1] Lopez, B., "Finite-Rate Surface Chemistry Modeling for High-Temperature Gas–Surface Interactions in CFD++," AIAA SciTech Forum, 2026.

[2] Marschall, J., and MacLean, M., "Finite-Rate Surface Chemistry Model, I: Formulation and Reaction System Examples," AIAA Paper 2011-3783, 42nd AIAA Thermophysics Conference, Honolulu, HI, 2011.

[3] MacLean, M., Marschall, J., and Driver, D. M., "Finite-Rate Surface Chemistry Model, II: Coupling to Viscous Navier–Stokes Code," AIAA Paper 2011-3784, 42nd AIAA Thermophysics Conference, Honolulu, HI, 2011.

[4] Zhluktov, S. V., and Abe, T., "Viscous Shock-Layer Simulation of Airflow past Ablating Blunt Body with Carbon Surface," Journal of Thermophysics and Heat Transfer, Vol. 13, No. 1, 1999, pp. 50–59.

Speaker: Dr Bruno Lopez (Metacomp Technologies Inc.)

12:00 → 14:00 Lunch

Participants are asked to arrange their own lunch and return 10 minutes prior to the start of the session

14:00 → 15:30 Radiation modeling and simulation: Tuesday afternoon 1

14:00 Sensitivity Analysis of Reaction Rate Uncertainties on Radiation in H2/He Ice Giant Entry Flows

During high-speed atmospheric reentry, radiation can make up to 20% of peak heating, as demonstrated by the Electric Arc Shock Tube (EAST) at the Ames Research Center. This means that thermal protection design requires accurate radiation modeling during reentry. This subject is of particular interest at the moment because both NASA [10, 9] and ESA [14] are considering missions that would enter the atmospheres of Ice Giants, where this effect would be significant [4]. However, the chemical reaction rates and pathways relevant to reentry in these atmospheres remain highly uncertain.

There is an ongoing effort to improve radiation modeling; work by Colonna et al. [5] and Carroll et al. [3] propose models that replicate experimental data reasonably well using two different sets of species and reactions, achieved by tuning reaction rates within their uncertainties. This highlights the need for a more systematic calibration approach. More recently, Ninni et al. [11] and Colonna et al. [6], present a new macroscopic model. In this model, the electronic energy levels are resolved, but not the vibrational ones, which are instead represented by a vibrational temperature. This model shows good agreement with the full State-to-State (StS) approach, suggesting that reduced-order models are a viable path forward.

A further distinction between models lies in how they treat radiation. Colonna et al. compare optically thick and optically thin plasma assumptions, while Carroll et al. perform a detailed a posteriori computation of radiation, assuming a quasi-steady state. By contrast, both Coelho and da Silva [4] and Sahai and Johnston [12] present approaches that fully couple to the radiative transfer to CFD. This has been considered necessary for Entry, Descent and Landing (EDL)
missions since 1968 [8].

Rather than proposing a new kinetic-radiative model, this work adopts an existing model and focuses on the systematic calibration of chemical reaction rates, with the sensitivity analysis presented here as the first step toward that goal. The forward model for Ice Giant reentry was constructed using three established software packages: the VKI Shocking code (1D inviscid post-shock relaxation) [1], the VKI Mutation++ library [13], and NASA Ames NEQAIR [2], which handle the fluid, thermochemical, and radiative aspects, respectively. The model includes 9 species (e−, H, H+, H−, H2, H2+ , H3+ , He, He+), StS modeling of H(n=1-10), and 119 reactions, making it broadly comparable to the model by Colonna et al. [5] but with fewer internal states. The sensitivity analysis of the effect of reaction rates on radiation was performed using a range of Quantities of Interest (QoIs) varying in both emission wavelength (Balmer α, β, γ and θ spectral lines) and position after the shock (1-2 cm, 2-3 cm, and 3-4 cm), revealing that H2 dissociation reactions and electron-impact excitation reactions have the greatest impact on the QoIs.

In the future, the forward model will be compared to experimental results from the EAST facility. EAST has had several campaigns at 89:11% volume H2:He [7] corresponding to the Uranus atmosphere, at speeds higher than 25 km/s. Using an Uncertainty Quantification framework, this will allow for the systematic calibration of the reaction rates.

[1] S. Boccelli, F. Bariselli, B. Dias, and T. E. Magin. Lagrangian diffusive
reactor for detailed thermochemical computations of plasma flows. Plasma
Sources Science and Technology, 28(6):065002, 2019.
[2] A. M. Brandis and B. A. Cruden. NEQAIR v15.0 release notes: Nonequilib-
rium and equilibrium radiative transport and spectra program. Technical
report, NASA Ames Research Center, Moffett Field, CA, 2019.
[3] A. T. Carroll, G. Blanquart, A. M. Brandis, and B. A. Cruden. State-
specific kinetic modeling for predictions of radiative heating in H2/He entry
flows. In AIAA SciTech 2024 Forum, Orlando, FL, 2024.
[4] J. Coelho and M. Lino da Silva. Aerothermodynamic analysis of Nep-
tune ballistic entry and aerocapture flows. Advances in Space Research,
71(8):3408–3432, 2023.
[5] G. Colonna, L. D. Pietanza, and A. Laricchiuta. Ionization kinetic model
for hydrogen-helium atmospheres in hypersonic shock tubes. International
Journal of Heat and Mass Transfer, 156:119916, 2020.
[6] G. Colonna, L. Walpot, D. Ninni, F. Bonelli, G. Pascazio, L. D. Pietanza,
and A. Laricchiuta. Multi-temperature model from state-specific data for
Hydrogen/Helium mixture in high-enthalpy flows. International Journal of
Heat and Mass Transfer, 259:128376, 2026.
[7] B. A. Cruden and D. W. Bogdanoff. Shock radiation tests for saturn and
uranus entry probes. In AIAA Aviation 2015 Forum, Dallas, TX, 2015.
[8] H. Hoshizaki and L. E. Lasher. Convective and radiative heat transfer to
an ablating body. AIAA Journal, 6(8):1441–1449, 1968.
[9] National Academies of Sciences, Engineering, and Medicine. Origins,
Worlds, and Life: A Decadal Strategy for Planetary Science and Astro-
biology 2023–2032. National Academies Press, Washington, D.C., 2023.
[10] National Research Council. Vision and Voyages for Planetary Science in
the Decade 2013–2022. National Academies Press, Washington, D.C., 2011.
[11] D. Ninni, F. Bonelli, G. Colonna, A. Laricchiuta, and G. Pascazio. Assess-
ment of hybrid macroscopic/State-to-State model for numerical simulation
of Ice Giant orbit insertion. International Journal of Heat and Mass Trans-
fer, 249:127188, 2025.
[12] A. Sahai and C. O. Johnston. On computationally efficient radiative trans-
fer calculations for three-dimensional entry problems. In AIAA SciTech
2023 Forum, National Harbor, MD, 2023.
[13] J. B. Scoggins, V. Leroy, G. Bellas-Chatzigeorgis, B. Dias, and T. E. Magin.
Mutation++: MUlticomponent thermodynamic and transport properties
for ionized gases in C++. SoftwareX, 12:100575, 2020.
[14] Voyage 2050 Senior Committee. Voyage 2050: Final recommendations
from the voyage 2050 senior committee. Technical report, European Space
Agency, 2021.

Speaker: Julien Clotuche (Université de Liège)

14:30 Characterization of Spectral Radiance Uncertainties for Ice Giant Entry Simulations and Experiments

Background
The 2023 Planetary Science Decadal Survey has deemed a mission to the Ice Giant planets a high priority for the next NASA Flagship Mission.$^1$ In order to safely enter hydrogen-helium-methane (H$_2$/He/CH$_4$) atmospheres that are characteristic of the Ice Giants, it is important to accurately characterize the aerothermal environment around the entry vehicle to predict quantities like convective and radiative heating, which will drive the design of the thermal protection system (TPS). Computational modeling tools are used to simulate the chemical kinetics in the nonequilibrium region of the flow between the shock and the surface of the TPS. It is desirable to validate computational models with experimental data, which typically comes from shock tube and expansion tunnel facilities that generate relevant aerothermodynamic quantities, like emission spectra. There are challenges associated with generating this data, such as difficulty obtaining high enough speeds to represent an Ice Giant entry trajectory and shock position uncertainty.$^2$ Because of these challenges as well as uncertainties in existing chemical kinetics models, previous studies have identified challenges with validating computational models of Ice Giant entry systems with experimental data.$^3$

The current study aims to investigate the existing gap between simulations and experiments for predicting spectral radiance in H$_2$/He/CH$_4$ systems with an uncertainty quantification (UQ) analysis that includes the uncertainties in both the chemical kinetics models implemented in simulations and in experimental measurements. This mixed uncertainty quantification analysis is a useful tool to determine the sensitivities of key quantities of interest (QoIs). The QoI in the present study is spectral radiance, which is measured experimentally and has implications for the radiative heating the vehicle will experience upon hypersonic entry. Initial results with the mixed UQ framework show large variations in spectral radiance predictions based on current uncertainty bounds,$^4$ calling for the need for a detailed rate assessment to determine the best uncertainty bounds to use in the mixed UQ analysis. The presentation will include a detailed assessment of the chemical kinetic rate model and uncertainty bounds associated with each rate, which will be implemented into the mixed UQ framework. Results will be shown from the mixed UQ framework with the updated rates and uncertainty bounds applied to a range of experimental conditions.

Methodology
The computational model used in the present work is a general-purpose nonequilibrium chemical kinetics solver called the Toolkit for Excitation, Reactions, and Radiation with Applications (TERRA) with NASA's radiation solver, NEQAIR. One-dimensional incident shock simulations are generated, and the resulting position, temperatures (translational-rotational and vibrational-electronic), and species number densities for a 12-species H$_2$/He/CH$_4$ model are passed into NEQAIR as a line-of-sight, which is then used to compute radiance and spectral radiance. This enables direct comparison to the experimental datasets, which come from the T6 Stalker Tunnel at the University of Oxford$^5$ and the Electric Arc Shock Tube (EAST) facility at NASA Ames Research Center.$^6$

The two main categories of uncertainty in numerical modeling are aleatory uncertainty, which is due to the randomness of uncontrollable factors like instrument noise, and epistemic uncertainty, which is due to an inadequate understanding of the physics model that is represented in the numerical tool. Both aleatory and epistemic uncertainties are propagated through the model simultaneously, though they are treated separately. The mixed UQ problem is set up in a nested loop such that the outer loop varies the epistemic uncertain parameters, which are the chemical kinetic rate parameters, and the inner loop varies the aleatory uncertain parameters, which are the freestream conditions from the experiments. The mixed UQ analysis is driven by UQLab, by which a polynomial chaos expansion (PCE) and Sobol’ indices are computed.$^7$ The PCE is computed using the Ordinary Least Squares (OLS) regression method to form a surrogate model of the system. Sobol’ indices are computed from the PCE coefficients, and are a useful metric for quantifying how much the uncertainty in an input parameter affects the prediction of a QoI, which in this study is spectral radiance.

Results
The mixed UQ framework is first applied to an experimental condition from the T6 Stalker Tunnel operating in shock tube mode with a velocity of 16.3 km/s, a pressure of 13.0 Pa, and a test gas composition by volume of 80% H$_2$/15% He/5% CH$_4$, then to another experimental condition with a velocity of 16.4 km/s, a pressure of 12.8 Pa, and a test gas composition by volume of 84.5% H$_2$/15% He/0.5% CH$_4$.$^5$ Sobol' indices are computed for the QoIs integrated spectral radiance within the wavelength range of interest from 350 - 570 nm and spectral radiance at the peaks of major spectral features, which are found around 430 nm, 468 nm, and 514 nm. These spectral features are mostly caused by the CH(A-X) radiation band, C$_2$ Swan band, atomic lines for neutral and atomic carbon, and the Balmer series for atomic hydrogen.

It is found that the Sobol' index contributions, and therefore uncertainty in spectral radiance predictions, are dominated by the CH$_3$ dissociation process that forms CH, followed by the H$_2$ dissociation process. Since CH is one of the strongest radiators in this system, and the Balmer series for atomic hydrogen also contributes to spectral features within the wavelength range of interest, it is expected that the processes that form these species would contribute most to uncertainty in spectral radiance. The spectral features that are caused by the C$_2$ Swan band also show high sensitivities to the only process that forms C$_2$ in the system, which is the CH-C exchange reaction. The sensitivities of spectral radiance are similar between the 5% methane condition and 0.5% methane condition, however, the contributions of the H$_2$ dissociation processes have higher Sobol' indices for the 0.5% methane condition than for the 5% methane condition. Although the contribution of H$_2$ dissociation is higher for the lower methane condition, the uncertainty in spectral radiance is still overall dominated by CH$_3$ dissociation, indicating that this is a key contributor to the discrepancy in spectral radiance predictions between simulations and experiments.

The presentation will show results of the mixed UQ framework applied to higher-velocity conditions from the EAST facility,$^6$ which are likely more representative of an Ice Giant entry trajectory. Comparisons of key sensitivities from the different facilities and conditions will be presented.

Conclusions
The mixed UQ framework is a powerful tool that can be used to identify the uncertain parameters that contribute most to uncertainty in spectral radiance predictions from a nonequilibrium chemical kinetics solver plus radiation solver that causes discrepancies in comparisons with experimental data. Future work includes reducing the uncertainty bounds on the largest contributors to spectral radiance uncertainty through a Bayesian inference analysis. This framework can be applied to different experimental datasets across different facilities, and can be used to identify which data is suitable for Bayesian inference and which is limited by experimental uncertainty. The framework can also be used to identify critical facility uncertainties that may limit the utility of the existing data. In general, this study investigates the existing gap between simulations and experiments for Ice Giant entry systems.

References

[1] “Origins, Worlds, and Life 2023”. In: National Academies Press (Oct. 2023).
[2] Alex T. Carroll et al. “State-Specific Kinetic Modeling for Predictions of Radiative Heating in H2/He Entry Flows”. In:AIAA SciTech 2024 Forum. American Institute of Aeronautics and Astronautics, Jan. 2024.
[3] Kaelan Hansson et al. “Analysis of Chemical Kinetic Parameters for Hydrogen Atmospheres”. In: AIAA SciTech 2021 Forum. American Institute of Aeronautics and Astronautics, Jan. 2021.
[4] Cate Leszcz, Timothy T. Aiken, and Iain D. Boyd. “Mixed Uncertainty Quantification for Hypersonic Entry into Hydrogen-Helium Atmospheres”. In: AIAA Aviation 2026 Forum. American Institute of Aeronautics and Astronautics, June 2026.
[5] Joseph Steer et al. “Commissioning of Upgrades to T6 to Study Giant Planet Entry”. In: Journal of Spacecraft and Rockets 61.6 (Nov. 2024), pp. 1545–1562. issn: 0022-4650.
[6] Brett A. Cruden and David W. Bogdanoff. “Shock Radiation Tests for Saturn and Uranus Entry Probes”. en. In: Journal of Spacecraft and Rockets 54.6 (Nov. 2017), pp. 1246–1257. issn: 0022-4650, 1533-6794.

Speaker: Cate Leszcz (University of Colorado Boulder)

Leszcz_RHTG_2026.pdf

15:00 Shock-Layer Radiation Uncertainty for a Uranus Probe

Introduction
The 2023 Decadal Survey [1], published by the National Academies of Sciences, Engineering, and Medicine, concluded that "The highest priority new Flagship mission for the decade 2023–2032 is the Uranus Orbiter and Probe mission". Part of the Uranus Orbiter and Probe (UOP) mission [2] that was used to inform the Decadal study was an entry probe to make scientific measurements of the Uranus atmosphere. A detailed investigation of the entry environments and uncertainties is needed for designing a reliable thermal protection system (TPS) in support of the development of such a probe.

The primarily H$_2$/He upper atmosphere of Uranus poses unique challenges not present for atmospheric entry into Earth or Mars. Most notably, the lack of oxygen removes oxidation as a mechanism for thermochemical ablation of the heatsheild. Entry into the N$_2$/CH$_4$ atmosphere of Titan is similar, but the entry conditions and heating environments are significantly less extreme than those expected when entering any of the Outer Planets. Unfortunately, there has only been one past entry into a primarily H$_2$/He environment, which was the Galileo probe that entered into Jupiter in 1995. However, the entry environments experienced by the Galileo probe were so extreme that lessons learned do not translate well to much lower energy entry conditions expected for a Uranus probe.

There have been limited studies of aeroheating environments or uncertainties of Uranus probes. Work by Tauber et al.[3] investigated the TPS requirements for a probe, similar to the Galileo probe configuration, entering Uranus at 22 and 26 km/s. Palmer et al.[4] investigated the aeroheating environment uncertainties on the same Galileo probe geometry entering Uranus at 22.3 km/s. Neither study considered the probe backshell; both only investigated forebody heating. Also, neither of these two past studies investigated the impact of atmospheric CH$_4$ on radiative heating. %Important lessons from these previous works were leveraged to inform the present study. Most notably, the work by Palmer et al. recommended a coupled flowfield/material response analysis for future work due to the strong contribution of catalytic heating.

The objective of this study is to investigate the radiative heating environments and uncertainties on a Uranus probe. Like the previous studies, the configuration of interest is the Galileo probe [5]. The most recent decadal survey entry conditions are investigated with varying amounts of CH$_4$ in the atmosphere.[2] The entry interface speed of this particular reference mission is about 19 km/s, which is far below previous investigations. Higher energy entry conditions are also explored here to quantify the radiative heating uncertainties should a higher speed entry be realized for a future mission. Radiative heating on both the forebody and backshell of the probe are investigated.

Approach
A coupled flowfield-radiation-material response approach is used to accurately model the flow physics around the probe. The flow field was modeled using the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) software, which is a finite-volume, Navier-Stokes flow solver. LAURA uses a second-order, upwind, discretization scheme with Roe's flux-difference splitting and Yee's Symmetric Total Variation Diminishing (STVD) formulation of the inviscid flux. The gas properties were modeled with a thermochemical nonequilibrium assumption using the two temperature model. Freestream composition was assumed to nominally be 85% H$_2$ and 15% He by volume. The volume fraction of CH$_4$ was increased to as much as 1% and replaced a proportional amount of H$_2$. The coupled radiation and ablation flow field was modeled using a 29 species model that included pyrolysis and char species from the thermal protection system.

Shock-layer radiation was modeled using the High-Temperature Aerothermodynamic Radiation (HARA) code. HARA uses atomic levels and lines obtained from the National Institute of Standards and Technology (NIST) database, Opacity Project databases, and atomic bound-free (photoionization) cross-sections from TOPbase. Radiation mechanisms considered include atomic line emission from H and C, and bands from the H$_2$, CH, C$_2$H, C$_2$H$_2$, C$_2$, C$_3$, CN, and CO molecules. Coupled radiation was modeled in the flowfield energy equations. A ray-tracing approach was applied for computing the radiative heating at the wall, while the tangent-slab approach was used to compute the divergence of the radiative flux. Previous work has shown this coupling strategy is sufficiently accurate for flowfield-radiation coupling.

A one-dimensional material response solver built into LAURA was used to model ablation and pyrolysis of the wall. This material response model was used to determine the energy transfer into a phenolic impregnated carbon ablator (PICA) TPS. The flow solver and the material response model are connected through a surface energy balance and a surface elemental mass balance. A finite rate surface chemistry modeling approach was used. The surface chemistry rate model included surface oxidation, carbonous sublimation, nitridation, and catalytic recombination of N$_2$ and H$_2$.

To investigate the impact of parametric uncertainties in the flowfield and radiation models, an efficient variant of the point-collocation non-intrusive polynomial chaos surrogate method was employed. This approach involved an iterative process to compute the non-zero terms of the underlying polynomial chaos model using only enough evaluations of the flowfield model to converge uncertainty interval predictions and Sobol index values based global nonlinear sensitivity estimates. This strategy enables evaluating hundreds of model parameters with minimal computational expense.

Results
Results from this study show that, during entry along the decadal survey conditions, radiative heating was found to be insignificant on the probe forebody relative to convective heating. Even assuming a 1% by volume fraction of CH$_4$ in the freestream, radiative heating did not significantly increase the total heating on the forebody. However, on the backshell, radiative heating is a significant portion of the total heating across the trajectory. Radiative heating was found to be most sensitive to the production rate of H in the flow field. At the higher entry speeds considered in this study, radiation remains only a small portion of the total heating but becomes increasingly impactful as emission from H$_2$ and H lines increases in the higher temperature, post-shock flow. When CH$_4$ is present, contributions from the CH radical and C$_2$ Swan band further contribute to the total radiative heating around the entire probe. Key sensitivities to model parameters were found to be the production of these participating species, including H, CH, and C$_2$.

Conclusion
The results from this study highlight the relative impact of radiative heating for a probe entering the Uranus atmosphere. Sensitivities to entry conditions and the amount of CH$_4$ in the atmosphere indicated the potential impact of radiative heating across a wide range of entry conditions. While the amount of CH$_4$ in the upper Uranus atmosphere is uncertain, even a small amount can significantly increase the radiative heating an entry probe may experience. Additionally, key modeling uncertainties identified in this work can be used to inform future ground test campaigns to improve modeling capabilities and radiative heating predictions for a future mission.

Bibliography
[1] National Academies of Sciences, Engineering, and Medicine, “Origins, Worlds, and Life: A Decadal Strategy for Planetary Science and Astrobiology 2023-2032”, The National Academies Press, 2023, doi. 10.17226/26522.

[2] Simon, A., Nimmo, F. and Anderson, R., “Uranus Orbiter and Probe: Journey to an Ice Giants System”, National Aeronautics and Space Administration, 2021.

[3] Tauber, M., Wercinski, P., Henline, W., Paterson, J. and Yang, L., “Uranus and Neptune atmospheric-entry probe study”, Journal of Spacecraft and Rockets, Vol. 31, No. 5, pp.799-805, 1994, doi. 10.2514/3.26515.

[4] Palmer, G., Prabhu, D. and Cruden, B. A., “Aeroheating Uncertainties in Uranus and Saturn Entries by the Monte Carlo Method”, Journal of Spacecraft and Rockets, Vol. 51, No. 3, pp. 801-814, 2014, doi. 10.2514/1.A32768.

[5] Milos, F. S., “Galileo Probe Heat Shield Ablation Experiment”, Journal of Spacecraft and Rockets, Vol. 34, No. 6, pp. 705-713, 1997, doi. 10.2514/2.3293.

Speaker: Dr Thomas West (NASA)

15:30 → 16:00 Coffee Break at the Palazzo Roberti Courtyard

Piazza XX Settembre, 60-62, 70042 Mola di Bari BA
https://maps.app.goo.gl/hwoVgZsAzCMpJNwZ6

16:00 → 17:00 State to state and Collisional Radiative Modelling: Tuesday afternoon 2

Convener: Annarita Laricchiuta (CNR ISTP Bari)

16:00 Analysis of hypersonic neutral-air flows using a consistent multi-internal-temperature kinetic formulation

1. Background of the study

The renewed interest in space exploration has increased the need for accurate and affordable models of atmospheric-entry flows. During planetary entry, hypersonic vehicles travel at velocities of the order of 10 km/s, generating a detached bow shock and severe thermal loads on the surface. Reliable prediction of this aerothermodynamic environment is therefore essential for thermal protection system design [1].

Across the shock layer, kinetic energy is converted into internal energy, and temperatures may reach values of the order of 10 000 K. In this regime, vibrational excitation, dissociation, ionization, and communication blackout may occur. Since fluid-dynamic, relaxation, and chemical time scales become comparable, local thermodynamic and chemical equilibrium assumptions are generally not valid [2].

A common approach for thermochemical non-equilibrium is the two-temperature model, where translational and rotational modes are described by the gas temperature, while vibrational and electronic modes share a separate temperature [3]. Although efficient, this model relies on prescribed Boltzmann distributions and empirical relaxation laws, which may be inaccurate when vibrational populations strongly depart from equilibrium.

A more detailed alternative is the vibrationally resolved state-to-state approach, where molecular vibrational levels are treated as independent pseudo-species [4]. This avoids imposing a predefined internal distribution, but the resulting number of species and kinetic processes makes the method expensive for multidimensional simulations. Reduced-order models based on StS data, such as the multi-internal-temperature (MiT) approach considered here [5, 6], aim to retain the main kinetic features while reducing the computational cost.

2. Methodology

The flow is modeled in the continuum regime by solving the Euler equations for a reactive neutral air mixture composed of N$_2$, O$_2$, NO, N, and O. The formulation includes conservation of species mass, momentum, and total energy, with additional variables depending on the thermochemical model.

Two descriptions are considered. The StS model explicitly resolves the vibrational levels of N$_2$ and O$_2$, treating each level as a pseudo-species evolving through vibration–translation, vibration–vibration, dissociation–recombination, and exchange processes. This provides a detailed reference solution but requires a large kinetic mechanism.

The reduced MiT model groups the vibrational levels of N$_2$ and O$_2$ into a limited number of subsets. Each group is described by a local Boltzmann distribution at its own internal temperature. Mass and vibrational-energy source terms are obtained by averaging the StS rate coefficients over the levels in each group, so that the reduced model remains consistent with the detailed kinetics.

Different numbers of groups and grouping strategies are tested to assess the trade-off between accuracy and cost. In particular, strategies with increased resolution in the high-energy part of the vibrational distribution are considered, since these levels strongly affect dissociation.

The governing equations are solved using a cell-centered finite-volume method on structured grids. Inviscid fluxes are computed with the upwind flux-vector-splitting scheme of Steger and Warming, while MUSCL reconstruction with a limiter provides second-order spatial accuracy near shocks. Time integration is performed through operator splitting: a frozen-flow step advances the fluid dynamics explicitly, whereas a chemical step updates relaxation and reaction source terms implicitly. Reduced kinetic rates are precomputed and stored in look-up tables.

3. Results

The model is first assessed on 0D reactors of pure oxygen, pure nitrogen, and five-species air under high-temperature non-equilibrium conditions. For O$_2$ and N$_2$, the agreement between MiT and StS improves as the number of groups increases. The single-group model cannot properly describe the underpopulation of high vibrational levels, whereas multi-group formulations progressively recover this effect. The five-group model provides temperature and mass-fraction evolutions close to the StS reference.

The air reactor confirms the same trend. Translational temperature is well reproduced by the MiT models, while some discrepancies remain in the species evolution, mainly related to oxygen dissociation. Higher-energy groups relax more slowly than low-energy groups, showing that a single vibrational temperature is not sufficient to capture the internal non-equilibrium distribution.

The model is then applied to a two-dimensional inviscid axisymmetric hypersonic flow past a sphere, representative of the experiment by Nonaka et al. [7]. The StS model accurately predicts the shock stand-off distance, while MiT solutions approach the StS result as the number of groups increases. The one-group case behaves similarly to a classical Park-type formulation.

The grouping strategy also affects the solution. Assigning more levels to the high-energy portion of the distribution improves the agreement with StS, especially for the shock stand-off distance, because it provides a more appropriate description of vibrational energy redistribution. From the computational point of view, the MiT approach yields CPU speed-ups of the order of 10$^3$ with respect to the full StS model, while GPU simulations also show significant acceleration (3.9 · 10$^1$ − 2.21 · 10$^2$).

4. Conclusions

A consistent multi-internal-temperature model has been implemented for hypersonic flows in thermochemical non-equilibrium. The method reduces the complexity of state-to-state kinetics by grouping vibrational levels into Boltzmann-like subsets, while deriving source terms from the detailed kinetic database.

The results show that the MiT formulation offers a good compromise between accuracy and efficiency. Increasing the number of groups improves agreement with the StS reference solution in both homogeneous reactors and multidimensional hypersonic-flow simulations. Multi-group models capture the delayed equilibration of high-energy vibrational levels and its impact on dissociation and shock-layer structure.

Overall, the MiT approach substantially reduces computational cost while preserving the main physical features of detailed non-equilibrium kinetics. It therefore represents a promising tool for high-fidelity simulations of atmospheric-entry flows, with future extensions toward viscous flows, complex geometries, and gas–surface interactions.

References

[1] Peter A Gnoffo. Planetary-entry gas dynamics. Annual Review of Fluid Mechanics, 31(1):459–494, 1999.

[2] John D Anderson Jr. Hypersonic and high-temperature gas dynamics. American Institute of Aeronautics and Astronautics, 2006.

[3] Chul Park. Nonequilibrium hypersonic aerothermodynamics. John Wiley & Sons, 1989.

[4] G Colonna, F Bonelli, and G Pascazio. Impact of fundamental molecular kinetics on macroscopic properties of high-enthalpy flows: The case of hypersonic atmospheric entry. Physical Review Fluids, 4(3):033404, 2019.

[5] Aurélien Guy, Anne Bourdon, and Marie-Yvonne Perrin. Consistent multi-internal-temperatures models for nonequilibrium nozzle flows. Chemical Physics, 420:15 – 24, 2013.

[6] Francesco Bonelli, Davide Ninni, Antonio Narracci, Gianpiero Colonna, and Giuseppe Pascazio. Assessment of a consistent multi-internal-temperature kinetic model for hypersonic neutral air flows using a finite volume solver. Computers Fluids, 301:106796, 2025.

[7] Satoshi Nonaka, Hiroyasu Mizuno, Kazuyoshi Takayama, and Chul Park. Measurement of shock standoff distance for sphere in ballistic range. Journal of thermophysics and heat transfer, 14(2):225–229, 2000.

Speaker: Francesco Bonelli (Politecnico di Bari)

16:30 Modeling and Simulation of Thermochemical Nonequilibrium Flows during Titan Atmospheric Entry

Background of the study

The dense and stable atmosphere characterizing Titan [1], Saturn's largest moon, make it a celestial body of great interest for the scientific community, as it may give insights into the formation of life [2], also due to the presence of organic compounds, such as methane.
With the scheduled launch of the NASA mission Dragonfly [3], aiming to deliver a nuclear-powered octocopter on Titan's surface, it is now essential to properly analyze the critical phase of the atmospheric entry, estimated at approximately 6 km/s.

The criticality of crossing the atmosphere at such high velocities lies in the collision with its molecules that generates a strong shock wave on the capsule's forebody, influencing the body's aerodynamic behavior and heating. For this reason, specifically designed computational fluid dynamics (CFD) solvers are adopted to predict flow behavior and involved phenomena such as chemical reactions, ionization, radiation and wall catalysis and ablation [4].

Polytechnic of Bari, in collaboration with the Institute for Plasma Science and Technology (ISTP) of CNR in Bari, developed a finite-volume multi-GPU code, Damiso [5], to run hypersonic high enthalpy gas dynamic simulation. The code exploits the GPU inherent parallelizing capabilities to solve the Navier-Stokes equations and contemporarily take into account non-equilibrium phenomena by means of thermochemical models such as the Multi-Temperature or the State-to-State [6].
The difference between the two models lies in the description of the internal energy. In the Multi-Temperature model species internal energies are defined by means of statistical distributions driven by characteristic temperatures and are accounted for introducing additional energy transport equations [7]. The State-to-State, on the other hand, solves the internal states of the most relevant particles by treating them as pseudo-species and formulating a continuity equation for each of them [8]. The more accurate description obtained entails a higher computational cost, but becomes essential under marked non-equilibrium conditions.

Methodology

The code adopts a finite-volume approach. The solution is obtained by splitting time integration into two different steps: a first one solving the fluid dynamics and a second step, to account for the thermochemical non-equilibrium.
In the first step, the system of Navier Stokes equations is solved under the perfect gas assumption by means of a third-order accurate Runge-Kutta scheme [9]. Inviscid fluxes are discretized by means of a Steger and Warming flux vector splitting approach [10] and reconstructed with a second order MUSCL scheme [11], whereas viscous fluxes are solved with a second order cell-centered scheme.
The chemical step adopts the implicit Gauss-Seidel method [12] to account for non-equilibrium by evaluating mass loss or production of each species by means of the Arrhenius relation for the Multi-Temperature model or more complex analytical forms for the State-to-State model.
As regards wall catalysis, it is evaluated by means of the $\gamma$ model [13] by defining a recombination efficiency $\gamma_c$ which represents the ratio between recombining particles and particles impinging on the wall, in terms of mass fractions.

To demonstrate the reliability of the tool, the verification is performed reproducing a literature test case of a capsule atmospheric entry simulation by NASA [14].
Two different mixtures are implemented: a neutral 12-species mixture ($CH_4$, $CH_3$, $CH_2$, $N_2$, $C_2$, $H_2$, $CH$, $NH$, $CN$, $N$, $C$ and $H$) and an 18-species one (which also includes cherged particles as $N_2^+$, $CN^+$, $C^+$, $N^+$, $H^+$ and $e^-$) to evaluate ionization effects.

Two-dimensional simulations are performed adopting the flow conditions corresponding to an altitude of 269 km, which is related to the peak convective heating condition along the reference entry trajectory [14].
The freestream composition is made of molecular nitrogen $N_2$ for the 95% and methane $CH_4$ for the remaining 5% by volume.
Two different Multi-Temperature models are implemented, namely Park [15] and Nelson [16], and are compared with a developed simplified State-to-State model.

Given the high computational cost of a full StS model and the major presence of $N_2$ and $CN$ downstream of the bow shock, the adopted StS formulation only adopts a detailed description of internal vibrational
energy levels for those two molecules, whereas all the other molecular species are described using a single vibrational level (and atomic species have no vibrational mode at all).

Results

Code verification involves primarily the analysis of temperature along the stagnation line and wall heat flux.

The first step involves a comparison of reference data with results obtained using Park's model with the 18-species ionized mixture.
Given the good agreement of the results, the model is considered verified and used as benchmark to assess ionization effects comparing 18-species simulation with a 12-species neutral mixture simulation.

Once the effects of ionization on the flow have been characterized, the subsequent analyses use the 12-species mixture due to the significantly higher computational cost of the ionized mixture.

In this framework, Park's model is first compared with Nelson's model to assess the differences between the two formulations and then adopted to determine the effects of catalysis on the flow behavior by comparing simulations with a fully catalytic wall ($\gamma$ = 1) and with a non-catalytic wall ($\gamma$ = 0)

Finally, Park's results are compared with the outcome of a StS simulation, resulting in a moderate difference between the two models.

Conclusion

Hypersonic atmospheric entry remains a major challenge in aerospace aerodynamics, requiring continuous research and development efforts.

The developed code is compared to a literature case by NASA to verify the implemented Multi-Temperature models in the case of an atmospheric entry at Titan. The solver is also employed to evaluate ionization effects in the flow and the impact of wall catalysis on the shock wave and on the heat flux on the capsule wall. Finally, a State-to-State formulation is adopted and its results compared to those of the Multi-Temperature models

Results demonstrate a good reliability of the model in capturing the main features of the flow, whereas future work should focus on a further improvement of the thermochemical model, enhancing the implemented simplified State-to-State model.

References

[1] Nixon, C. A., “The Composition and Chemistry of Titan’s Atmosphere,” ACS Earth and Space Chemistry, Vol. 8, No. 3, 2024, p. 406–456. https://doi.org/10.1021/acsearthspacechem.2c00041.

[2] Niemann, H. B., Atreya, S. K., Demick, J. E., Gautier, D., Haberman, J. A., Harpold, D. N., Kasprzak, W. T., Lunine, J. I., Owen, T. C., and Raulin, F., “Composition of Titan’s lower atmosphere and simple surface volatiles as measured by the Cassini-Huygens probe gas chromatograph mass spectrometer experiment,” Journal of Geophysical Research: Planets, Vol. 115, No. E12, 2010. https://doi.org/10.1029/2010JE003659.

[3] Jet Propulsion Laboratory, “Solar System Exploration: This Is the 2006 Solar System Exploration Roadmap for NASA’s Science Mission Directorate,” Technical Report JPL D-35618, National Aeronautics and Space Administration, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, Sep. 2006.

[4] Anderson, J., Hypersonic and High-Temperature Gas Dynamics, 2nd ed., American Institute of Aeronautics and Astronautics, Reston, Virginia, 2006. https://doi.org/10.2514/4.861956.

[5] Pascazio, G., Ninni, D., Bonelli, F., and Colonna, G., “Hypersonic flows with detailed state-to-state kinetics using a GPU cluster,” Plasma Modeling: Methods and Applications, edited by G. D. Colonna, Institute of Physics Publishing, 2022, Chap. 10, 2nd ed. https://doi.org/10.1088/978-0-7503-3559-1ch10.

[6] Bonelli, F., Ninni, D., Narracci, A., Colonna, G., and Pascazio, G., “Assessment of a consistent multi-internal-temperature kinetic model for hypersonic neutral air flows using a finite volume solver,” Computers & Fluids, Vol. 301, 2025, p. 106796. https://doi.org/10.1016/j.compfluid.2025.106796.

[7] Park, C., Nonequilibrium Hypersonic Aerothermodynamics, John Wiley & Sons, New York, 1990.

[8] Capitelli, M., Armenise, I., Bruno, D., Cacciatore, M., Celiberto, R., Colonna, G., De Pascale, O., Diomede, P., Esposito, F., Gorse, C., Hassouni, K., Laricchiuta, A., Longo, S., Pagano, D., Pietanza, D., and Rutigliano, M., “Non-equilibrium plasma kinetics: a state-to-state approach,” Plasma Sources Science and Technology, Vol. 16, No. 1, 2007, p. S30. https://doi.org/10.1088/0963-0252/16/1/S03.

[9] Butcher, J. C., Numerical Methods for Ordinary Differential Equations, 2nd ed., John Wiley & Sons, 2008.

[10] Steger, J. L., and Warming, R., “Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods,” Journal of Computational Physics, Vol. 40, No. 2, 1981, pp. 263–293. https://doi.org/10.1016/0021-9991(81)90210-2.

[11] Van Leer, B., “Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method,” Journal of Computational Physics, Vol. 32, No. 1, 1979, pp. 101–136. https://doi.org/10.1016/0021-9991(79)90145-1.

[12] Verwer, J. G., “Gauss-Seidel Iteration for Stiff ODEs from Chemical Kinetics,” SIAM Journal on Scientific Computing, Vol. 15, No. 5, 1994, pp. 1243–1250. https://doi.org/10.1137/0915076.

[13] Goulard, R., “On catalytic recombination rates in hypersonic stagnation heat transfer,” Journal of Jet Propulsion, Vol. 28, No. 11, 1958, pp. 737–745. https://doi.org/10.2514/8.7444.

[14] Takashima, N., Hollis, B., Olejniczak, J., Wright, M., and Sutton, K., “Preliminary Aerothermodynamics of Titan Aerocapture Aeroshell,” 36th AIAA Thermophysics Conference, 2003, p. 4952. https://doi.org/10.2514/6.2003-4952.

[15] Park, C., “A review of reaction rates in high temperature air,” 24th Thermophysics Conference, American Institute of Aeronautics and Astronautics, Buffalo, NY, USA, 1989, p. 1740. https://doi.org/10.2514/6.1989-1740.

[16] Nelson, H. F., Park, C., and Whiting, E. E., “Titan atmospheric composition by hypervelocity shock-layer analysis,” Journal of Thermophysics and Heat Transfer, Vol. 5, No. 2, 1991, pp. 157–165. https://doi.org/10.2514/3.243.

Speaker: Antonio Narracci

17:30 → 19:00 Walking Tour of the Old Mola di Bari

meeting point TBD

Wednesday 23 September

09:00 → 10:30 State to state and Collisional Radiative Modelling: Wednesday morning 1

Convener: Gianpiero Colonna (CNR-ISTP Bari)

09:00 Comprehensive Validation of Electronic Excitation and Ionization Kinetics in Oxygen–Nitrogen–Argon Plasmas

Background

Recent years have seen a concerted effort to improve models of plasma formation in hypersonic flows. Validating these models has long been hampered by a lack of experimental data capable of characterizing ionization and its precursor processes -- electronic excitation in particular. Meeting this need requires shock tube experiments that probe the relevant species in suitable test gas mixtures with low detection limits, low measurement uncertainty, and high time resolution.

In previous works, the authors carried out experimental and modeling studies of electronic excitation and ionization in 1–2\% N$_2$–Ar$^,$ and 1\% O$_2$–Ar$^,$ mixtures. Measurements of atomic excited state number densities, together with electron number density in the O$_2$–Ar case, validated collisional-radiative models of these mixtures at a precision not previously achievable. A key limitation, however, was the narrow range of mixtures these studies could access: typically 98–99\% argon, a dilution needed to sustain the high temperatures required for detectable populations of the target electronic levels.

Two recent advances lift this constraint. The development of a ring amplified shock tube in the Hanson Research Group at Stanford University has increased the sensitivity of infrared laser absorption diagnostics by up to a hundredfold, opening a new generation of experiments at lower temperatures, where the heavy-particle excitation processes of greatest interest dominate, and in less dilute, more diverse mixtures. Alongside this gain, a suite of new diagnostics has come online, covering electronically excited states of O, N, Ar, N$_2$, and NO, as well as free electrons and the ground electronic level of N$_2^+$.

In this work, we present a detailed modeling study of data from a recent Stanford shock tube campaign spanning pure argon, O$_2$–Ar, N$_2$–Ar, and O$_2$–N$_2$–Ar mixtures at varying concentrations, with mixtures chosen to isolate key rate coefficients of interest to hypersonic flow modeling. In some of these experiments, time histories of as many as twelve parameters were measured simultaneously, offering an unprecedented opportunity to constrain and improve models of electronic excitation and ionization in shock-heated gases.

Methodology

Across the experimental campaign, number densities were measured for free electrons, N$_2^+$(X$^2\Sigma_g^+$), N$_2$(A$^3\Sigma_u^+$), NO(A$^2\Sigma^+$), the fourth through seventh electronic levels of atomic oxygen, the fourth, fifth, and eighth levels of atomic nitrogen, and the second and twelfth electronic levels of argon. Doppler broadening of several atomic lines yields the translational temperature, while Stark effects allow the free electron temperature and number density to be probed. The mixtures span pure argon, 1–30\% N$_2$ in Ar, 1–15\% O$_2$ in Ar, and several N$_2$–O$_2$ mixtures dilute in argon.

The experiments are simulated with the TERRA code at the University of Colorado Boulder using a recently developed three-temperature collisional-radiative (CR) model. Each simulation includes an enthalpy source term accounting for the non-ideal pressure rise measured in the experiment, following prior findings on the importance of such a term.

For each experiment, a sensitivity analysis is performed with more than 1,000 uncertain parameters, each with literature-informed uncertainty intervals. Sobol' indices and mutual information are computed at each data point; the latter incorporates the measurement uncertainty to quantify how much each measurement can reduce the uncertainty in a given rate parameter. Together, these analyses identify which parameters are active in shaping the measured time histories across all experiments and diagnostics, and reveal whether each measurement falls within the model's range of feasible predictions. A measurement that does not signals a clear need for model improvement, potentially through the inclusion of collisional processes not previously accounted for.

With the active parameter set established, the final step is a Bayesian inference of the most sensitive rate parameters using the same surrogates built for the sensitivity analysis. Here we focus on a limited set of experiments, with the goal of developing an inference framework that scales to the full dataset. The simplest mixture to probe is pure argon, followed by O$_2$–Ar and N$_2$–Ar, likely leveraging data from the literature or from previous test campaigns to constrain additional rates in the model, such as those for dissociation.

Results

Comparisons with the measured time histories are underway for the argon, O$_2$–Ar, N$_2$–Ar, and O$_2$–N$_2$–Ar data. In the O$_2$–N$_2$–Ar and O$_2$–Ar mixtures, predicted oxygen, argon, and nitrogen excited state number densities overshoot the measurements by up to a factor of three across much of the dataset. Predictions of N$_2$(A) and NO(A), by contrast, agree well with the measurements, except at very early times where the models overpredict the transient peak in these states.

Electron number density predictions in N$_2$–O$_2$–Ar likewise exceed the measurements, with charge exchange involving N$_2^+$ playing a major role in the overall ionization rate. The new N$_2^+$ measurements offer direct insight on this process, allowing models of charge exchange to be substantially improved and the electron number density data to be leveraged further for validating ionization reactions in hypersonic air flows.

Conclusion

The data recently gathered at Stanford offer an unprecedented opportunity to advance the state of the art in kinetic models of excitation and ionization behind strong shock waves. Through detailed comparison, sensitivity analysis, and Bayesian inference, we aim to exploit this extensive dataset to reduce the uncertainty in existing kinetic models for ionized hypersonic flows.

Speaker: Timothy Aiken (University of Colorado)

RHTG Abstract - MURI Final.pdf

09:30 Numerical Analysis of a Non-Equilibrium Gas with a Vibrational-State Specific Model -- Application to the Shock Layer past a Sphere Entering a Nitrogen Atmosphere

Key words
State-to-state modeling, hypersonic flow, aerothermodynamics, CFD.

Introduction
During the atmospheric entry of a spacecraft at hypervelocity, the gas in the shock layer goes through high temperatures and through various thermochemical non-equilibrium states. For decades, the scientific community has worked to better understand the behavior of excited species in non-equilibrium plasmas. In the widely used global chemical mechanism approaches -- among them the well-known models developed by Park -- the modeling consists in considering the chemical species as a whole without distinguishing their excited states. The population number density of their excited states is then estimated either by assuming a Boltzmann distribution at an excitation temperature or by assuming the quasi-steady state.
For the past recent years, another methodology has been developed based on a complete description of the flow field with considering every (or several) excited states of each particle as independent species. This approach is very attractive because of its expected accuracy in giving a detailed description of a plasma, but it is very challenging to implement in CFD codes.
In this framework, the present study is a contribution to the progressive work for computing a reactive and non-equilibrium gas flow through the shock layer surrounding an axi-symmetric blunt body entering a Nitrogen atmosphere, with detailed collisional-radiative models. The selected state-to-state model recently implemented in the in-house code PINENS (Parallel Implicit Non-Equilibrium Navier-Stokes) is a state-specific vibrational model, that is a simplified version of CoRaM-N$_2$, a collisional-radiative (CR) model developed for nitrogen [AnnaloroBultelOmaly-2014-JTHT]. This model takes into account the species N$_2$ and N, and is vibrationnally specific for the N$_2$ molecules on their ground electronic state. It allows to simulate the phase of ladder-climbing vibrational excitation and the resulting dissociation of N$_2$.
Two trajectory point for the entry of a simple axi-symmetric body -- a 1-m radius sphere -- are considered. The first point correspond to an altitude of 67 km, where the density of the atmosphere is $1.47 \cdot 10^{-4}$ kg /m$^3$, and the velocity of the sphere is 11.25 km/s. The second point correspond to a lower altitude of 37 km, where the density is $6.0 \cdot 10^{-3}$ kg /m$^3$, and the velocity of the sphere is 6.19 km/s.

Vibrational-state specific model and mathematical formulation
The vibrationally specific model used for the analysis of the non-equilibrium gas in the shock layer takes into account heavy, neutral particles. It considers each of the 68 vibrational states of N$_2$ ($0 \le v \le v_{max} = 67$) on the ground electronic state as well as the ground electronic state of N. According to the CoRaM-N$_2$ model that is used as the basis to derive the present vibrational-state specific model, the vibrational excitation of molecules N$_2$ takes place through vibration--translation processes under molecular impact (VT-m processes), through vibration--vibration processes under molecular impact (VV-m processes), or through vibration--translation processes under atomic impact (VT-a processes). It results 6817 forward collisional elementary processes. The data used for the rate coefficients for these processes were calculated by Armenise et al. and Esposito et al. The backward collisional elementary processes are calculated from the forward rate coefficient and the corresponding equilibrium constant using the detailed balance principle.
The equations to be solved are the usual Navier-Stokes equations, except that a mass conservation equation is written for each vibrational level of N$_2$(v) instead of one conservation equation of mass for N$_2$. As for the equation of vibrational energy of N$_2$ usually used in the global models (Landau-Teller, Millikan-White), it is no longer needed in the detailed model.
Each species $s$ on its excited state $v$ -- named "pseudo-species'' and noted $sv$ -- has a mass density $\rho_{sv}$ and the total mass density of the gas mixture is $\rho = \sum_{sv=1}^{n_{sv}} \rho_{sv}$. For an axi-symmetric flow, one then has to solve 72 equations: 69 conservation equations for the ``species-state'' N and N$_2$(v), two equations for the conservation of the momentum, and one equation for the conservation of the total energy. The set of conservative equations is closed with an adequate equation of state.

Results
For an atmosphere initially composed of 100% of N$_2$ on v=0 vibrational level and, according to the considered vibrational state-to-state model, the molecules N$_2$ on their zero-vibrational level collide, get excited, and -- depending on the type of collisions -- get dissociated across the shock wave. These collisional processes lead to a gas mixture composed of the two species N$_2$ and N, N$_2$ being on various vibrational levels depending on the excitation processes considered. The vibrational-state specific model -- split into several groups of reactions -- is implemented in PINENS code step-by-step in order to show the specific effect of each process group on the population densities of the 68 vibrational levels of N$_2$ and of the atomic species N, throughout the shock layer.

The first group of processes to be considered in the numerical simulations is the 67 (VT-m) processes; then the 4489 (VV-m) exchanges are added, then the single (VT-m-D) process, then the 67 (VV-m-D) processes, then the 2125 (VT-a) processes, and finally the 68 (VT-a-D) processes are added. For each group of processes added, the effect on the N$_2$(v) population densities is noticeable : the population of N$_2$(v=0) decreases to the profit of populating the other vibrational levels of N$_2$, and to the profit of producing N atoms when dissociation processes are considered. However, it has to be noted that the (VV-m) and (VV-m-D) processes generate no visible effect on the population densities except in the boundary layer area. Regarding the global behavior of the shock layer, the introduction of each group leads to reduce the temperature within the shock layer and to reduce the shock layer width. These results are observed for both entry velocities (V$_\infty$ = 11.25 and 6.19 km/s), but noticeable differences is observed on the shock standoff distance and on the flow temperature between the 2 cases.

The Boltzmann diagrams draw the densities of N$_2$(v) versus the energy of the vibrational levels expressed in eV. The Boltzmann distribution is reached when the curves representing the level populations (or mass fractions) -- expressed in logarithmic scale -- versus the energies of the levels -- expressed in linear scale -- are linear. The Boltzmann diagrams then obtained at various locations along the stagnation line across the shock layer, show that the curves are linear only outside the shock wave and outside the boundary layer, meaning that the Boltzmann distribution is reached only outside these zones. This is well known, but it is clearly shown with using the vibrational-state specific model. In some cases, however, when not all the processes are taken into account, the Boltzmann distribution is reached nowhere in the shock layer.

Preliminary conclusion
A vibrational-state specific model issued from the collisional radiative model CoRaM-N$_2$ implemented in the PINENS code is used for simulating the non-equilibrium flow past a sphere entering a Nitrogen atmosphere at 11.25 and 6.19 km/s. The main conclusion is that the vibration-vibration exchanges through molecular impact, leading or not to dissociation, have very little effect on the population densities. On the other hand, clear evidence is shown of the progressive effect of the vibration-translation exchanges through molecular and atomic impacts. The study also showed that the Boltzmann distribution is obtained only in specific positions in the shock layer. Obtaining such results in reasonable computational time showed that it is possible to predict the vibrational level population distributions throughout an axi-symmetric shock layer with a detailed kinetics model.

Acknowledgements
Centre de Calcul Intensif d’Aix-Marseille is acknowledged for granting access to its high performance computing resources.

Reference
[AnnaloroBultelOmaly-2014-JTHT]
Annaloro J., Bultel A., Omaly P. (2014)
``Collisional-Radiative Modeling Behind Shock Waves in Nitrogen'',
J. of Thermophysics and Heat Transfer, Vol.~28, No.~4, pp.~608-622.
doi: 10.2514/1.T4263.

Speaker: Dr Marie-Claude DRUGUET (Aix-Marseille University - CNRS UMR 7343 - IUSTI)

10:00 Assessment of the Quasi-Steady State approximation in a recombining Nitrogen / Argon plasma flow

1. Introduction

The radiative heat flux on a capsule during atmospheric re-entry represents a significant fraction of the total flux on the backshell, and depends on the population of the excited energy levels in the plasma around the capsule. This population does not follow a Boltzmann distribution due to non-equilibrium recombination in the afterbody region.
The Quasi-Steady State approximation has been used extensively to calculate this distribution of energy states, due to its lower computational cost. It consists in assuming that the production/depletion rates of excited species are far greater than their densities’ evolution over time, which can then be neglected. This means assuming that excited states adapt instantly to the changes in ground level densities, which are instead simulated.
In recent work, [Johnston and Panesi, 2018] showed that this hypothesis is not necessarily respected in all the flow field around the capsule. We test the validity of QSS for simulating the experiment ran by [Tibère-Inglesse et al., 2018] at the EM2C laboratory, on a nitrogen-argon plasma forced to recombine under nonequilibrium conditions at atmospheric pressure. We will use a State-to State collisional-radiative model for $N_2 / Ar$ developed as a vibronic-specific model by [Mariotto, 2023] and subsequently reduced to an electronic-specific model by [Dubuet, 2024].
The results show very good agreement between a full time-dependent simulation and the QSS approximation.

2. The Quasi-Steady State hypothesis

To use the QSS approximation, we must first simulate the 2D or 3D flow field, calculating its temperature and pressure, but only calculating the densities of the ground states for all chemical species with the appropriate time-dependent lagrangian master equation:

$\frac{dn_i}{dt} = S_{\text{kin}}(i) + S_{\text{rad}}(i) + {S}_{\text{diff}}(i)$

This accounts for the production / depletion of the specie through chemical reactions, radiative processes and diffusion. The densities of the specie $i$ depends then on the densities of all the other species included in the system.
We can then use the QSS hypothesis to calculate the densities of all excited states, which are necessary to estimate the radiative heat flux emitted towards the capsule. This turns all ordinary differential equations into algebraic equations, making the system significantly easier to solve. It only requires as inputs the temperature, pressure and densities of the ground states, which in our case of $N_2/Ar$ we took as:

$N ({}^4S), N^+({}^3P), N_2(X), N­_2^+(X), Ar({}^1S), e^-$

3. Methodology and results

A full time-dependent simulation of the condition of Tibère-Inglesse’s experiment was run as “benchmark”, with both the electronic and vibronic-specific model, and concentrations were compared to experimental data.
20 points along the plasma torch were then chosen to run a QSS simulation, using the ground state densities from the time-dependent simulation. The resulting excited states densities were compared and expressed as a percentage of the “benchmark” result, for a select set of species of interest. Another analysis was made to verify which are the levels that deviate further percentually from the benchmark.
The results for the electronic-specific model show a very good agreement between QSS and time-dependent simulations, with interest species predicted with 98% accuracy and all species within 95%. Another simulation was conducted with a more relaxed set of constraints that did not include ions $N^+, N_2^+$ and this showed larger discrepancies, especially for ionized species, of up to 8%.
The vibronic-specific model was also tested by only imposing the density of the first vibronic state for molecular species: $N_2(X, v=0), N­_2^+(X, v=0)$. The agreement for these results was worse, but still within an order of magnitude.

References

Dubuet, U., “Kinetics of a Nonequilibrium Recombining Air/Argon Plasma,” Theses. Université Paris-Saclay, 2024.

Mariotto, P., “Kinetics of Nonequilibrium Recombining Nitrogen-Argon Plasmas,” Paris-Saclay University, 2023. https://doi.org/10.5281/zenodo.18845333

Tibère-Inglesse, A., Mcguire, S., Mariotto, P., and Laux, C., “Validation Cases for Recombining Nitrogen and Air Plasmas,” Plasma Sources Science and Technology, Vol. 27, No. 11, 2018, p. 115010. https://doi.org/10.1088/1361-6595/aada61

Johnston, C. O., and Panesi, M., “Impact of State-Specific Flowfield Modeling on Atomic Nitrogen Radiation,” Physical Review Fluids, Vol. 3, No. 1, 2018, p. 013402. https://doi.org/10.1103/PhysRevFluids.3.013402

Dubuet, U., Mariotto, P., Laux, C. O., and Perrin, M.-Y., “Electronic-Specific Modeling of a Nonequilibrium Recombining N2/Ar Plasma and Comparison with Experiments,” Plasma Sources Science and Technology, Vol. 35, No. 4, 2026, p. 045007. https://doi.org/10.1088/1361-6595/ae50b5

Speaker: Marco Carpanese (Laboratoire EM2C, CNRS UPR-288, CentraleSupélec, Université Paris-Saclay and Università degli Studi di Padova)

10:30 → 11:00 Coffee Break at the Palazzo Roberti Courtyard

Piazza XX Settembre, 60-62, 70042 Mola di Bari BA
https://maps.app.goo.gl/hwoVgZsAzCMpJNwZ6

11:00 → 12:00 State to state and Collisional Radiative Modelling: Wednesday morning 2

Convener: Gianpiero Colonna (CNR-ISTP Bari)

11:00 Unpacking the Millikan and White Relaxation Fits

Hypersonic computational fluid dynamics (CFD) codes must account for chemical and thermodynamic changes in the flow that occur at timescales that are similar to the flow time. These include chemical reactions such as dissociation and ionization as well as thermal relaxation. The relaxation terms account for the finite time required to excite (usually vibrationally or electronically) the atoms and molecules in the flow. These two processes are modeled using two different parameterizations. In NASA codes for example, the chemical processes are modeled using modified Arrhenius reactions with detailed balance and the Park temperature model. Meanwhile, the relaxation processes are fit using a relaxation time parameterized by Landau and Teller and refit by Millikan and White (which added high temperature corrections from Park).
Modern CFD codes are slowly moving to new computational architectures generally characterized by the GPU. These are effectively large vector machines that gain performance by batching repetitive tasks into a single operation over a large array. This puts pressure on the software engineer to merge as many processes as possible into one general implementation. However, the physics as outlined above forces the software to calculate chemical source terms in two stages: the relaxation and then the chemistry.
This work begins with the relatively simple question of whether one can express the vibrational relaxation process as a chemical reaction. For example, consider a nitrogen molecule colliding with an atom. The reaction $$N_2 + N \leftrightarrow N_2 + N$$ clearly does not change the densities of either species. However, by evaluating the forward rate at one temperature and the backward at another, as is already typical for hypersonic codes, one can force an energy transfer to occur. Using some simple fitting one can arrive at reaction rate constants that capture the Millikan and White fits.
The reaction parameterization and the Millikan and White fits are different parameters and cannot result in the same average energy transfer at all combinations of translational and vibrational temperature. Notably, the reaction fit diverges from the Millikan and White fit at high translational and low vibrational temperature. At first glance, this suggests that using a reaction parameterization is impossible.
However, what has not been validated is the overall validity of the Millikan and White fit at these conditions. At present, state to state models and quantum chemistry solutions are available to calculate these reaction rates. Torres, for example, calculated vibrational relaxation times using the Direct Molecular Simulation (DMS) method. However, his results provide only an average value over vibrational temperature. Contours of instantaneous vibrational energy transfer rate as a function of translational and vibrational temperature are not available. In this work, QCT simulations of the N3 system are produced to compare against Millikan and White, a reaction parameterization, and the results of Torres.

Speaker: Kaelan Hansson (AMA Inc at NASA Ames)

11:30 Quintet A'' CNN PESs for CN Excitation Studies

Background

Titan's atmosphere is composed mostly of N$_2$ with small amounts of CH$_4$, and so, shock layers around craft entering Titan's atmosphere will contain a variety of molecules formed from H, C, and N atoms, including the cyanogen radical CN. Analysis has shown that the radiative heat flux predicted by computational fluid dynamics (CFD) simulations of Titan entry has up to 14\% uncertainty due to the rate coefficients for collisional (de)excitation reactions that control the population of CN in its excited states.[1]
\begin{equation}
\textrm{CN(X }^2\Sigma^+_g\textrm{) + M }\leftrightarrow \textrm{ CN(A }^2\Pi, B ^2\Sigma^+_g \textrm{) + M } \hspace{2cm} 1
\end{equation}

The red and violet emission bands from CN's first and second excited states, respectively, are known to be large sources of radiative heat flux on capsules entering Titan's atmosphere.[2,3] So, the simulated population of CN in its first and second excited states is very important, but, currently has some inherent uncertainty coming from the data for the rate coefficients for reaction 1.

The goal of the current work is to provide improved rate coefficient data for these reactions from first principles quantum chemistry calculations. To this end, we have calculated single point energies and state couplings for the CNN states that correspond to the ground and first excited states of CN by solving the Schr\"{o}dinger equation under the Born-Oppenheimer approximation. These energies were fit to functional forms to produce Potential Energy Surfaces (PESs). The PESs are made up of three pairwise diatomic terms, fit with physics based functions, and one three-body interaction term, fit using a parametrically managed neural network. Following the Compatibilization by Deep Neural Network (CDNN) approach of Meng et al, this neural network simultaneously discovers a diabatic basis and couplings for the states.[4] In such a diabatic basis, the state couplings are smooth and well behaved, and the adiabatic basis can be easily recovered if necessary. Nonadiabatic dynamics calculations using either basis can now be performed to determine the heavy particle (de)excitation rate coefficients at conditions relevant to shock layers around vehicles entering Titan's atmosphere.

Methodology

Electronic Structure Calculations
We use the electronic structure code MPEC to calculate ab initio single point energies using the Improved Internally Contracted Multi Reference Configuration Interaction with Single and Double excitations (i$^2$c-MRCI(SD)) method.[5] Such calculations require reference orbitals, which we generated using the Complete Active Space Self Consistent Field (CASSCF) method.

There are Quintet A'' and Triplet A'' manifolds for CNN that link the CN(X,A,B)+N($^4$S$_o$) states. Reference orbitals were generated for the lowest 24 states of both of these symmetries at a large number of geometries of the CNN system using CASSCF. In these calculations we used augmented-correlation-consistent-polarized-Valence-Triple-Zeta (aug-ccpVTZ) basis sets for each atom, and an active space consisting of 9 orbitals. The 1s and 2s orbitals for each atom were kept doubly occupied, and the remaining 8 electrons are distributed across the 9 active orbitals. The CASSCF reference orbitals were then used in i$^2$c-MRCI(SD) calculations, where excitations were allowed out of all 2s and 2p orbitals.

Functional Forms
The triatomic CNN energies were fit in a manner similar to Meng et al, where the three body potential is expressed as a sum of three pairwise additive terms, fit with physics-based functions as described in Ref. 6, and a three body interaction term fit with a deep neural network.[4]

Dynamics Simulations
Nonadiabatic dynamics calculations using the CN$_2$ surfaces described here are currently in progress. Both Tully's Fewest Switches Surface Hopping (FSSH) and the Coherent Switching with Decay of Mixing (CSDM) methods are being used to determine rate coefficients for reaction 1 and others.[7,8]

Results

While dynamics calculations are still in progress, the fit PESs already illustrate important features of the CNN system. For the lowest two Quintet A'' states there are more avoided crossings at lower energies for collinear geometries than for perpendicular bisector geometries. These features indicate that the heavy particle (de)excitation in reaction 1 is more likely to occur through collinear geometries because the states of interest are more closely coupled there.

Conclusions and Further Work

This work has produced ab initio PESs that describe the CNN complex and allow nonadiabatic dynamics simulations of CN (de)excitation by N atoms. Data from high-level electronic structure calculations were fit and diabatized with a parametrically managed neural network. The topology of these fits suggests that collisional (de)excitation of CN by N atoms is likely to proceed through collinear geometries. Thorough analysis of dynamics calculations will show the relative importance of different reaction pathways and determine improved rate coefficients that can be used in CFD simulations to lower uncertainties in radiative heat flux predictions for atmospheric entry to Titan.

References

1. Thomas K West IV et al. “Uncertainty analysis of radiative heating predictions for Titan entry”. In: Journal of Thermophysics and Heat Transfer 30.2 (2016), pp. 438–451.
2. Aaron M Brandis and Brett A Cruden. “Titan Atmospheric Entry Radiative Heating”. In: 47th AIAA Thermophysics Conference. 2017, p. 4534.
3. LM Walpot et al. “Convective and Radiative Heat Flux Prediction of Huygens’s Entry on Titan”. In: Journal of Thermophysics and Heat Transfer 20.4 (2006), pp. 663–671.
4. Qinghui Meng et al. “Automated Learning of a Dense Manifold of Electronic States and Electronic Energy Transfer and Reactions in Singlet O Collisions with N$_2$”. In: Research (2026), p. 0992.
5. David W Schwenke. “Introducing MPEC: Massively Parallel Electron Correlation”. In: The Journal of Chemical Physics 158.8 (2023).
6. Richard L Jaffe, David W Schwenke, and Marco Panesi. “Chapter 3: First Principles Calculation of Heavy Particle Rate Coefficients”. In: Hypersonic Nonequilibrium Flows: Fundamentals and Recent Advances. American Institute of Aeronautics and Astronautics, Inc., 2015.
7. John C Tully. “Molecular Dynamics with Electronic Transitions”. In: The Journal of Chemical Physics 93.2 (1990), pp. 1061–1071.
8. Chaoyuan Zhu et al. “Coherent Switching with Decay of Mixing: An Improved Treatment of Electronic Coherence for Non-Born–Oppenheimer Trajectories”. In: The Journal of Chemical Physics 121.16 (2004), pp. 7658–7670

Speaker: Eric Geistfeld (AMA Inc. @ NASA Ames Research Center)

12:00 → 14:00 Lunch

Participants are asked to arrange their own lunch and return 10 minutes prior to the start of the session

14:00 → 15:30 Radiation modeling and simulation: Wednesday afternoon 1

Convener: Christian Mundt

14:00 Spectral Model Reduction for Overlapping Radiative Systems during Hypersonic Entry

Objective
The radiation field arising from photophysical and photochemical processes can significantly influence energy transfer and thermochemical composition in a range of scientific and engineering applications. The primary challenge while determining radiative transfer stems from the rapid fluctuations in emission/absorption properties with respect to frequency. Fundamental radiative transitions, namely bound-bound, bound-free, and free-free, in atomic and molecular species involve photons with specific energies. The resultant spectral dependence of spontaneous/stimulated emission and absorption coefficients is resolved by a hierarchy of models that typically offer a trade-off between fidelity and concomitant costs. The line-by-line (LBL) approach [1] provides an exact representation of radiative properties by employing a finely discretized spectral grid comprising of potentially millions of frequency points. Since computational costs scale with the number of individual frequencies, an LBL spectral description combined with the necessary spatial-angular discretization often renders complex three-dimensional (3D) simulations practically unfeasible. Narrow-band models [2] represent a step towards improving efficiency by appropriately averaging radiative properties across a narrow spectral range. However, the degree of coarsening performed on the spectral grid is still inadequate for enabling cost-effective analysis, especially with flow-radiation coupling, for large-scale problems.

Methodology
The critical need to mitigate computational overheads has motivated the development of wide-band methods [2] that aggregate individual frequency points into fewer reduced-order groups. The transport equations governing group-wise radiative intensities are derived by integrating the monochromatic radiative transfer equations (RTE) over the frequency intervals contained within the group. While group-wise emission is simply a summation of frequency-wise contributions, formulating a closure for the group-averaged absorption coefficient necessitates knowledge of the unknown spectral intensity distribution. Previous work [3] by the author demonstrated that utilizing a simple Planck distribution for reconstructing the spectral intensity, often referred to as Planck-averaging, yields accurate results even for complex radiative problems owing to constrained entropy maximization. Furthermore, a newly proposed non-equilibrium grouping strategy, i.e., the rationale for dividing discrete frequency points into reduced-order groups, allowed both total quantities of interest as well as detailed spectral features to be predicted for different entry scenarios with up to two orders-of-magnitude speed-ups. Recent advances [4] have focused on evolving the requisite numerical framework for constructing independent reduced-order spectral databases. These databases inherently capture the physical dynamics of radiative transitions rather than relying on calibration against a constrained set of flow simulations. Consequently, such reduced-order models (ROMs) can be readily applied to a wide gamut of entry scenarios while maintain high levels of physical realism and computational efficiency. Another key challenge addressed in subsequent developments has been ensuring that ROMs can retain sufficient accuracy while tackling multiple radiative systems that overlap in the frequency domain. Modifications to the grouping methodology allows the interaction between disparate species to inform the model reduction while operating within the same numerical architecture designed for single-species ROMs.

Results
The current work provides a detailed overview of the new non-equilibrium model reduction paradigm that is aimed at being gas flow-agnostic, allows non-Boltzmann internal state populations, and effectively processes spectral interplay between disparate species. The efficacy of these ROMs has been evaluated using both 1D lines-of-sight calculations and predictions of 3D radiative heat flux to entry vehicles. The investigation initially considers non-interacting radiative systems (N, CN-C2, CO2-CO) before advancing to a comprehensive treatment of Earth entry radiation (involving spectral overlap between N, O, and N2). The ROM methodology consistently accelerates simulations by two to three orders-of-magnitude compared to full set predictions while reproducing both detailed frequency features and spectrally integrated total intensity/heat flux.

Bibliography
[1] J. M. Lamet, Y. Babou, P. Riviere, M. Y. Perrin and A. Soufiani, "Radiative transfer in gases under thermal and chemical nonequilibrium conditions: Application to earth atmospheric re-entry," Journal of Quantitative Spectroscopy and Radiative Transfer, pp. 235-244, 2008.
[2] M. F. Modest, Radiative heat transfer, Academic Press, 2013.
[3] A. Sahai, C. O. Johnston, B. Lopez and M. Panesi, "Comparative analysis of reduced-order spectral models and grouping strategies for non-equilibrium radiation," Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 242, 2020.
[4] A. Sahai and C. O. Johnston, "Generalized reduced-order spectral models for non-equilibrium radiative transfer in complex hypersonic entry environments," Journal of Quantitative Spectroscopy and Radiative Transfer (Under Review), 2026.

Speaker: Amal Sahai (AMA Inc. at NASA Ames Research Center)

RHTG2026_Abstract.pdf

14:30 HELIOSPARK: A modular CFD solver for thermochemical nonequilibrium hypersonic flows

Background

Hypersonic flows are characterized by strong thermochemical nonequilibrium and complex physical phenomena, making both experimental investigations and numerical simulations particularly challenging. Trustworthy and scalable computational tools are therefore essential for the study of atmospheric entry, hypersonic flight, and other high-enthalpy aerothermodynamic applications. SPARK [1] is a software package dedicated to high-enthalpy aerothermodynamics, providing computational tools for CFD and line-by-line radiation simulations.

Methodology

This work presents HelioSPARK (HelioS), a new high-enthalpy CFD solver written in C++ and developed within the AMReX framework [2]. The solver is designed for block-structured adaptive mesh refinement (AMR) and large-scale high-performance computing. HelioS solves the compressible multi-species Navier–Stokes equations, including conservation of mass, momentum, total energy, chemical species, and internal energy modes. Advective fluxes are computed explicitly using the Colella–Glaz approximate Riemann solver [3], while diffusive fluxes (viscous stresses, species diffusion, and heat conduction) can be treated either explicitly or semi-implicitly. Stiff source terms, including finite-rate chemistry and internal energy exchange, are integrated locally in each computational cell using the CVODE implicit solver from the SUNDIALS library [4]. Time integration is performed using either Strang splitting or Spectral Deferred Correction (SDC) methods.

The solver employs the thermodynamic and kinetic database available within SPARK [1]. Thermodynamic properties are evaluated using NASA-9 polynomial fits, supporting one to four temperature formulations (1T–4T). HelioS includes multi-species finite-rate chemistry, transport properties computed either from Gupta–Yos curve fits or Wright and Levin tabulated data. Rotational, vibrational, and electronic energy modes can be represented using either characteristic temperatures or discrete energy levels.

Results

The solver, more specifically with 2 to 4 temperatures models, is currently undergoing verification and validation through a series of canonical and hypersonic benchmark cases. Verification includes oblique shock-wave problems for numerical solver verification and embedded-boundary verification cases. The validation process includes hypersonic conical bi-ramp simulations compared against experimental data and hypersonic sphere atmospheric-entry simulations benchmarked against SPARK CFD. Early results, for a single temperature model, demonstrate stable and robust numerical behavior across the verification cases, while the validation process is providing encouraging agreement with experimental measurements and reference numerical solutions. These test cases are intended to assess the accuracy and robustness of the numerical implementation for high-enthalpy thermochemical nonequilibrium flows.

Conclusion

HelioS provides a modular and scalable CFD framework for high-enthalpy hypersonic aerothermodynamics, combining adaptive mesh refinement with thermochemical nonequilibrium models. The ongoing verification and validation campaign aims to establish the solver as a reliable platform for future research and engineering applications involving atmospheric entry and other hypersonic flow problems.
The modular software architecture also provides a foundation for future extensions toward state-to-state kinetics and coupled radiation transport.

Acknowledgements

This work was supported by the FCT – Fundação para a Ciência e a Tecnologia, I.P., under projects
UID/50010/2025 (https://doi.org/10.54499/UID/50010/2025),
UID/PRR/50010/2025 (https://doi.org/10.54499/UID/PRR/50010/2025),
UID/PRR2/50010/2025 (https://doi.org/10.54499/UID/PRR2/50010/2025),
and LA/P/0061/2020 (https://doi.org/10.54499/LA/P/0061/2020).

References

[1] Lopez, B., and Lino Da Silva, M., "SPARK: A Software Package for Aerodynamics, Radiation and Kinetics," AIAA AVIATION Forum, AIAA Paper 2016-4025, 2016. https://doi.org/10.2514/6.2016-4025

[2] Zhang, W., et al., "AMReX: a framework for block-structured adaptive mesh refinement," Journal of Open Source Software, Vol. 4, No. 37, 2019, p. 1370. https://doi.org/10.21105/joss.01370

[3] Colella, P., and Glaz, H. M., "Efficient Solution Algorithms for the Riemann Problem for Real Gases," Journal of Computational Physics, Vol. 59, No. 2, 1985, pp. 264–289. https://doi.org/10.1016/0021-9991(85)90146-9

[4] Hindmarsh, A. C., Brown, P. N., Grant, K. E., Lee, S. L., Serban, R., Shumaker, D. E., and Woodward, C. S., "SUNDIALS: Suite of Nonlinear and Differential/Algebraic Equation Solvers," ACM Transactions on Mathematical Software, Vol. 31, No. 3, 2005, pp. 363–396. https://doi.org/10.1145/1089014.1089020

Speaker: Joaquim Nogueira

15:00 Radiative Heat Transfer Modeling of High-Enthalpy Flows Applied to Chemical Rocket Propulsion Systems

High-temperature thermal radiation is a long-standing modeling challenge shared by very different classes of high-enthalpy flows, from atmospheric re-entry to chemical rocket propulsion. In rocket engines, the combustion products of solid, hybrid and liquid propellants (H$_2$O, CO$_2$, CO, soot for hydrocarbon-fuelled systems, and Al$_2$O$_3$ particles for aluminized propellants) behave as strongly non-grey participating media, and radiative heat transfer can locally contribute a significant, and in some regimes dominant, share of the total wall heat flux, affecting nozzle and combustion-chamber thermal protection design, fuel-grain regression in hybrid engines, and the aerothermal environment of reusable boosters during supersonic retro-propulsion (SRP). Over the past several years, the T(H)RUST group at Sapienza University of Rome has developed and progressively validated a common numerical framework, based on the Discrete Transfer Method (DTM), to address this problem consistently across propulsion architectures and flow regimes, rather than treating each application in isolation (1). This work aims to show how this problem can be tackled through a unified numerical framework spanning propulsion architectures and flow regimes, and how radiative heat transfer can be an extremely relevant contribution to the overall thermal loads generated by the high-enthalpy flows produced by rocket engines.

The core of our framework is an in-house DTM solver, recently released as open-source software (2), which solves the radiative transfer equation for participating medium and diffusely-reflecting walls and can be coupled, one-way or two-way, to CFD solvers. Depending on the required accuracy and affordable computational cost, gas radiative properties are modeled at different levels of fidelity: line-by-line calculations as a benchmark, statistical narrow-band (SNB) model as a practical spectral reference, gray-gas models based on mean Planck absorption coefficients, and the Weighted-Sum-of-Gray-Gases (WSGG) approach; custom WSGG formulations, calibrated up to 300 bar and 4000 K to cover liquid-rocket-engine (LRE) conditions, were also developed. Soot radiation is modeled through Rayleigh-approximation models with temperature-dependent complex refractive index, coupled, where relevant, to soot-formation models based on mixture-fraction or C$_2$H$_2$-precursor chemistry. Properties of alumina particles are computed according to Mie theory. This framework has been applied to solid-rocket-motor nozzle ablation (3), hybrid-rocket fuel regression (4,5), LRE thrust-chamber wall heat flux (6,7), and the aerothermal environment of a reusable launcher during retro-propulsion manouvers (8). As a unifying example, the same methodology is applied to estimate the radiative wall heat flux of a representative hydrocarbon-fuelled LRE across two conditions within its life cycle: steady in-chamber/nozzle operation, and the plume/recirculation environment generated during an supersonic retro-propulsion (SRP) descent, using consistent spectral and soot modeling assumptions in both cases.

For the representative hydrocarbon-fuelled LRE considered, radiative heat transfer is found to be a relevant fraction of the total wall heat flux in both operating conditions. Inside the combustion chamber, gas-phase (H$_2$O/CO$_2$) radiation typically accounts for 5-10% of the total heat flux, locally rising up to 30% in the cylindrical section and near the injection plate. Analysis of the open literature revealed a lack of reduced-order spectral models calibrated for the high pressure and temperatures typical of LRE combustion chambers, which motivated the development of new WSGG formulations validated up to 300 bar and 4000 K. Addition of soot further increases the radiative share on the total heat load.
During SRP, the same combustion products, once expelled and mixed with atmospheric air, contribute to the heating of the rocket base plate and side wall, with the radiative share of the total heat flux rising up to about 70-75% under high-thrust conditions, exceeding the convective contribution.

Radiative heat transfer modeling in high enthalpy flows and especially in propulsive systems remains a genuinely complex problem, involving strongly non-grey, high-temperature, high-pressure participating media whose accurate description generally requires computationally expensive spectral calculations. However, industrial practice, and in particular engine development, relies on extensive parametric analyses across operating conditions and design variants, for which such high-fidelity tools are rarely affordable, creating a need for reliable models with a computational cost compatible with these design phases. The unified framework and body of work presented here show that radiative heat loads are not a negligible detail in the thermal assessment of rocket propulsion systems, from combustion chambers to vehicle recovery, but also that dedicated reduced-order and global models, when properly developed and validated against spectral references over the relevant temperature and pressure range, can reproduce this contribution with good accuracy at a small fraction of the cost of full spectral calculations, making systematic, physically consistent radiative assessments practically feasible for engineering design.

(1) Francesco Nasuti et al., "Progresses in Applied Research on Liquid Rocket Propulsion by T(H)RUST Research Team at Sapienza University of Rome", 75th International Astronautical Congress (IAC), 2024.

(2) Marco Fabiani, ``GROOT.'' Zenodo, May 21, 2026, https://doi.org/10.5281/zenodo.20327076.

(3) Daniele Bianchi et al., "Numerical Modeling and Experimental Validation of Thermochemical Ablation in Solid Rocket Motor Nozzles", 11th EUCASS, 2025. https://doi.org/10.13009/EUCASS2025-739.

(4) Marco Fabiani et al., "Numerical Analysis of Gas and Soot Radiation in Hybrid Rockets with Pyrolyzing Fuels", 35th International Symposium on Space Technology and Science, 2025.

(5) Marco Fabiani et al., "Radiative Wall Heat Transfer Evaluation in Hybrid Rocket Thrust Chambers",AIAA SciTech 2024 Forum. https://doi.org/10.2514/6.2024-1608.

(6) Marco Fabiani et al., "Spectral and Global Radiative Heat Transfer Models for Liquid Propellant Rocket Engines", Journal of Propulsion and Power, Vol.41, No.5, 2025, pp.650-664. https://doi.org/10.2514/1.B39892.

(7) Marco Fabiani et al., "Reduced-order Models for Radiative Heat Loads Estimation in Liquid Rocket Engines", 76th International Astronautical Congress, Sydney, Australia, 2025.

(8) Marco Grossi et al., "Numerical Investigation of Thermal Loads during Supersonic Retropropulsion of a Reusable Launch Vehicle", 27th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, Naples, Italy, 2026, https://doi.org/10.2514/6.2026-5034.

Speaker: Dr Marco Fabiani (Sapienza University of Rome)

15:30 → 16:00 Coffee Break at the Palazzo Roberti Courtyard

Piazza XX Settembre, 60-62, 70042 Mola di Bari BA
https://maps.app.goo.gl/hwoVgZsAzCMpJNwZ6

16:00 → 17:00 Radiation modeling and simulation: Wednesday afternoon 2

Convener: Mario Lino da Silva (Instituto de Plasmas e Fusão Nuclear - Instituto Superior Tecnico)

16:00 A CFD-to-Radiation Framework for Line-by-Line Infrared Emission Modelling of High-Temperature Exhaust Plumes

High-temperature exhaust plumes may represent a significant source of infrared radiation in propulsion-related high-speed flows. Their emission depends on the local thermochemical state of the gas, the spatial distribution of radiating species, self-absorption along the optical path, and the viewing direction. A consistent coupling between CFD flow-field solutions and spectrally resolved radiative transfer is therefore required to predict observable infrared quantities and to assess the interaction between radiation and the plume flow field.
In this work, a CFD-to-radiation framework is presented for predicting infrared emission from high-temperature exhaust plumes. The methodology adopts a one-way coupling strategy, in which temperature, pressure, species concentrations, and geometrical information extracted from the CFD solution are used to reconstruct the radiating and absorbing gas domain. Spectral absorption coefficients are evaluated through a detailed line-by-line treatment based on molecular spectroscopic databases, accounting for transition line positions, temperature-dependent line intensities, pressure-broadening effects, and the local thermochemical state of the plume.
Radiative transfer is then solved for multiple prescribed observation directions through a line-of-sight marching procedure. Along each ray, the emission–absorption equation is integrated using a segment-wise analytical solution, where the local source function is given by the Planck spectral radiance at the gas temperature. This formulation naturally accounts for both local gas emission and attenuation by the intervening plume medium. The resulting spectral radiance is integrated over selected infrared bands and projected onto an equivalent observation plane, providing synthetic radiometric maps and band-integrated plume intensities.
The framework is demonstrated on an axisymmetric high-temperature exhaust plume reconstructed in three dimensions and analysed over a range of viewing directions. The results highlight the influence of plume morphology, projected emitting area, optical path length, and self-absorption on the angular dependence of the observed infrared radiation. To mitigate the computational cost of line-by-line calculations, the framework includes thermochemical clustering, spectral chunking, precomputed Planck functions, and line-of-sight geometry caching. These strategies enable practical multi-band and multi-angle analyses while preserving the high-resolution spectral description of the gas radiation.
Overall, the proposed framework provides a computationally efficient way to exploit high-fidelity line-by-line radiation modelling for plume analyses. This enables practical multi-band and multi-angle predictions while offering a modular foundation for future fully coupled CFD-radiation simulations, in which radiative source terms could be fed back into the flow solver.

Speaker: Salvatore Esposito (CIRA)

16:30 Transmission of radiation from hot vehicles to LEO-sensors

Radiation emitted at high altitude is modified as it propagates through Earth’s upper
atmosphere toward space-based observers. Even in the rarefied upper atmosphere, long path
lengths and strongly wavelength-dependent absorption and scattering processes can lead to
substantial attenuation depending on spectral region, source altitude, and viewing geometry. In this
work, wavelength-resolved atmospheric transmission functions are derived for radiation emitted
between 30 and 130 km altitude and propagating outward to space at viewing angles between 0°
and 90°, covering the ultraviolet, visible, and near-infrared spectral range below 1100 nm.les to LEO-sensors

Speaker: Christian Mundt

Thursday 24 September

09:00 → 10:30 Radiation modeling and simulation: Thursday morning 1

Convener: Dr Markus Fertig (German Aerospace Center)

09:00 A Coupled Post-Shock Nonequilibrium Flow and Spectral Radiation Solver for Stagnation-Point Radiative Heating: FIRE II Validation with Error Structure Analysis

Topic
Experimental and numerical modelling improvements of radiative heat transfer: refinement, verification, validation and comparison for space object re-entry simulation tools

Background

Radiative heating dominates the total heat load for vehicles entering planetary atmospheres above 10 km/s. The FIRE II flight experiment [1] measured stagnation-point radiative fluxes of 1100–1530 W/cm$^2$ at 67–77 km altitude, exceeding 70% of total heating. High-fidelity codes (VSL2T–NEQAIR, LAURA–HARA, DPLR–NEQAIR) solve viscous shock-layer equations coupled with line-by-line radiation transport but require HPC resources and demand expert setup. Engineering correlations such as Tauber–Sutton [4] provide rapid estimates but return only a single wall-flux value without spectral or spatial resolution. A tool filling this gap — spectrally resolved shock-layer radiation in seconds — would benefit parametric pre-design, mission trade studies, and arc-heater ground-test correction, where facilities (NASA Ames IHF, JAXA JXWT) reproduce convective but not radiative heating.

Methodology

This paper presents two coupled analysis tools: psf2t, a 1-D post-shock two-temperature (2-T) ODE solver, and SPIRE (SPectral Inviscid Radiation for Entry), a coupled spectral radiation code.

psf2t implements Park's [2] 2-T model with 11-species air, 11 reaction sets, Millikan–White–Park relaxation, and Gupta et al. [5] thermodynamic coefficients for all species including molecular ions. A key innovation is the use of spatial coordinate x as the independent variable, guaranteeing uniform resolution throughout the shock layer. The integration terminates at the boundary-layer edge (estimated via a Reynolds-number correlation), not at the vehicle wall.

SPIRE integrates the 1-D radiative transfer equation from the shock to the BL edge with four-angle Gauss–Legendre quadrature. Spectral contributions include: 57 atomic/ionic lines (NIST ASD) with per-line RTE, full electronic partition functions from NIST energy levels, and Doppler broadening; bound-free and free-free continuum at $T_{ve}$; N2+ Meinel bands; and N2 LBH + NO molecular continua. The output is the spectrally resolved $q_{rad}$, BLE — the physically correct outer boundary condition for coupled radiation–convection–ablation BL analysis.

To compare with Cauchon's [1] wall measurements, BL transmittance factors ($\tau_{lines}$ = 0.783, $\tau_{cont}$ = 0.526) are applied. The overall 22–25% BL absorption is consistent with Johnston's [3] prediction of 20–40%.

Results

Validation uses three FIRE II trajectory points at approximately 11.3 km/s. Flow field: BL-edge temperature predicted within +5 to +21% of reference values; pressure within $\pm$16%. The x-based formulation achieves 0.007 cm maximum spatial gap versus 0.07 cm for time-based integration.

Radiation: Shock-layer $q_{BLE}$ = 1428, 1975, and 1912 W/cm$^2$ for the three cases. Wall fluxes after BL transmittance are 1110, 1488, and 1447 W/cm$^2$, yielding errors of +0.9%, −2.7%, and +2.6% versus Cauchon [1].

Key findings from error structure analysis: (1) Full electronic partition functions reduce atomic line emission by 16–18%, shifting $\tau_{lines}$ from 0.630 (two-level) to 0.783 (full), demonstrating that the two-level approximation was being absorbed by the transmittance. (2) Temperature sensitivity analysis ($\pm$10% perturbation) reveals extreme sensitivity: a 10% reduction in T causes $q_{BLE}$ to fall below Cauchon's [1] measurements, yielding non-physical $\tau > 1$. This proves that the fitted $\tau$ is an integrated correction factor absorbing genuine BL absorption, flow-solver overestimate, and limited line-database compensation simultaneously. (3) Gupta [5] thermodynamic coefficients for molecular ions correct a significant high-temperature extrapolation error, reducing N2+ peak concentration by 22%.

Computation time is under 5 seconds on a standard laptop.

Conclusion

A coupled 1-D 2-T flow solver and spectral radiation code have been established and validated against FIRE II within $\pm$3% at the wall. The error structure analysis demonstrates that the fitted transmittance is not a pure BL transmittance but an integrated correction factor whose components cannot be separated without independent $q_{BLE}$ or $\tau_{BL}$ calculations. This finding motivates ongoing work on viscous BL solver coupling and expanded line databases. The transparent reporting of error structure, rather than claiming accuracy, is central to the present work.

References

[1] Cauchon, D. L., NASA TM X-1402, 1967.
[2] Park, C., Nonequilibrium Hypersonic Aerothermodynamics, Wiley, 1990.
[3] Johnston, C. O., Ph.D. Dissertation, Virginia Tech, 2006.
[4] Tauber, M. E. and Sutton, K., J. Spacecraft and Rockets, 28(1), 1991.
[5] Gupta, R. N. et al., NASA RP-1232, 1990.

Acknowlegdement

This work was supported by the SNU Aerospace Integrated Wind Tunnel Center

Speaker: Jaejeong Na (Aerospace Integrated Wind Tunnel Center, Seoul National University, South Korea)

09:30 Impact of two-dimensionality and shock-speed variation on Earth-return shock-tube experiments

Introduction

The vast distances between Earth and other celestial bodies within our solar system requires space vehicles to transit between them with very large velocities. This ensures transit time is not prohibitively long, however results in vehicles entering the destination atmosphere with an extremely high velocity. This in turn requires significant deceleration of the vehicle upon arrival, commonly vehicle drag provides the deceleration necessary to slow the vehicle to near subsonic speeds.
The strong bow shock processes the free-stream atmosphere to extremely high pressures and temperatures, resulting in thermochemical non-equilibrium as the gas dissociates and ionises.
These phenomena affect the heat flux (with both convective and radiative contributions), drag, and communication processes of hypersonic vehicles [1].

Hypersonic ground testing facilities enable such entry flow conditions to be interrogated prior to vehicle commissioning. In particular, shock tubes offer the ability to analyse the post-shock environment, with spectroscopic measurements commonly used to investigate the relevant thermochemical processes. However, these facilities are not exactly analogous to a normal shock problem, with viscous effects affecting boundary layer growth and shock structure, and non-ideal behaviour unique to individual experiments and experimental facilities resulting in shock speed variation [2-7].
As a primary use of shock tube datasets is to validate, improve or quantify the uncertainty of thermochemical models, numerical results generated using such thermochemistry models for comparison to experimental datasets must also account for these shock-tube flow behaviours [8]. This requires an a posteriori approach, using experimental measurements to reconstruct the experimental flow behaviour with improved fidelity [9,10]. In particular, recent advances in a posteriori modelling of hypersonic shock tubes enables two-dimensional reconstruction of experimental conditions, accounting for both shock trajectory and resolving the boundary layer growth and properties [11].

A recent work postulated that observed infrared emission lines from atomic species may be more susceptible to two-dimensional effects, with the line-of-sight measurement observing any shock curvature and radial variation in gas properties in the boundary layer [10]. Additionally, it has been identified that these lines are sensitive to variations in shock speed [4]. Therefore this work will analyse the influence of two-dimensional and shock trajectory effects on atomic emission lines in the infrared region.

Methodology

Flow Solvers

Two numerical solvers will be utilised in this analysis, NESS2D and NESS2D-t [11, 12]. NESS2D is a steady, viscous, two-dimensional a posteriori method, with a two-temperature reacting gas thermochemistry model. This method uses an outflow pressure variable to hold the shock at a desired position in the domain, resulting in a two-dimensional flow solution for a constant shock-speed experiment [11].
NESS2D-t is an extension of the NESS2D method, and evolves the test slug down the tube using the Newton-Raphson method to solve both the backward Euler problem and the outflow pressure required to pin the shock at the desired location within the flow domain. NESS2D-t therefore inherently captures both the influence of the transient boundary layer growth on the core flow, the boundary layer properties themselves, and the influence of the variation in shock speed [12].

Radiance Model

NASA's NEQAIR v15.2 [13, 14] is a line by line code developed to estimate radiance emissions, given a specified profile of temperatures and number densities.
This allows an estimate of predicted radiance to be made by coupling a shock tube solver's output of spatially resolved temperature and number density profiles with the NEQAIR program.

To ensure two-dimensional effects are captured, each radial slice at each axial station is solved independently using the non-local, non-Boltzmann line-of-sight (\texttt{N F N}) radiance solution [15]. However, this is a simplified approach as it removes dependence on non-local effects in the axial direction and any optical effects which require a ray tracing algorithm to be captured.
For the comparisons using the centreline result, it is assumed that the centreline solution is homogenous across the diameter of the tube, with the boundary at the last line-of-sight point modelled as a greybody with 0 emissivity and a transmissivity of 1.
Additionally, the vibrational weighting of non-equilibrium excitation was computed using the lowest vibrational level. This is achieved by setting the $\mathrm{NEQ}_{\mathrm{QSS},\mathrm{EXC},V}$ flag as 1, which is the new default behaviour in NEQAIR 15.3.

To enable comparison to experimental results, where possible the experimentally determined spatial resolution functions (SRF) and instrument line shapes (ILS) were used to convolve the NEQAIR simulations.

Experimental and Numerical Setup

The test series chosen for analysis was series 50 from the NASA-EAST test facility, as it was previously identified as being affected by shock speed variation effects [4].
This series ran tests at a variety of pressures through 79% $N_2$ and 21% $O_2$ gas, focussing on lunar return speeds between 8-11 km/s through a 10.16 cm diameter tube.
This work enables the influence of the shock trajectory to be isolated from the two dimensional effects, by comparing the synthetic integrated line-of-sight of the full NESS2D-t result, the NESS2D-t centreline and the steady NESS2D result using the shock speed observed at the viewing window.

For brevity, results will focus on test ES50-40, nominally an 8.56 km/s shock through 26.6 Pa synthetic air. However, there is significant deceleration of the shock wave, shown in Figure 1, where the shock velocity decreased by 2 km/s over approximately 4 m to be 8.56 km/s at the viewing window of the optical emission spectroscopy (OES).

Figure 1. Shock speed profile for ES50-40, a 8.56 km/s shock through 79% $N_2$, 21% $O_2$ gas by volume at 26.6 Pa.

The mesh converged domain used a clustered, rectangular structured mesh [11], with 400 and 150 axial and radial points respectively. The Cruden 2017 thermochemistry model was used as the reaction scheme [16], the collision integrals recommended by Wright [17] were used by the in-house OCEAN library to evaluate the multicomponent transport properties.

Overview of Results

The centreline comparison of temperatures and number density profiles (Figures 2 to 5) immediately demonstrates the importance of including the effect of shock trajectory, with the difference between the steady centreline temperature and the transient formulation totalling 2000 K by 100 mm post shock. Visible departure begins from 30 mm post shock, therefore it is expected that this will be reflected in the synthetic spectra produced using the respective methods.

Figure 2. Temperature profiles for ES50-40, a 8.56 km/s shock through 79% $N_2$, 21% $O_2$ gas by volume at 26.6 Pa.

Similarly, the influence of shock trajectory has a significant influence on the electron number density, growing to be nine times larger compared to the steady case.

Figure 3. Electron number density profiles for ES50-40, a 8.56 km/s shock through 79\% $N_2$, 21\% $O_2$ gas by volume at 26.6 Pa.

This increased temperature profile at the rear of the test slug of the NESS2D-t solution is a direct consequence of that gas being processed by a significantly stronger shock.
This also increases the ionisation the transient NESS2D-t result, while the atomic number density of oxygen drops by 30\%, and the number density of atomic nitrogen decreases by 24\% compared to the steady NESS2D result.

Figure 4. Atomic oxygen number density profiles for ES50-40, a 8.56 km/s shock through 79\% $N_2$, 21\% $O_2$ gas by volume at 26.6 Pa.

Figure 5. Atomic nitrogen number density profiles for ES50-40, a 8.56 km/s shock through 79\% $N_2$, 21\% $O_2$ gas by volume at 26.6 Pa.

As an interesting outcome, the centreline mass loss due to the boundary layer growth shown in Figure 6 demonstrates quite good agreement between the NESS2D steady result, and the transient model of NESS2D-t. However, there is significant departure from the Mirels boundary layer [2] profile, due to the dual effects of shock curvature and the simplifying assumptions made by Mirels regarding the local resizing of the boundary layer [2].

Figure 6. Mirels number profiles for ES50-40, a 8.56 km/s shock through 79\% $N_2$, 21\% $O_2$ gas by volume at 26.6 Pa.

The wavelength region selected for analysis is between 700-900 nm, where strong atomic lines are present. Particularly, the radiance centred around 745, 820 and 868 nm corresponds to atomic nitrogen transitions, while the lines centred at 777 and 844 nm correspond to atomic oxygen transitions. These atomic lines are particularly strong in this case, due to the significant dissociation and ionisation present, thus allow the influence of flow two-dimensionality to be investigated at multiple transitions.

We begin with the two atomic oxygen lines, the 777 nm triplet and the 844 nm triplet. Figure 7 depicts the emitted radiance associated with the 777 nm triplet (integrated radiance between 770-785 nm), immediately the issues with using this line for inferring information about the core flow become apparent. The three approaches diverge from approximately 7 mm post shock onward, corresponding to which is the location where the boundary layer becomes sufficiently large to begin absorbing the emission from the core flow. This results in the predicted radiance being approximately 15 times smaller when the boundary layer effects are included, with the experimental value existing between the radially homogenous solution and that which includes boundary layer effects. The thermochemically non-equilibrium flow environment within the boundary layer results will have high uncertainty due to the effects of surface catalycity [10], as well as the optical effects neglected in this analysis. These difficulties limit the utility of the 777 nm line for use in thermochemical model evaluation, and care should be taken if it is to be used for spectral fitting.

Figure 7. Atomic O radiance between 770-785 nm for ES50-40, a 8.56 km/s shock through 79\% $N_2$, 21\% $O_2$ gas by volume at 26.6 Pa.

In comparison, the atomic oxygen triplet at 844 nm displays some boundary layer dependence, however the NESS2D-t centreline solution is consistently within 7\% of the full solution. Additionally, the importance of modelling the variable shock speed is clear, with the steady NESS2D simulation completely unable to capture the behaviour of the integrated radiance. This analysis indicates that the 844 nm transition is the more reliable atomic oxygen line to model, despite it being a weaker transition compared to the 777 nm line.

Figure 8. Atomic O radiance between 838-849 nm for ES50-40, a 8.56 km/s shock through 79% $N_2$, 21% $O_2$ gas by volume at 26.6 Pa.

Finally, the three atomic nitrogen lines, the 745 nm, 820 nm and the 868 nm are depicted in Figures 9-11. Agreement between the steady and transient solutions is poor after 20 mm, with the transient modelling significantly improving agreement with the experimental results.

Figure 9. Atomic N radiance between 738-752 nm for ES50-40, a 8.56 km/s shock through 79\% $N_2$, 21\% $O_2$ gas by volume at 26.6 Pa.

Furthermore, the absorption of the emitted radiance the boundary layer improves agreement with experiment in each of the Figures, with the effect of the boundary layer becoming more pronounced from 50 mm post-shock.

Figure 10. Atomic N radiance between 810-830 nm for ES50-40, a 8.56 km/s shock through 79% $N_2$, 21% $O_2$ gas by volume at 26.6 Pa.

This culminates in a discrepancy between centreline NESS2D-t and the full NESS2D-t result of 8\% by 100 mm post shock, consistent for all of the atomic nitrogen lines in the infrared region.

Figure 11. Atomic N radiance between 854-876 nm for ES50-40, a 8.56 km/s shock through 79\% $N_2$, 21\% $O_2$ gas by volume at 26.6 Pa.

Conclusion

This work offers novel insights into the influence of two-dimensional effects and shock speed variation on atomic line features in the infrared region. In particular, this work highlights issues with the oxygen 777 nm line being sensitive to the properties of the boundary layer, however the 844 nm oxygen triplet remains relatively unaffected by the boundary layer properties. The remaining atomic features in the infrared region had agreement within 8\% between the full NESS2D-t model and the centreline NESS2D-t result, with the visible divergence increasing steadily from 50 mm post-shock. This work informs both uncertainty quantification of thermochemistry models, and the importance of using wavelength regions which behave quasi-one-dimensionally if using a quasi-one-dimensional approach to spectral fitting or rate optimisation.
Further work to examine the ultra-violet region, and the broader envelope of test-conditions, will further improve understanding of regions and conditions where two-dimensional effects are prevalent.

References

[1] Ramjatan, S., Lani, A., Boccelli, S., Van Hove, B., Karatekin, O., Magin, T., and Thoemel, J., “Blackout analysis of Mars entry missions,” Journal of Fluid Mechanics, Vol. 904, 2020. https://doi.org/10.1017/jfm.2020.714.

[2] Mirels, H., “Test time in low-pressure shock tubes,” Physics of Fluids, Vol. 6, No. 9, 1963, pp. 1201–1214.
https://doi.org/10.1063/1.1706887.

[3] De Boer, P. C., “Curvature of shock fronts in shock tubes,” Physics of Fluids, Vol. 6, No. 7, 1963, pp. 962–971.
https://doi.org/10.1063/1.1706852.

[4] Collen, P. L., Satchell, M., Di Mare, L., and McGilvray, M., “The influence of shock speed variation on
radiation and thermochemistry experiments in shock tubes,” Journal of Fluid Mechanics, Vol. 948, 2022, p.
A51. https://doi.org/10.1017/jfm.2022.727.

[5] Satchell, M., “Numerical Simulation and Modeling of Shock Tube Experiments,” Ph.D. thesis, University of
Oxford, 2021.

[6] Clarke, J., Di Mare, L., and McGilvray, M., “Spatial Transformations for Reacting Gas Shock Tube Experiments,” AIAA Journal, Vol. 61, No. 8, 2023, pp. 1–10. https://doi.org/10.2514/1.j062604.

[7] Steer, J., Clarke, J., Collen, P. L., McGilvray, M., and di Mare, L., “Non-equilibrium thermochemistry in real
shock tubes,” Journal of Fluid Mechanics, Vol. 1032, 2026, p. A51. https://doi.org/10.1017/jfm.2026.11341.

[8] Clarke, J., Glenn, A. B., McGilvray, M., and Luca, D. M., “Numerical Simulations of Carbon Contaminants in T6 Shock Tube Tests,” AIAA SCITECH 2024 Forum, American Institute of Aeronautics and Astronautics, Reston, Virginia, 2024, pp. 1–22. https://doi.org/10.2514/6.2024-0868, URL
https://arc.aiaa.org/doi/10.2514/6.2024-0868.

[9] Clarke, J., Brody, S., Steer, J., McGilvray, M., and Di Mare, L., “Quasi-one-dimensional non-equilibrium
method for shock tube and stagnation line flows,” Physics of Fluids, Vol. 36, No. 9, 2024.
https://doi.org/10.1063/5.0218676.

[10] Clarke, J., “Numerical Modelling of Hypersonic Shock Tunnels in Thermochemical Non-Equilibrium,” Ph.D.
thesis, University of Oxford, 10 2025. https://doi.org/10.5287/ora-xoom0wx8z.

[11] Clarke, J., Steer, J., McGilvray, M., and Mare, L. D., “Two-Dimensional a Posteriori Method for Nonequilibrium Shock Tube Flows,” AIAA Journal, 2026, pp. 1–20. https://doi.org/10.2514/1.J066567, URL
https://arc.aiaa.org/doi/10.2514/1.J066567.

[12] Clarke, J., Steer, J., McGilvray, M., and Mare, L. D., “Two-dimensional a posteriori modelling of unsteady
non-equilibrium shock tube flows,” , 2026. Manuscript submitted for publication.

[13] Whiting, E. E., Chul, P., Liu, Y., Arnold, O., and Paterson, A., “NEQAIR96, Nonequilibrium and Equilibrium
Radiative Transport and Spectra Program: User’s Manual,” Tech. Rep. December, NASA, 1996.

[14] Park, C., “Nonequilibrium Air Radiation (NEQAIR) Program: User’s Manual,” Tech. Rep. NASA-TM-86707,
National Aeronautics and Space Administration, 1985. URL https://ntrs.nasa.gov/citations/19850022467.

[15] Cruden, B. A., and Brandis, A. M., “Updates to the NEQAIR Radiation Solver,” 6th International Workshop
on Radiation of High Temperature Gases in Atmospheric Entry, 2014.

[16] Cruden, B. A., and Brandis, A. M., “Measurement of Radiative Non-equilibrium for Air Shocks Between 7-9
km/s,” 47th AIAA Thermophysics Conference, American Institute of Aeronautics and Astronautics, Reston,
Virginia, 2017, pp. 1–36. https://doi.org/10.2514/6.2017-4535.

[17] Wright, M. J., Bose, D., Palmer, G. E., and Levin, E., “Recommended collision integrals for transport
property computations, part 1: Air species,” AIAA Journal, Vol. 43, No. 12, 2005, pp. 2558–2564.
https://doi.org/10.2514/1.16713.

Speaker: Justin Clarke (Oxford University)

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10:00 Radiative Heating on the Mars Sample Retrieval Lander: Simulation, Validation, and Uncertainty

The Mars Sample Retrieval lander mission was designed to be the first stage of NASA's Mars Sample Return program. It would land a stationary payload to process samples collected by the Perseverance rover and place them on board a rocket for their journey to Earth. In total, the lander would be the largest entry mass and volume ever placed on the Martian surface. Furthermore, the entry speed, in its final iteration, was approximately eight kilometers per second. Most Martian landers previously landed in the five kilometer per second regime.
One of the many new design challenges of the lander was the increased radiative heat load. As one moves from a five km/s entry to an eight km/s entry, the shock layer contains enough thermal energy to both dissociate the carbon dioxide in the atmosphere and electronically excite the resulting CO molecules. This transitions the radiative heating from an infrared signal from the CO2 vibrational bands to a strong ultra-violet signal from CO (the 4th positive band). This radiative heating surpassed the convective heating of previous missions like Mars Science Laboratory (MSL) and Mars2020. This new physics required validation to certify the mission design.
The Electric Arc Shock Tube (EAST) is NASA's workhorse facility for ground-based measurements of radiative emission from high-speed flows. Simulations against EAST optical emission spectroscopy data formed the core of this validation effort. The simulations were performed using DPLR and NEQAIR, NASA's hypersonic CFD code and spectral solver, respectively.
The baseline simulations showed a large underprediction of VUV radiation, as high as a factor of two at some conditions. The primary cause was attributed to the lack of heavy particle excitation in the baseline model. However, even with these corrections, one could not bound the experimental data. In fact, using a Boltzmann model of excited states, one could not produce a conservative simulation at peak heating conditions.
This discrepancy was hypothesized to be the result of deceleration effects in EAST rather than a systematic problem in the model. A new technique was developed to account for deceleration effects. The method relies on the assumptions of Shock Tube Informed Bias (STIB) to, instead of mapping shock tube data to CFD flow solutions, map CFD flow solutions onto a deceleration shock trajectory. This was shown to result in a large change in predicted radiative heating bringing predictions more in line with experimental data.
Even with these adjustments, there continued to be discrepancies between model predictions and experimental data from EAST. For mission design, some margin factor must be calculated to provide a useful upper bound. This calculation, if done rigorously, is extremely computationally expensive or intractable. In this work, three methods were presented, starting with the methods developed for other NASA missions such as Dragonfly and ending with an approximate Bayesian inversion. These methods all produced different estimates of the radiative heating uncertainty, varying from 100% to 30%.

Speaker: Kaelan Hansson (AMA Inc at NASA Ames)

10:30 → 11:00 Coffee Break at the Palazzo Roberti Courtyard

Piazza XX Settembre, 60-62, 70042 Mola di Bari BA
https://maps.app.goo.gl/hwoVgZsAzCMpJNwZ6

11:00 → 12:00 High speed facilities, flight testing and propulsion: Thursday morning 2

Convener: Kohei Shimamura (Tokyo Metropolitan University)

11:00 Non-equilibrium scaling between H2–M shock layers using test gas substitution

Test gas substitution offers the ability to overcome the total enthalpy limitations of ground test facilities and increase the temperature range over which hydrogen thermochemistry can be studied. The substitution involves modifying the nominal H2–He mixture by substituting He with Ne and/or increasing the fraction of diluent gas in the initial mixture. Such a modification decreases the specific heat capacity of the mixture and allows higher temperatures to be reached for a given incident shock speed. Similarity between substituted flows based on the theory of binary scaling has been proposed in the literature, however the extent of the similarity, and the validity of the underpinning assumptions, have never been rigorously reviewed. We performed a systematic study of similarity between flows with different initial H2 fractions (𝑟), and flows with matching 𝑟 but Ne used in place of He. We show analytically that a direct non-equilibrium scaling between flows with different 𝑟 is not possible because of the different sizes of the third-body pool, a violation of the requirements of binary scaling. We find that, in cases of a 1:1 Ne for He substitution, the increased molar mass of the Ne atom can change the behaviour of second-order flow processes such as diffusion and conduction that affect the similarity, but not strongly for the test cases analysed. Forced recombination due to an isothermal wall boundary condition and optical thickness of the H–𝛼 are shown to be likely responsible for discrepancies observed in the literature. We conclude that the substitution is valuable method for the study of high-temperature hydrogen thermochemistry, but the expected region of similarity should be strictly defined to ensure that substituted conditions are useful.

Speaker: Matthew Mcgilvray (University of Oxford)

11:30 Acceptance Testing of the ESTHER shock tube in operational configuration: First outcomes

On November 2025, ESTHER carried out its first shot in full operational configuration, reaching an estimated velocity of 8km/s. Since then the operational acceptance tests have been ongoing, validating several design choices, yet highlighting a series of flaws in the design that have been under correction during this acceptance campaign, which is scheduled to close at the end of 2026.

This presentation presents the outcomes and lessons learned of this ongoing qualification campaign.

Speaker: Mario Lino da Silva (Instituto de Plasmas e Fusão Nuclear - Instituto Superior Tecnico)

12:00 → 14:00 Lunch

Participants are asked to arrange their own lunch and return 10 minutes prior to the start of the session

14:00 → 15:30 EDL instrumentation: Thursday afternoon 1

Convener: Dr Louis Walpot (ESA/TEC-MPA)

14:00 Entry modelling and instrumentation: impacts to aerothermal research

Introduction

The Entry Modeling & Instrumentation (EM&I) portfolio develops validated models, tools, and flight‑ and ground‑test data to improve reliability assessments and design margins for planetary and Earth‑return entry systems. Integrating three tightly coupled components: Entry Systems Modeling, Entry Science Investigation, and Flight Test & Instrumentation. EM&I provides an end‑to‑end capability spanning aeroheating prediction, material‑response modeling, and mission verification and validation. This multi‑center, multi‑disciplinary effort couples high‑fidelity CFD and DSMC flowfield simulations with nonequilibrium radiation transport and thermal‑protection‑system (TPS) multi‑physics solvers, enabling mission designers to quantify entry environments and margins for systems such as Dragonfly, Mars Sample Return, and Artemis/Orion.

Shock‑layer kinetics and radiation.

A major focus of EM&I is advancing the state of the art in shock‑layer kinetics and radiation. The NEQAIR/HARA radiation‑analysis suite remains a mission workhorse supporting design and post‑flight reconstruction for missions including OSIRIS‑REx, Hayabusa‑2, and Artemis‑1, and has recently been updated with improved rates and non‑Boltzmann modeling for complex, high‑temperature flows. In parallel, EM&I is maturing NERO, a high‑throughput 3‑D radiation solver that achieves 2–3 orders‑of‑magnitude speed‑ups relative to legacy methods, enabling fast turnaround and coupled multi-physics aeroshell‑heating simulations that account for complex geometries. EM&I also accelerates fundamental data generation through MPEC molecular electronic‑structure computations, targeting key radiating species such as CN and $CO^+$ and supplying essential inputs to aerothermal CFD and radiation‑transport models. Coupling infrastructure, including the Ares framework and the GLUE library for unstructured environment exchange and dusty‑flow radiation, further integrates these physics into a unified, mission‑ready workflow.

NASA–ESA $H_2$–$He$ modeling effort.

A significant new thrust within EM&I is the joint NASA–ESA $H_2$–$He$ modeling effort, established to address the aerothermal challenges of future entries at Saturn, Uranus, and Neptune. Gas‑giant entries can exceed 25 km/s, producing extreme convective and radiative heating that strongly drive TPS design. The five‑year collaboration seeks to generate benchmark datasets for high‑speed entry into hydrogen–helium atmospheres, improve modeling of both convective and radiative heat fluxes, and quantify the influence of trace species, particularly methane ($CH_4$). Even small $CH_4$ concentrations (order of a few %) could potentially increase shock‑layer radiation.

Complementary high‑enthalpy facilities across NASA and ESA, including shock tubes and plasma wind tunnels, provide controlled conditions to study kinetics, radiation transport, and energy‑exchange processes in relevant mixtures. These data underpin advances in 3‑D radiation modeling, state‑to‑state $H_2$–$He$ nonequilibrium chemistry, and potential flight‑instrument concepts such as narrowband radiometers for real‑time atmospheric‑composition sensing.

Impact and infusion.

By unifying advanced kinetics,radiation, and materials modeling with robust flight and ground validation, EM&I reduces design conservatism while protecting required margins for mass‑ and thermally‑constrained missions. Its multi‑physics advances, including NEQAIR/HARA updates, NERO acceleration, MPEC molecular data, and Ares coupling, are already infusing current mission analyses and enabling faster, higher‑fidelity assessments of shock‑layer environments and TPS performance across NASA and international partners.

Brief Presenter Biography

Dr Brandis is a senior research scientist employed in the aerothermodynamics branch at NASA Ames. He is the DrEAM lead investigator, Dragonfly aerothermal lead and PI for NASA’s Entry Systems Modeling
project.

Speaker: Dr Aaron Brandis (NASA Ames Research Center)

14:30 A TPS-embedded Sensor-Suite for Ice Giant Aerocapture Featuring a Spectrometer

Background of the Study
Aerocapture is a flight manoeuvre to enable orbit insertion by using the atmosphere to decelerate a spacecraft more mass efficiently than a typically used orbit insertion burn. The flight manoeuvre is of particular interest for missions to the ice giant planets as it could significantly reduce the interplanetary travel time.
However, aerocapture was never performed to this date, and no spacecraft has yet entered the atmosphere of an ice giant planet. State of the art numerical methods predict harsh flight conditions for such a mission, but still ablative heat shield materials are theoretically capable of handling the expected loads.
The atmospheric density and composition of the ice giant planets is not known precisely, which motivates a planetary probe mission to these planets in the first place. Whether the predictions for the atmospheric composition and the resulting load onto the spacecraft are correct, can only be verified by including a sensor-suite into the spacecraft’s Thermal Protection System (TPS).
Methodology
A sensor-suite is designed to be embedded into the ablative TPS of a spacecraft flying to the ice giant planets. Next to temperature and pressure gauges, this sensor-suite includes a miniature spectrometer. Challenges for such an instrument are optical access, extreme thermal loads, and potential signal contamination from pyrolysis gases.
A breadboard system is manufactured and tested in the plasma wind tunnel facility PWK4 at ice giant aerocapture peak heating conditions in multiple experiments.
Results
The sensor-suite’s instrumentation is operational throughout the entire duration of the ablation experiments. The data recorded is reproduceable between experiments and generally follow the expected trends.
Data from the miniature spectrometer is validated against the measurements from a high-resolution laboratory spectrometer.

Speaker: David Steuer (HEFDiG, Institute of Space Systems, University of Stuttgart)

15:00 Spectroscopy measurements on the KREPE-2 and KREPE-3 hypersonic flight experiments

The Kentucky Re-Entry Universal Payload System (KRUPS) is a university-led program that designs, tests, and flies instrumented orbital re-entry capsules that return flight data for the validation of atmospheric entry models. KREPE-2 successfully demonstrated onboard spectroscopy using a Hamamatsu C12880MA mini-spectrometer coupled to the stagnation region of the thermal protection system, providing time-resolved measurements of shock-layer radiation during atmospheric re-entry.

For KREPE-2, each of the five KRUPS capsules was instrumented with a spectrometer, and recorded the maximum and average emission of six-binned spectra. A physics-based forward model incorporating instrument response, blackbody radiation, atomic and molecular emission, atmospheric effects, and surface albedo is used to interpret these spectrally sparse measurements. Early results imply dominant contributions of Planck radiation from the capsule itself during the initial hypersonic descent, as well as additional species currently under investigation, such as CN, C2, Na, and C, while later measurements become increasingly influenced by atmospheric scattering and ocean albedo.

KREPE-3 expands the program to twelve re-entry capsules equipped, with most of them equipped with wither UV or UV-visible spectrometers, enabling more comprehensive characterization of shock-layer radiation and spacecraft demise. Combined with ongoing Bayesian inversion developments, these unique flight data will support the validation of radiation models and the development of next-generation thermal protection systems.

Speaker: Alexandre Martin (University of Kentucky)

15:30 → 16:00 Coffee Break at the Palazzo Roberti Courtyard

Piazza XX Settembre, 60-62, 70042 Mola di Bari BA
https://maps.app.goo.gl/hwoVgZsAzCMpJNwZ6

16:00 → 17:00 Plasma facilities, simulations and diagnostics: Thursday afternoon 2

Convener: Dr Louis Walpot (ESA/TEC-MPA)

16:00 Tunable Diode Laser Absorption Spectroscopy for Characterizing Magnetic Field Deformation in Hypersonic Flows

Background
Magnetohydrodynamic (MHD) aerobraking is a promising active thermal protection method for atmospheric re-entry. The Lorentz force generated by the interaction between the ionized shock layer and an applied magnetic field increases the shock standoff distance. This increase reduces the wall heat flux and augments drag through the reaction force [1]. Previous demonstration tests were conducted under low magnetic Reynolds number conditions (Rem < 1), in which the magnetic field was expected to undergo negligible deformation. In realistic flight scenarios, a high magnetic Reynolds number (Rem ≫ 1) is expected for vehicles with a large characteristic length and during high-velocity entry where there is a high degree of ionization. Under high-Rem conditions, the magnetic field can no longer be assumed to be rigidly fixed, but instead is expected to advect significantly with the plasma flow, such that its deformation must be taken into account [2]. Consequently, the Lorentz force may no longer act as intended, and the thermal protection effect and drag augmentation may be degraded. Correctly designing and evaluating MHD aerobraking for large flight vehicles under realistic flight conditions therefore requires capturing this field deformation. Corresponding experiments are required to better understand this phenomenon and to benchmark the sophisticated numerical simulation tools required to simulate this effect. This study describes a technique to measure this deformation experimentally through a non-contact, fast-response magnetic field measurement.
The authors have previously measured the magnetic field around a spherical model in the HEK-X expansion tube at the JAXA Kakuda Space Center by combining tunable diode laser absorption spectroscopy (TDLAS) with the Zeeman effect to exploit the resulting spectral splitting [3]. The split components were clearly observed at the stagnation point at the front of the model, where the flow comes to rest. At observation positions radially away from the stagnation point, the splitting profile became complex because the relative angle between the polarization plane and the magnetic field vector varies. The complex profile indicates that the split components can be enhanced through appropriate polarization control. In this study, the complex spectral profiles arising at locations such as the model shoulder are simplified through polarization control to accommodate a variety of measurement positions, and experiments aimed at detecting magnetic field deformation under high magnetic Reynolds number conditions are conducted in the X2 expansion tube at the University of Queensland.

Methods
Existing HEK-X data are used as the reference condition (Rem < 1), and tests under conditions expected to yield a high magnetic Reynolds number are conducted in the X2 expansion tube (University of Queensland). Argon is used as the test gas, and the Ar I 794.8 nm transition is measured with a DFB laser. The magnetic field is estimated from the splitting width of the absorption spectrum. Utilizing the fact that the splitting profile is determined by the relative angle between the polarization and the magnetic field, a half-wave plate is used to rotate the polarization and optimize the relative angle at each observation position, enhancing the spectral splitting. The derived magnetic field is evaluated by comparison with the static field.

Results and Conclusion
The effectiveness of polarization control was confirmed in a preliminary test using a DC discharge tube that generates a steady-state argon plasma. Varying the relative angle of the polarization with the half-wave plate systematically changed the intensity ratio between the split and unsplit components, demonstrating that the splitting profile can be controlled through polarization control. The results show that the splitting can be clearly resolved even at observation positions away from the stagnation point. Building on these results, tests under high magnetic Reynolds number conditions are conducted in the X2 expansion tube to detect magnetic field deformation as a deviation from the static field distribution. The proposed method provides a foundation for measuring magnetic field deformation under Rem ≫ 1 conditions using absorption spectroscopy with the Zeeman effect.

References
[1] Lefevre, A., Gildfind, D. E., Gollan, R. J., Jacobs, P. A., and James, C. M., "Magnetohydrodynamic Experiments of Total Heat Flux Mitigation for Superorbital Earth Reentry," AIAA Journal, Vol. 60, No. 9, 2022, pp. 5046-5059.
[2] Van Oeveren, S. B., Gildfind, D. E., Wheatley, V., and Gollan, R. J., "Numerical Study of Resistive Magnetohydrodynamics for a Superorbital Entry," AIAA SciTech Forum, AIAA SCITECH 2025 Forum, Orlando, FL, 6-10 January 2025.
[3] Muramatsu, T., Shimamura, K., Kakami, A., Katsurayama, H., Gildfind, D., Yatsuyanagi, S., and Tanno, H., "Characterization of Magnetic Field in Hypersonic Flow Using Tunable Diode-Laser Absorption Spectroscopy," AIAA SCITECH 2026 Forum, Orlando, FL, 12-16 January 2026, AIAA 2026-0676.c1.

Speaker: Takeaki Muramatsu (Tokyo Metropolitan University)

19:30 → 22:30 Social Dinner at the Restaurant "Pugliainbocca"

Via Principe Amedeo, 43, 70042 Mola di Bari BA
https://maps.app.goo.gl/2ZJzYgA933PQA2BdA

Friday 25 September

08:30 → 09:00 Bus ride to SITAEL

meeting point TBD

09:00 → 09:30 SITAEL: Marco Molina - SITAEL company presentation

09:30 → 10:30 SITAEL: Visit to the SITAEL HeadQuarter and laboratories

10:30 → 11:00 Coffee Break

11:00 → 12:30 High speed facilities, flight testing and propulsion: Friday morning

Convener: Dr Aaron Brandis (NASA Ames Research Center)

11:00 Investigations in the NASA Ames Low Density Shock Tube

At the previous RHTG meeting, we presented the history, initial design and construction of the Low Density Shock Tube (LDST), part of the Electric Arc Shock Tube (EAST) facility at NASA Ames. Since this meeting the LDST has become operational with one completed test series performed for Dragonfly entry to Titan and a second test series planned for comparing to shock radiation data in air mixtures collected in the 10.16 cm High Velocity Shock Tube (HVST) in EAST. LDST is a 54.3 cm diameter tube, with test section located 20.7 m from the primary diaphragm. The larger diameter LDST offsets a loss of test time expected at low pressures, allowing LDST to operate at lower density conditions than can be obtained in HVST. Additionally, LDST displays reduced shock deceleration due to a larger core to boundary layer ratio and a greater signal to noise ratio in absorption and emission due to increased optical pathlengths. This paper will discuss some of the initial results in LDST, including challenges of operation and comparison to HVST conditions.

The first significant challenge of operation is due to optical scattering within the tube, causing a significant signal in front of the shock that perturbs the target radiation measurement by as much as 30%. A detailed model of scattering is constructed which is consistent with the pre-shock signal being driven by diffuse scattering. The origin of diffusely scattered radiation covers a length scale that is several times larger than the tube diameter. Given that the measurement window in LDST is approximately 1/4th of the tube diameter, this requires knowledge of radiation sources that are not measured during the test. The model constructed shows that a simple correction of pre-shock signal subtraction is good to better than 10%. For future testing, a vacuum compatible black anodization is performed and this effect will be demonstrated in the coming test series.

A second operational challenge is an observed non-planarity at higher operation velocities. A similar issue observed in the old EAST LDST was attributed to poor quality of tube fabrication causing wave patterns in the tube. The fabrication issues are largely corrected in the new LDST, ruling out this phenomenon as a primary cause. Currently, this phenomenon is thought to be due to some of the specifics of the arc driver operation. To obtain complete discharge of the driver, it is necessary to fix the operating voltage above 20 kV, which limits the ability to tune the shock velocity by voltage modification. Instead, a mixture of Argon and Helium is used where the mixture ratio determines the velocity. At higher velocities, where the Helium ratio exceeds 60%, loss of planarity is observed. This roughly corresponds to where the radial fraction of Helium exceeds the diffusional mixing length with Argon, resulting in a stratified driver gas that travels faster on the side near the fill port. Strategies such as alternating gas load or increasing the driver gas mixing time have shown an initial improvement in planarity. Since then a dynamic driver gas mixing panel has been designed that will be used in the next test series, and efficacy of this approach will be discussed. Additionally, a 1 m buffer section, which is filled at higher pressure than the test gas, is being installed between the driver and driven section, which may help to planarize the shock interface and has been shown to improve test times in HVST.

Data collected in the first LDST test series includes spatially resolved emission data around the CN Violet and Red features, time-resolved scanning diode laser absorption, microwave interferometry and broadband ultraviolet absorption spectroscopy. The emission and absorption data show temporal trends in CN number densities and temperatures. The magnitude of radiance has been demonstrated to show quantitative agreement to overlap conditions in HVST, provided the data is presented in terms of particle (or Lagrangian) time. These data will be briefly discussed. The initial tests of the upcoming test series will span from 3-5 km/s and will be covered in this talk. This includes infrared and ultraviolet measurements of NO radiation with concurrent laser and broadband absorption spectroscopies. The improved signal to noise in the infrared spectrum is hoped to resolve some discrepancies in NO temperature and state population analysis previously presented for these conditions. Subsequent tests in the 8-10 km/s range, examining areas of significant model disagreement around lunar return, are planned but will not be covered in this talk.

Speaker: Brett Cruden (AMA Inc/NASA Ames)

11:30 Recent and Ongoing Upgrades to UQ's X2 Expansion Tube to Enhance Experimental Breadth, Experiment Quality, Condition Characterisation, and Experimental Measurements

The X2 expansion tube at the University of Queensland (UQ) is a long-running, high-enthalpy facility for planetary entry simulation, capable of reproducing conditions across all major planetary atmospheres at speeds up to 20 km/s. To meet increasing demands for higher fidelity and broader condition coverage, X2 is currently undergoing a comprehensive upgrade program aimed at expanding capability and improving experimental fidelity which will be discussed in this work.

X2 is capable of testing test models of up to around 100 mm diameter for around 100 microseconds. The ability to perform experiments with test models means that X2 is well equipped to study important planetary entry phenomena such as convective and radiative heat flux, thermochemical relaxation, shock standoff and novel phenomena such as magnetohydrodynamic aerobraking where magnets are used to influence the ionised post-shock planetary entry flow. X2 is also equipped with comprehensive physical and optical experimental hardware such as high-speed heat flux gauges, ultra-high-speed cameras, and an emission spectroscopy system ranging from the vacuum ultraviolet (VUV) down to 120 nm and the mid wave infrared (MWIR) up to 5 micron which allows us to comprehensively study the majority of important planetary entry phenomena.

At this point, X2 has been operational for 30 years. Recently we have engaged in a sustained effort to enhance and upgrade X2 to support its next 30 years and prepare it to take the high-fidelity experimental data required to continue improving our understanding of planetary entry phenomena. These upgrades target three key advances: (1) continuous expansion of the achievable velocity envelope, (2) improved reconstruction and diagnostics of test conditions, and (3) higher fidelity through reduced contamination and improved facility characterisation. This will be achieved through a multi-pronged approach of developing new facility driver conditions to increase the facility’s performance envelope at both the low and the high end, performing more detailed diagnostic measurements to improve test condition characterisation, and developing a high-vacuum system for X2’s shock tube to minimise contamination in our experiments.

Currently, with its powerful free-piston driver, X2 can achieve test conditions between roughly 6 and 15 km/s in air, which increases to up to 20 km/s for lighter giant planet entry hydrogen/helium test gases. Conditions around 3 km/s can be achieved using a fixed volume ‘cold driver’, but currently a gap exists between the capabilities of the cold driver and the current minimum performance free-piston driver condition. Recent work has been focused on designing new low compression ratio free-piston driver conditions to fill this gap. New conditions have been designed, preliminary ‘blanked off’ tests have been performed to test the driver conditions, new diaphragms have been procured, and in the coming months these new driver conditions will be tested on the facility.

In a similar manner, new driver conditions at the higher end have also been designed recently, allowing us to target even faster giant planet entry conditions above 20 km/s. Preliminary experiments have been performed which confirmed the higher performance of these conditions, and we are currently designing a heavier piston to better allow these conditions to be performed routinely on the facility.

Being a free-piston driven test facility, X2 is powered by a free-piston which compresses the facility’s driver gas up until a steel diaphragm ruptures, and then continues to compress the driver gas after diaphragm rupture to maintain an approximately constant driver pressure throughout the experiment. To better understand the driver and to aid in designing the new driver conditions and to understand the effect that the driver may have on X2 test conditions, we are in the process of installing an ‘instrumented pressure plate’ at the end of X2’s driver which will allow us to measure driver pressure, pressure next to the primary diaphragm, and hopefully piston position with a microwave system for every experiment. We are also in the process of installing a series of pressure ports down the length of X2’s driver to both track the piston and to measure the pressure behind it as travels down the tube. The pressure behind the piston is an important metric for understanding the pressure losses through the facility’s launcher which holds the piston before the experiment and through which compressed air from the facility’s high pressure reservoir flows through to propel the piston during its stroke.

In an expansion tube, like any shock tube based facility, measurements of facility shock speeds down the length of the facility’s driven tubes are necessary to aid reconstruction of the generated test conditions. Recently, there has been an acknowledgement that the shock speed history down the whole length of a facility’s driven tubes is important for properly understanding the final generated test condition. To address this, we have developed a microwave interferometry system for X2 which provides high-resolution shock speed measurements approximately every tube diameter down the full length of the facility for most test conditions. We are currently in the process of setting this system up so it will be used for all future X2 experiments and improving data analysis methods to increase measurement resolution even further for where it is needed.

In some cases the microwave interferometry system is not able to be used. For these cases, we have developed a new shock speed measurement system using ionisation gauges which discharge a capacitor when the flow passes a probe by placing two closely spaced electrodes in the flow at the surface of the probe. This system has the benefit of working well for low density conditions, which may give a very small voltage response when traditional high-speed pressure transducers or ‘PCBs’ are used for shock speed measurements. It also has the added benefit that any number of probes can be ‘daisy chained’ on a single instrumentation channel, making it a cheap and efficient way to perform medium resolution shock speed measurements for low density conditions. Currently we have been able to optimise the circuit to achieve a signal to noise ratio at shock arrival of 400 for these probes compared to 60 for a pressure transducer for an 18 km/s giant planet entry condition with an acceleration tube fill pressure of 0.5 Pa and a post-shock pressure of the order of a kilopascal. In the future, we are planning to further optimise the circuit to hopefully increase this signal to noise ratio further. We currently have two probes installed at the end of X2’s acceleration tube across from our standard PCB pressure transducer mounts. In the future, we have plans to install another 10 probes down the full length of X2’s acceleration tube after the circuit has been fully optimised.

While many X2 experiments are performed with air test gases, being a facility focused on the study of planetary entry, we also perform experiments using giant planet (hydrogen/helium), Venus and Mars (carbon dioxide and nitrogen), and Titan entry test gases (nitrogen and methane). When using non-air test gases especially, any residual air in the shock tube before the test gas is filled or water vapour which outgasses out of the facility’s walls when the shock tube is held at vacuum before the experiment, causes error which would not be present in the real planetary entry scenario. Currently, we use a standard rotary vane pump to evacuate X2’s shock tube, reaching ultimate pressures of the order of 10 Pa. This is not ideal for ensuring that all of the air is removed from the shock tube and that outgassing is maximised before the shock tube is filled, ensuring a high purity test gas. The tube is flushed with test gas several times to try to get all of the air out, but a better solution is needed. For this reason we are designing an automated system with a conformal poppet valve and a turbo pump to reach much lower base pressures and greatly increase the purity of the test gas for all of our experiments.

This presentation will discuss the current progress of these upgrades and how they are setting the X2 facility up for the future. Together, these upgrades position X2 for a new generation of high-fidelity planetary entry experiments, with improved coverage of the velocity space, enhanced diagnostic capability, and significantly reduced uncertainty in test condition reconstruction.

Speaker: Chris James (The University of Queensland)

12:00 Relevance of gas-phase radiation in cubesat-class hybrid rocket propulsion

The rapid growth of small-satellite and CubeSat missions has increased the demand for compact propulsion systems capable of providing safe, flexible, and reliable in-space maneuvering capability. Mission scenarios involving orbit insertion, formation flying, constellation reconfiguration, collision avoidance and de-orbiting require propulsion technologies that can be integrated within highly constrained platforms while preserving operational robustness. In this context, hybrid rocket engines represent a promising solution for small spacecraft because they combine intrinsic safety, throttling potential, restart capability, and relatively simple system architecture. However, their application to CubeSat-class propulsion requires accurate predictive models of internal ballistics and fuel regression, since the regression rate directly controls the mixture ratio, chamber pressure, thrust level, and overall engine performance. Among the mechanisms governing fuel regression, the wall heat balance plays a central role and results from the coupled contribution of convective and radiative heat transfer. While thermal radiation has been investigated in medium- and large-scale hybrid rocket engines, its relevance in small-scale configurations remains less clearly established, especially for hydrogen-peroxide-based systems intended for CubeSat propulsion. In this work, gas-phase thermal radiation is investigated in a 10 N-class hybrid rocket engine designed for small-satellite applications. The analysis is carried out through a coupled Computational Fluid Dynamics-gas/surface interaction framework, which allows the reacting flow field, wall heat transfer, and solid fuel regression to be predicted in a consistent manner. The numerical model solves the steady-state RANS equations for compressible, multicomponent reacting flows, using SST turbulence closure and a non-premixed combustion model based on the mixture fraction approach, in which a PDF formulation is coupled with chemical equilibrium calculations to account for turbulence-chemistry interaction. The fuel surface is treated through an iterative gas/surface interaction procedure, in which the local regression rate, wall temperature, and fuel mass injection are obtained from coupled surface mass and energy balances with Arrhenius-type HDPE pyrolysis. Radiative heat transfer in the participating medium is modeled through a WSGGM/DTRM approach, in which the spectral behavior of the gas is represented by a weighted sum of gray gases and the radiative transfer equation is solved by tracing discrete rays through the computational domain. The gas phase is treated as a non-scattering participating medium, and the radiation calculation accounts for the main radiatively active combustion products, namely H2O and CO2. After validation against experimental firing tests of a small-scale hydrogen-peroxide/HDPE hybrid rocket engine, the model is used to examine how chamber pressure, propellant combination, and geometric scale affect the radiative contribution to the wall heat balance. To further assess the robustness of the scale comparison, a dedicated geometric-scaling analysis is also performed. In this case, the pre- and post-chamber lengths of the small-scale GOX/HDPE engine are reduced to match the normalized geometric parameters of a reference large-scale configuration, while maintaining comparable oxidizer mass flux and port-to-injector diameter ratio.
The experimental reference consists of a pressure-regulated firing campaign designed to reproduce the operating envelope of a low-thrust hybrid rocket engine for small-satellite applications. The engine integrates a catalytic decomposition chamber, where hydrogen peroxide is converted into a high-temperature H2O/O2 mixture, with an axial gas-injection system feeding a combustion chamber composed of a pre-chamber, a cylindrical single-port HDPE grain, and a post-chamber. Since the target thrust level is of the order of a few newtons, the oxidizer mass flow rates are necessarily small, whereas the oxidizer mass flux is governed by the compact port geometry and falls in the range of about 19-33 kg/m2s. Under these experimentally validated operating conditions the results show that, for HTP-based operation in the 10 N thrust class, thermal radiation provides only a limited contribution to the fuel surface energy balance. Across the validated firing tests, the radiative fraction remains below 5% of the total wall heat flux, indicating that convective heat transfer dominates under practical CubeSat-scale operating conditions. Increasing the chamber pressure leads to a clear increase in the radiative wall heat flux, mainly because the higher gas density and larger partial pressures of the radiatively participating species increase the absorption coefficient and, consequently, the optical thickness of the medium. However, this enhancement does not translate into a comparable increase in the relative contribution of radiation to the overall wall heat balance. Within the investigated operating envelope, convective heat transfer remains the dominant mechanism, and radiation continues to represent only a secondary contribution to the total heat flux. A different behavior is obtained when the same small-scale engine is operated with gaseous oxygen. In this case, the higher combustion temperature leads to a marked increase in radiative heating, with the radiative contribution rising from 4.5% in the H2O2/HDPE case to 17.5% in the GOX/HDPE configuration. The comparison with a dynamically comparable 1 kN-class GOX/HDPE engine further shows that the increase in characteristic dimension leads to longer radiative path lengths and higher optical thickness, raising the radiative contribution up to 28.1%. The additional geometrically normalized small-scale analysis confirms that pre- and post-chamber geometry affects the detailed thermal field and wall heat balance: when the small-scale geometry is modified to match the normalized large-scale configuration, the radiative contribution decreases from 17.5% to 8.9%. Nevertheless, the overall physical trend remains unchanged.
Overall, the study shows that gas-phase radiation can be reasonably neglected as a first-order contribution in hydrogen-peroxide-based CubeSat-scale hybrid rocket engines operating under practical conditions, whereas it becomes increasingly relevant for higher-temperature propellant combinations and larger characteristic dimensions. The geometric-scaling analysis further indicates that differences in pre- and post-chamber layout influence the quantitative value of the radiative heat-flux fraction but do not modify the main conclusion regarding the governing role of propellant thermochemistry and optical thickness. These findings provide a validated numerical reference for the design and modeling of small-scale hybrid rocket engines for small-satellite missions and help define the conditions under which radiative heat transfer must be explicitly included in predictive internal-ballistics tools.

Speaker: Sergio Cassese (University of Naples "Federico II")

12:30 → 13:00 Wrap-up Closure, RHTG-11

13:00 → 13:30 Bus ride back to Mola di Bari city center