High-power inductively coupled plasma (ICP) wind tunnels are widely used to reproduce high-enthalpy environments relevant to atmospheric entry and hypersonic testing. Despite their importance, radiative heat transfer in ICP facilities is commonly neglected or modeled using simplified optically thin assumptions, and the impact of non-equilibrium radiation on plasma dynamics remains poorly quantified. In this work, a loosely coupled, multi-physics framework is developed to systematically investigate radiative cooling effects in the 350 kW Plasmatron X facility at the University of Illinois Urbana-Champaign. The approach self-consistently couples a magnetohydrodynamic plasma framework with a spectral radiative transport solver, eliminating the need for optically thin or empirical models. Simulations are performed for nitrogen and air plasmas over a wide range of operating pressures (1–101 kPa) and powers (100–350 kW). The results reveal a strong pressure dependence of radiative losses, with radiation contributing negligibly at low pressures, but becoming a dominant energy sink at elevated pressures. At atmospheric pressure, radiative losses account for up to approximately 32% and 22% of the input power for nitrogen and air plasmas, respectively, leading to substantial reductions in core plasma temperatures. Nitrogen plasmas consistently exhibit higher radiative losses than air as a result of increased concentrations of radiatively active species and higher electron number densities. Pressure–power maps of radiative heat loss relative to input power are constructed to quantify combined operating effects and to provide guidance for facility operation and modeling fidelity. Finally, an assessment of self-absorption demonstrates that the Plasmatron X torch operates predominantly in an optically thin regime, even at the highest power and pressure conditions considered.

Particle-laden effects in high-speed flows require a coupled Euler and Lagrangian prediction technique with varying fidelity of thermochemical models, depending on the simulation conditions of interest. This requirement makes the development of a conventional monolithic solver challenging to manage the different fidelity of the thermochemical models within a single computational framework. To address this, the present study proposes a multi-solver framework for the coupled Euler-Lagrangian predictions applicable to various particle-laden high-speed flow conditions. Volumetric and surface couplings are established between a particle solver ORACLE (OpenFOAM-based lagRAngian CoupLEr) and a thermochemical nonequilibrium flow solver based on an adaptable data exchange algorithm. The developed framework is then validated by predicting particle-laden supersonic nozzle flows and aerothermal heating around a hypersonic Martian atmospheric entry capsule. Finally, a quasi-1D approximation is proposed in conjunction with a surrogate method to efficiently and accurately predict particle-laden surface erosion, with quantified parametric uncertainty, for hypersonic aerothermal characterization.

Radiative transfer interactions with material ablation are critical contributors to vehicle heating during high-altitude, high-velocity atmospheric entry. However, the inherent complexity of fully coupled multi-physics models often necessitates simplifying assumptions, which may overlook key phenomena that significantly affect heat loads, particularly radiative heating. Common approximations include neglecting the contribution of ablation products, applying simplified frozen wall boundary conditions, or treating radiative transfer in a loosely coupled manner. This study introduces a high-fidelity, tightly coupled multi-solver framework designed to accurately capture the multi-physics challenges of hypersonic flow around an ablative body. The proposed approach consistently accounts for the interactions between shock-heated gases, surface material response, and radiative transfer. Our results demonstrate that including radiative heating in the surface energy balance substantially influences the ablation rate. Ablation products are shown to absorb radiative heat flux in the vacuum-ultraviolet spectrum along the stagnation line, while strongly emitting in off-stagnation regions. These findings emphasize the necessity of a tightly coupled multiphysics framework to faithfully capture the complex, multidimensional interactions in hypersonic flow environments, which conventional, loosely coupled models fail to represent accurately.

The dynamics for the NO(X2Π) + N(4S) ↔ N2(X1Σg+) + O(3P) reaction was followed in the 3A' electronic state using state-to-state (STS) and Arrhenius-based rates from two different high-level potential energy surfaces represented as a reproducing kernel Hilbert space (RKHS, PESB for "Basel PES") and permutationally invariant polynomials (PIPs, PESM for "Minnesota PES"). Despite the different number of bound states supported by PESB and PESM, the ignition points from STS and Arrhenius rates are at ∼10-6 s whether or not reverse rates are from assuming microreversibility or explicitly given. Conversion from NO to N2 is incomplete if Arrhenius rates are used, but complete turnover is observed if STS information is used. This is due to non-equilibrium energy flow and state dynamics, which requires a state-based description. Including full dissociation asymptotically leads to the correct 2:1 [N]:[O] concentration with little differences for the species' dynamics depending on the PES used for the STS information. In conclusion, concentration profiles from coarse-grained simulations are consistent over 14 orders of magnitude in time using STS information based on two different high-level PESs.

This work aims to study the energy transfer and recombination processes in N$_{2}$$\left(^{1}\sum^{+}_{g}\right)$+N$\left(^{4}S_{u}\right)$ and O$_{2}$$\left(^{3}\sum^{+}_{g}\right)$+O$\left(^{3}P_{2}\right)$ chemical systems when the system is suddenly cooled in a 0-D isothermal reactor thereby inducing strong non-equilibrium. A state-to-state (StS) study of the non-equilibrium phenomenon is crucial for developing accurate and efficient reduced-order models that can accurately capture the thermophysics involved. The gas mixture, consisting primarily of atoms at a high initial temperature of 10,000 K, is suddenly plunged into a low-temperature heat bath to simulate non-equilibrium recombination conditions. The population distribution of microscopic energy levels for each system is determined by solving a system of master equations. The conventional assumption of faster equilibration of rotational mode as compared to the vibrational mode holds for $ N_2 +N$, while it is not a very strong assumption for $ O_2 +O$ as the two relaxation time scales are comparable. Effective recombination rate constants for the quasi-steady state (QSS) period are calculated using the population distribution obtained by solving the master equations. It was also observed that the relaxation time constants for heating and cooling are different, with the time constant being lower for the cooling case due to anharmonicity effects in expanding flows. An attempt has also been made to use the insights from the StS analysis to determine an accurate binning strategy for the recombination processes involved in the two chemical systems.

In this work, we propose the thermochemical nonequilibrium model for electronic energy for hypersonic air flows. To decompose high- fidelity physical data into macroscopic quantities, electronic state-to-state analyses were conducted using isolated chemical reactor calculations. The excitation of electronic energy induced by heavy particle and electron impacts was analyzed, and the preferential behavior of electronic states in chemical reactions were investigated. Based on these findings, the electronic relaxation time, electron-electronic coupled ionization reaction rates, and the electronic energy loss ratio due to chemical reactions are proposed as parameters for modeling the thermochemical nonequilibrium of electronic energy. The proposed set of parameters was implemented in the formulation that separates the electronic energy pools from the free-electron. To investigate the validity of the proposed model, a calculation of nonequilibrium air behind a strong shock wave are simulated. The results show improved accuracy in representing the nonequilibrium behavior of electronic energy.

This work presents a vibrational and electronic (vibronic) state-to-state (StS) model for nitrogen plasmas implemented within a multi-physics modular computational framework to study non-equilibrium effects in inductively coupled plasma (ICP) discharges. The vibronic master equations are solved in a tightly coupled fashion with the flow governing equations eliminating the need for invoking any simplifying assumptions when computing the state of the plasma, leading to a high-fidelity physical modeling. The model's computational complexity is reduced via a maximum entropy coarse-graining approach, verified through zero-dimensional isochoric calculations. The coarse-grained StS model is employed to study the plasma discharge in the ICP facility at the von Karman Institute for Fluid Dynamics, Belgium. Results reveal pronounced discrepancies between StS predictions and those obtained based on local thermodynamic equilibrium (LTE) models, which are conventionally used in the simulation of such facilities. The analysis demonstrates a substantial departure of the internal state populations of atoms and molecules from the Boltzmann distribution. This has significant implications for energy coupling dynamics, affecting the discharge morphology. Further analysis reveals a quasi-steady-state population distribution in the plasma core, allowing for the construction of an efficient and 'self-consistent' macroscopic two-temperature (2T) formulation. Non-LTE simulations indicate significant disparities between the StS model and the commonly used Park 2T model, whereas the newly proposed 2T model aligns closely with StS simulations, capturing key features of non-equilibrium plasma formation. In particular, the current study highlights the importance of the vibrational-translational energy transfer term in shaping the plasma core morphology, suggesting a notable sensitivity to heavy-impact vibrational excitations and dissociative processes.

High-speed entry vehicles are subjected to harsh environments when entering the atmosphere. The high temperatures in this regime can lead to electronic excitation and ionization, producing large amounts of electromagnetic radiation as electrons transition between energy states. Furthermore, the high-temperature gas may chemically react with thermal protection system material, causing ablation and pyrolysis products to be injected into the near-wall region. Not only are both of these phenomena challenging to model in isolation, but they also may interact with each other. These interactions necessitate using a coupled simulation framework to adequately model the planetary entry environment. Such a framework is developed in this paper by joining together flow, radiation, and material response solvers. The coupled codes are used to study the impact of radiation and material response on the Stardust capsule during Earth entry. Using the framework, it is seen that ablation creates a notable decrease in the heat flux at the vehicle surface, while radiation has a much smaller effect. Furthermore, under the assumptions and limitations of the current study, the ablation products are shown to have minimal impact on the radiative character of the boundary layer, as the near-wall gas is still dominated by nitrogen and oxygen, with very little contribution to emission or absorption by carbon species.

Inductively coupled plasma (ICP) torches generate high-enthalpy jets to study the thermochemical response of materials at high temperatures. The current paper presents a simulation framework capable of modeling the plasma jet generated by an ICP facility in a three-dimensional and time-accurate manner. This framework provides a valuable resource for studying the hydrodynamics of plasma jets and for assisting in the design of experimental campaigns. The framework is applied to study the plasma jet in the University of Illinois at Urbana-Champaign Plasmatron X ICP facility and compare predictions with experimental data obtained using high-speed imaging. The comparison shows that the numerical results are qualitatively similar to the experimental data, providing preliminary validation for the simulation framework. The high-fidelity spatio-temporal numerical data are used to visualize and analyze the plasma jet. Under the adopted operating conditions, the plasma jet is found to be highly turbulent, with periodic releases of hot pockets of gas from the jet inlet being observed. The baroclinic torque is shown to have a significant effect in destabilizing the plasma jet flow field.

This work aims to study the energy transfer and recombination processes of N-2 ((1)Sigma(+)(g))+N(S-4(u)) and O-2(3) Sigma(+)(g) + O (P-3(2)) chemical systems in a 0-D isothermal reactor. The gas mixture which consiStS primarily of atoms and a small percentage of molecules, initialized at a high internal temperature of 10000 K, is suddenly plunged into a heat bath at a lower temperature of upto 2500 K for nitrogen and 1500 K for oxygen thus inducing recombination. The internal energy state population distribution for each molecular system is determined for a wide range of simulation conditions by numerically solving a system of master equations. The internal, rotational and vibrational temperatures are extracted from the population distribution by computing average energy. The conventional assumption of faster equilibration of rotational mode as compared to the vibrational mode holds for N-2+N chemical system while it is not a very strong assumption for O-2+O as the two relaxation times are comparable. A macroscopic recombination rate constant is calculated by solving the master equations to determine an effective rate constant for the quasi-steady state (QSS) period. The QSS assumption holds well for high-lying energy levels while the low-lying energy levels experience a change in relative population distribution as recombination progresses.

This work proposes a preferential model of species electronic energy transfer interacting with other energy modes in hypersonic flows. The model has been grounded on the foundation of higher fidelity state-to-state(StS) simulations as the reference data. Zero-dimensional isothermal chemical reactor calculations are carried out using a StS model, which considers the state-to-state collisional transitions among the species electronic states. It is then followed by the model reduction to compress the information obtained from the StS calculations into a modified two-temperature(2T) model formulation by updating existing chemical-kinetic parameters and adding physical terms that have been missed. As a verification, one-dimensional post-normal shock flows in a pure nitrogen mixture are then simulated. With the proposed preferential model, the degree of ionization along the shock layer is predicted with improved accuracy, while further improvement can be achieved regarding the prediction of molecular dissociation.

This study aims to model collisional-radiative transitions in hypersonic shock layers in a self-consistent manner. To achieve this purpose, sets of electronic state-resolved chemical kinetics are constructed for N-2-O-2 and N-2-CH4 mixtures to study hypersonic atmospheric entry conditions to Earth and Titan. The constructed model is then applied to two-dimensional axisymmetric flows around a 3 m radius sphere including afterbody region. As a comparative group, the conventional quasi-steady-state model is considered with a reduced-order model closure on top of the electronic state-resolved approach to have consistency between the two models. The result shows that; (1) the electronic populations are not in the quasi-steady-state (QSS) near the shoulder and the afterbody and (2) this causes underprediction of the afterbody radiative heating.

This paper investigates the impact of different reaction mechanisms, from dissociation to exchange and inelastic processes, on the evolution of a..2 +.. chemical system at non-equilibrium in a 0D reactor at high temperatures. The problem is representative of shock-heated gas and it is of interest for hypersonic applications e.g., to understand the complex thermochemical processes occurring ahead a spacecraft entering the atmosphere. We perform an adjoint-based sensitivity analysis exploiting two different molecular internal models of increasing fidelity. Namely, the rovibrational State-to-State model and the Vibrational-Specific model. The sensitivity to the reaction rates is assessed for the global dissociation rate. Results offer insights concerning the impact of individual reaction coefficients on the objective function, providing an in-depth understanding of their role in the thermochemical evolution of the system.

During high-speed atmospheric entry, molecules can become excited due to the extreme temperatures, releasing large amounts of electromagnetic radiation as the electrons transition between energy states. This radiation creates a cooling effect in the shock layer, decreasing the stand-off distance of the shock wave, as well as increasing the heat flux to the vehicle surface as photons are absorbed by the wall. Due to these effects, it is important to determine under what conditions strong radiation is expected so that it can be accounted for in the design process. This paper focuses on the impact of radiation on NASA's Dragonfly mission, which aims to deliver an exploratory rotorcraft to Saturn's moon, Titan. Simulations are carried out for the Dragonfly capsule's trajectory as it enters Titan's atmosphere using a two-way coupling between US3D and MURP, where the former handles the flow physics and the latter the radiation transport. This coupling framework is leveraged to determine the significance of radiative heating on the afterbody and the necessary fidelity required to achieve a reasonable prediction. It is shown the wavelength range considered creates the largest impact on the solution. Accounting for non-Boltzmann radiation is shown to decrease the radiative heat flux, which is in line with previous studies.

The present work focuses on the study of non-equilibrium effects in radio frequency inductively coupled plasmas (ICP) using state-of-the-art electronic State-to-State (StS) model. A multi-physics computational framework has been developed to simulate the magnetohydrodynamics (MHD) phenomena inside ICPs. The fluid governing equations are discretized in space based on a cell-centered finite volume method. A preconditioned compressible formulation is adopted to tackle the stiffness resulting from low Mach numbers. Non-local thermodynamic equilibrium (NLTE) calculations are performed using either multi-temperature or State-to-State models. Electromagnetic equations are solved via a mixed finite element method. Two solvers, one for the fluid and the other for the electromagnetic phenomena, are coupled in an explicit fashion to model NLTE ICP discharges. Calculations performed using a two-temperature NLTE model highlight the importance of non-equilibrium modeling in the torch. Further, simulations performed using an electronic State-to-State model show significant deviations of the population of high-lying states from local equilibrium (e.g., Boltzmann distribution).