Physical models for nonequilibrium plasma flow simulations at high speed re-entry conditions

The project focuses on diatomic gases with vibrational and electronic mode disequilibrium, environments commonly encountered in the shock layer of spacecrafts while re-entering into earth atmosphere. The known-how gained during former aerospace missions allows for the key role of Computational Fluid Dynamics (CFD) simulations in the development of hypersonic applications to be highlighted in strong interaction with ground testing. The relevance of these simulations is linked to aerothermochemistry features such as high-temperature gas effects in hypersonic flows. For instance, the design of the heat shield used to protect spacecraft is based on the estimation of the heat fluxes to the vehicle surface by means of experimental and numerical resources. CFD predictions of these quantities strongly rely upon the accuracy of the model used to describe the flow. During the entry of a spacecraft into a planetary atmosphere, the translational energy of the fluid particles rises through the shock. A high number of collisions is then needed to equilibrate the internal energy modes (electronic for atoms; rotational, vibrational, and electronic for molecules) with the translational one. Hence, these modes turn out to be in nonequilibrium at the convective time scale. In addition, particles dissociate, recombine, and ionize in the shock-layer, the flow is found to be in chemical nonequilibrium. The prediction of the heat fluxes strongly depends on the completeness and accuracy of the physical model used to describe thermo-chemical nonequilibrium phenomena. There is thus a critical need to develop an accurate model for the Lunar and Martian return missions. In this manucript, we present a finite rate chemistry mechanism to determine the species concentration. The rotational mode is considered in equilibrium with the translational mode. Vibrational energy and free electron kinetic energy equations deal with thermal nonequilibrium. Radiative heating can approach and possibly exceed the level of convective heating that results from the frictional flow of the atmosphere over the thermal protection material. This situation occurs during Earth's reentries at given the large amount of radiators produced in the shock layer at hypervelocity ($v > 10$ km/s). Radiation modeling involves the determination of population distributions over the internal energy levels and of the radiative contribution of each of these levels. In flight conditions, the electronic energy level populations are expected to depart from equilibrium. We will resort here to a hybrid collisional-radiative/Boltzmann model. The model adopted, combines an electronic collisional-radiative model to determine the population of the electronic energy levels by solving a system of rate equations and Boltzmann distributions for the rotational and vibrational energy level populations. One-dimensional shock-tube and nozzle flow solvers have been developed in order to validate the models. The models have been assessed by means of comparison between the computed results and data obtained by hypervelocity demonstrators and shock-tube experiments representative of flight conditions. The detailed CR model employed for the analysis of nonequilibrium flows in compressing as well as expanding situations has been used as a baseline to create a new reduced kinetic mechanisms for air flow conditions typical of reentry applications. The number of electronic levels of atoms and molecules considered in the model has been reduced by grouping similar energy levels. This allowed us to extend the use of the CR model for 2 and 3D computational fluid dynamic simulations. The final part of the thesis is devoted to the implementation of the simplified model in multidimensional (2D and 3D) solver for re-entry application, which allows to simulate the flowfield surrounding a space vehicle while reentering into earth atmosphere

Adaptive physics-informed neural operator for coarse-grained non-equilibrium flows

This work proposes a new machine learning (ML)-based paradigm aiming to enhance the computational efficiency of non-equilibrium reacting flow simulations while ensuring compliance with the underlying physics. The framework combines dimensionality reduction and neural operators through a hierarchical and adaptive deep learning strategy to learn the solution of multi-scale coarse-grained governing equations for chemical kinetics. The proposed surrogate's architecture is structured as a tree, with leaf nodes representing separate neural operator blocks where physics is embedded in the form of multiple soft and hard constraints. The hierarchical attribute has two advantages: i) It allows the simplification of the training phase via transfer learning, starting from the slowest temporal scales; ii) It accelerates the prediction step by enabling adaptivity as the surrogate's evaluation is limited to the necessary leaf nodes based on the local degree of non-equilibrium of the gas. The model is applied to the study of chemical kinetics relevant for application to hypersonic flight, and it is tested here on pure oxygen gas mixtures. In 0-D scenarios, the proposed ML framework can adaptively predict the dynamics of almost thirty species with a maximum relative error of 4.5% for a wide range of initial conditions. Furthermore, when employed in 1-D shock simulations, the approach shows accuracy ranging from 1% to 4.5% and a speedup of one order of magnitude compared to conventional implicit schemes employed in an operator-splitting integration framework. Given the results presented in the paper, this work lays the foundation for constructing an efficient ML-based surrogate coupled with reactive Navier-Stokes solvers for accurately characterizing non-equilibrium phenomena in multi-dimensional computational fluid dynamics simulations

Impact of State-Specific Flowfield Modeling on Atomic Nitrogen Radiation

A hypersonic flowfield model that treats electronic levels of the dominant afterbody radiator, N, as individual species is presented. This model allows electron-ion recombination rate and two-temperature modeling improvements, the latter which are shown to decrease afterbody radiative heating by up to 30%. This increase is primarily due to the addition of the electron-impact-excitation energy-exchange term to the energy equation governing the vibrational-electronic-electron temperature. This model also allows the validity of the often applied quasi-steady state (QSS) approximation to be assessed. The QSS approximation is shown to fail throughout most of the afterbody region for lower electronic states, although this impacts the radiative intensity reaching the surface by less than 15%. By computing the electronic state populations of N within the flowfield solver, instead of through the QSS approximation in the radiation solver, the coupling of nonlocal radiative transition rates to the species continuity equations becomes feasible. Implementation of this higher- fidelity level of coupling between the flowfield and radiation solvers is shown to increase the afterbody radiation by up to 50% relative to the conventional model

Extension of Multiband Opacity-Binning to Molecular, Non-Boltzmann Shock Layer Radiation

For accurate predictions of shock layer radiative heating to reentry vehicles, the smeared rotational band (SRB) model is appropriate for molecular band systems with negligible self absorption, meaning they are optically-thin. However, for band systems with noticeable self absorption, the orders-of-magnitude more computationally expensive line-by-line (LBL) approach is required. Considering past and proposed NASA missions, the molecular band systems most likely to require the LBL approach are the CO 4th-Positive, CN Violet, and CO2 IR bands. The CO 4th- Positive and CN Violet bands are required for Mars entry at velocities greater than 6 km/s, with the CN Violet band also required for Titan entry. These two bands typically emit strongly in flow regimes with non-Boltzmann upper electronic state populations. The CO2 IR band is required for Mars entry at velocities below 5 km/s. This ro-vibrational band system is typically assumed to contain Boltzmann populations of radiating levels (the quality of this assumption is the subject of other studies)

Microscopic Simulation and Macroscopic Modeling for Thermal and Chemical Non-Equilibrium

This paper deals with the accurate microscopic simulation and macroscopic modeling of extreme non-equilibrium phenomena, such as encountered during hypersonic entry into a planetary atmosphere. The state-to-state microscopic equations involving internal excitation, de-excitation, dissociation, and recombination of nitrogen molecules due to collisions with nitrogen atoms are solved time-accurately. Strategies to increase the numerical efficiency are discussed. The problem is then modeled using a few macroscopic variables. The model is based on reconstructions of the state distribution function using the maximum entropy principle. The internal energy space is subdivided into multiple groups in order to better describe the non-equilibrium gases. The method of weighted residuals is applied to the microscopic equations to obtain macroscopic moment equations and rate coefficients. The modeling is completely physics-based, and its accuracy depends only on the assumed expression of the state distribution function and the number of groups used. The model makes no assumption at the microscopic level, and all possible collisional and radiative processes are allowed. The model is applicable to both atoms and molecules and their ions. Several limiting cases are presented to show that the model recovers the classical twotemperature models if all states are in one group and the model reduces to the microscopic equations if each group contains only one state. Numerical examples and model validations are carried out for both the uniform and linear distributions. Results show that the original over nine thousand microscopic equations can be reduced to 2 macroscopic equations using 1 to 5 groups with excellent agreement. The computer time is decreased from 18 hours to less than 1 second

Deep Learning Closure of the Navier-Stokes Equations for Transition-Continuum Flows

The predictive accuracy of the Navier-Stokes equations is known to degrade at the limits of the continuum assumption, thereby necessitating expensive and often highly approximate solutions to the Boltzmann equation. While tractable in one spatial dimension, their high dimensionality makes multi-dimensional Boltzmann calculations impractical for all but canonical configurations. It is therefore desirable to augment the Navier-Stokes equations in these regimes. We present an application of a deep learning method to extend the validity of the Navier-Stokes equations to the transition-continuum flows. The technique encodes the missing physics via a neural network, which is trained directly from Boltzmann solutions. While standard DL methods can be considered ad-hoc due to the absence of underlying physical laws, at least in the sense that the systems are not governed by known partial differential equations, the DL framework leverages the a-priori known Boltzmann physics while ensuring that the trained model is consistent with the Navier-Stokes equations. The online training procedure solves adjoint equations, constructed using algorithmic differentiation, which efficiently provide the gradient of the loss function with respect to the learnable parameters. The model is trained and applied to predict stationary, one-dimensional shock thickness in low-pressure argon

Calculation of Thermochemical Properties of Carbon-cluster Ablation Species

Carbon clusters and hydrocarbons are constituents of the pyrolysis gases injected into the boundary layer of a space vehicle with a carbonaceous heat shield. These molecules have absorption spectra in the VUV and UV region that match the emission spectra of atomic nitrogen and oxygen. Hence, they can potentially absorb the radiation impinging on the heat shield of the space vehicle. This paper studies the ground state thermochemical properties and low-lying excited electronic states of potential radiation absorbing molecules present in the boundary layer using ab initio quantum chemistry methods. These results provide a more accurate prediction of the radiative heat flux on the surface which can lead to improvement in the design of the thermal protection system

The Effect of the Spin-Forbidden Co((sup 1) Sigma plus) plus O((sup 3) P) Yields CO2 (1 Sigma (sub G) plus) Recombination Reaction on Afterbody Heating of Mars Entry Vehicles

Vibrationally excited CO2, formed by two-body recombination from CO((sup 1) sigma plus) and O((sup 3) P) in the wake behind spacecraft entering the Martian atmosphere reaction, is potentially responsible for the higher than anticipated radiative heating of the backshell, compared to pre-flight predictions. This process involves a spin-forbidden transition of the transient triplet CO2 molecule to the longer-lived singlet. To accurately predict the singlet-triplet transition probability and estimate the thermal rate coefficient of the recombination reaction, ab initio methods were used to compute the first singlet and three lowest triplet CO2 potential energy surfaces and the spin-orbit coupling matrix elements between these states. Analytical fits to these four potential energy surfaces were generated for surface hopping trajectory calculations, using Tully's fewest switches surface hopping algorithm. Preliminary results for the trajectory calculations are presented. The calculated probability of a CO((sup 1) sigma plus) and O((sup 3) P) collision leading to singlet CO2 formation is on the order of 10 (sup -4). The predicted flowfield conditions for various Mars entry scenarios predict temperatures in the range of 1000 degrees Kelvin - 4000 degrees Kelvin and pressures in the range of 300-2500 pascals at the shoulder and in the wake, which is consistent with a heavy-particle collision frequency of 10 (sup 6) to 10 (sup 7) per second. Owing to this low collision frequency, it is likely that CO((sup 1) sigma plus) molecules formed by this mechanism will mostly be frozen in a highly nonequilibrium rovibrational energy state until they relax by photoemission

Multi-domain analysis and prediction of the light emitted by an inductively coupled plasma jet

Inductively coupled plasma wind tunnels are crucial for replicating hypersonic flight conditions in ground testing. Achieving the desired conditions (e.g., stagnation-point heat fluxes and enthalpies during atmospheric reentry) requires a careful selection of operating inputs, such as mass flow, gas composition, nozzle geometry, torch power, chamber pressure, and probing location along the plasma jet. The study presented herein focuses on the influence of the torch power and chamber pressure on the plasma jet dynamics within the 350 kW Plasmatron X ICP facility at the University of Illinois at Urbana-Champaign. A multi-domain analysis of the jet behavior under selected power-pressure conditions is presented in terms of emitted light measurements collected using high-speed imaging. We then use Gaussian Process Regression to develop a data-informed learning framework for predicting Plasmatron X jet profiles at unseen pressure and power test conditions. Understanding the physics behind the dynamics of high-enthalpy flows, particularly plasma jets, is the key to properly design material testing, perform diagnostics, and develop accurate simulation modelsComment: 22 pages (including figures, appendix, and references); 13 figure