In supersonic and hypersonic flows, thermal and chemical non-equilibrium is one of the fundamental aspects that must be taken into account for the accurate characterization of the plasma. In this paper, we present an optimized methodology to approach plasma numerical simulation by state to-state kinetics calculations in a fully 3D Navier-Stokes CFD solver. Numerical simulations of an expanding flow are presented aimed at comparing the behavior of state-to-state chemical kinetics models with respect to the macroscopic thermochemical non-equilibrium models that are usually used in the numerical computation of high temperature hypersonic flows. The comparison is focused both on the differences in the numerical results and on the computational effort associated with each approach.

A Monte Carlo method has been developed for the calculation of binary diffusion coefficients in gas mixtures. The method is based on the stochastic solution of the linear Boltzmann equation obtained for the transport of one component in a thermal bath of the second one. Anisotropic scattering is included by calculating the classical deflection angle in binary collisions under isotropic potential. Model results are compared to accurate solutions of the Chapman-Enskog equation in the first and higher orders. We have selected two different cases, H(2) in H(2) and O in O(2), assuming rigid spheres or using a model phenomenological potential. Diffusion coefficients, calculated in the proposed approach, are found in close agreement with Chapman-Enskog results in all the cases considered, the deviations being reduced using higher order approximations. (C) 2011 Elsevier Inc. All rights reserved.

The present paper describes a Monte Carlo code to simulate the cascade of electron-hole pairs and phonons generated when a low-energy X-ray photon is absorbed by a material. The model has been applied to study the response to UV or soft X-ray radiation of diamond and silicon, focused on the case of two-layer material made of diamond film grown on silicon. Typically the statistical distribution of the electron-hole cascade is macroscopically parameterized by the mean energy required to create an electron-hole pair W and the Fano factor F. The results for the pure materials are in agreement with the values present in the literature. Moreover we found an enhancement of the Fano factor and a super-Poissonian behaviour of the statistical distribution of the pairs, typical of correlated systems.

A simplified method to calculate the electronic partition functions and the correspondingthermodynamic properties of atomic species is presented and applied to C(I) up to C(VI) ions. Themethod consists in reducing the complex structure of an atom to three lumped levels. The groundlevel of the lumped model describes the ground term of the real atom, while the second lumpedlevel represents the low lying states and the last one groups all the other atomic levels. It is alsoshown that for the purpose of thermodynamic function calculation, the energy and the statisticalweight of the upper lumped level, describing high-lying excited atomic states, can be satisfactorilyapproximated by an analytic hydrogenlike formula. The results of the simplified method are ingood agreement with those obtained by direct summation over a complete set (i.e., including allpossible terms and configurations below a given cutoff energy) of atomic energy levels. Themethod can be generalized to include more lumped levels in order to improve the accuracy.

The paper presents three collisional-radiative models developed to investigate non-equilibrium chemistry andradiation in hypersonic shock tubes operating with different planetary atmospheres. An hybrid collisional-radiative model,employing the state-to-state kinetics of electronically excited states of molecules and the multi-temperature approximationfor the vibrational degree of freedom is presented first, and applied to the numerical rebuilding of experimental shock tubeemission spectra. Next, an hybrid collisional-radiative model for ionized air is presented. This model consider the state-tostateapproach for electronic states of atoms and the multi-temperature model for the vibrational populations of diatomicmolecules in their ground electronic state. A radiative transport equation is also solved to determine radiative source termsin the kinetic scheme and the enthalpy production due to radiation. The third model considers the state-to-state collisionalradiativemodel of Jupiter's atmosphere, self-consistently coupled with the Boltzmann equation for free electrons and theradiative transfer equation for the radiation transport in one-dimensional slab geometry.

An efficient algorithm to calculate the contribution of electron-electron collisions in the Boltzmann equation for free electrons, in the two-term approximation is presented. The electron-electron collision term must be energy-conserving, while, due to non-linearity, commonly used algorithms do not satisfy this requirement. The efficiency of the algorithm make feasible the use of a non-linear iterative solver to conserve electron energy in electron-electron collisions.

A CFD solver, using Residual Distribution Schemes on unstructured grids, has been extended to deal with inviscid chemical non-equilibrium flows. The conservative equations have been coupled with a kinetic model for argon plasma which includes the argon metastable state as independent species, taking into account electron-atom and atom-atom processes. Results in the case of an hypersonic flow around an infinite cylinder, obtained by using both shock-capturing and shock-fitting approaches, show higher accuracy of the shock-fitting approach.

An approximate method for calculating the electronic partition functions of atomic systems is reported. The method is based on the idea of combining a multitude of atomic energy levels into two or three grouped levels. Dimensionless formulation suitable for practical calculations is presented. Application to real systems shows that two grouped levels are enough to model hydrogen-like and noble gas atoms, whereas three grouped levels are required to describe atoms with low lying excited states. Two methods for the calculation of degeneracy and energy values of the grouped levels are investigated. Representative mono-atomic LTE plasma properties calculations are reported. The results agree with accurate computations using partition functions that include several thousands energy levels.

A Roe's flux-difference splitting scheme has been implemented using the NVIDIA CUDA architecture andhas been applied to solve the two-dimensional compressible Euler equations. Different standard test caseshave been considered in order to estimate the speed-up of GPU computing with respect to CPU calculation.A detailed description of the kernel configuration has been provided and a theoretical analysis of theGPU execution time as a function of the number of threads managed by the kernels is also reported. Theloss of performance has been fully described consequent to the use of zero-copy memory. Significantperformance improvements have been obtained by using a more recent GPU and CUDA Toolkit. A testcase on multi-GPU architecture has been presented in the domain decomposition approach.

A collisional-radiative model (CRM) of a plasma composedof H2, H+2 , H, H+, He, He+, e?, is appliedto study the relaxation processes behind an hypersonicshock wave under conditions reproducing an atmosphericentry in Jupiter's atmosphere. The CRM is coupled witha Boltzmann equation solver, for the determination of theelectron energy distribution function, and with a radiativetransfer equation for calculating the specific intensityIn , radiative rate coefficients and radiative energy transferin one-dimensional slab geometry. The model predictshighly non-equilibrium electron and atomic distributionsas well as strong reabsorption of atomic radiationin the post-shock region. A comparison among distributionsobtained using optically thick and optically thinplasma approximation against the fully coupled calculationis also presented.

An advanced self-consistent plasma physics model including non-equilibrium vibrational kinetics, a collisional radiative model for atomic species, a Boltzmann solver for the electron energy distribution function, a radiation transport module coupled to a steady inviscid flow solver and, has been applied to study non-equilibrium in high enthalpy flows for Jupiter's atmosphere. Two systems have been considered, a hypersonic shock tube and nozzle expansion, emphasizing the role of radiation reabsorption on macroscopic and microscopic flow properties. Large differences are found between thin and thick plasma conditions not only for the distributions, but also for the macroscopic quantities. In particular, in the nozzle expansion case, the electron energy distribution functions are characterized by a rich structure induced by superelastic collisions between excited species and cold electrons.

Non-equilibrium effects in hydrogen plasmas have been investigated in different systems, ranging from RF plasmas to corona discharges. The existing measurements of vibrational and rotational temperatures, obtained by different spectroscopical techniques, are reported, rationalized by results calculated by kinetic models. Input data of these models are discussed with particular attention on the dependence of relevant cross sections on the vibrational quantum number. Moreover, the influence of the vibrational excitation of H(2) molecules on the translational distribution of atoms in ground and excited levels is shown. Finally, a collisional radiative model for atomic hydrogen levels, based on the coupling of the Boltzmann equation for electron energy distribution function (EEDF) and the excited state kinetics, is presented, emphasizing the limits of quasi-stationary approximation. In the last case, large deviations of the EEDF and atomic level distributions from the equilibrium are observed.

A Graphics Processing Unit (GPU)-CUDA C and (Multi-core)-OpenMP versions of the Reaction Ensemble Monte Carlo method (REMC) are presented. The REMC algorithm is a powerful tool to investigate the equilibrium behavior of chemically reacting systems in highly non-ideal conditions. Both the GPU and the Multi-core versions of the code are particularly efficient when the total potential energy of the system must be calculated, as in the constant-pressure systems. Results, obtained in the case of Helium plasma at high pressure, show differences between real and ideal cases.

Advanced models of elementary processes in plasmas are based on the self--consistent approach, solving at the same time the Boltzmann equation for free electrons and the master equation for the evolution of species concentration and the distribution of internal state. In some conditions, it is very important also to couple these models with the radiation transport, to consider non--local effects, because the radiation emitted in one location can be absorbed in a different position. This aspects is very important in high pressure, conditions met in high pressure pulsed discharges. The new set of e-molecule cross sections, extend the available data, considering processes for the whole vibrational ladder, has dramatic effects on the kinetics, increasing considerably the energy injected in internal degrees of freedom. This work is intended to investigate such effects, comparing results obtained by using old cross section set or recently calculated complete set.

A zero-dimensional collisional-radiative (CR) model, coupled self-consistently with the electron Boltzmann equation, has been applied to the description of a metallic-laser induced plasma at experimental conditions typical of LIBS experiment. To take in account expansion effects, the experimental temperature and total number density as function of time have been used as input data. Plasma composition and the simultaneous time evolution of both heavy particle level distributions and the electron energy distribution function have been calculated by taking into account the most relevant collisional and radiative processes. This approach estimates the hierarchy of the elementary processes during the expansion and possible deviations from LTE conditions. The comparison of the experimental and theoretical results shows a good agreement, but at the same time new questions arise on the analysis of spectroscopic results and on the assumption generally made in LIBS.

The Two-Level Distribution (TLD) model has been improved for extension to air kinetics. The model is based on the evidence that rate coefficients are strictly correlated to the tail of the vibrational distribution rather than to vibrational temperature. TLD model reproduces, with high accuracy and low computational resources, the results obtained using detailed State-to-State (STS) kinetics. © 2012 American Institute of Physics.

A model to predict the emissivity and absorption coefficient of atomic hydrogen plasma is presented in detail. Non-equilibrium plasma is studied through coupling of the model with a collisional-radiative code for the excited states population as well as with the Boltzmann equation for the electron energy distribution function.

The space exploration is nowadays assisted by realistic modeling of re-entry conditions of space vehicles in planetary atmospheres, for the design of thermal protection systems. The detailed kinetic modeling relies on the accurate description of elementary process dynamics, including the role of the excitation of the internal degrees of freedom of chemical species. Efforts in the construction of a complete and consistent dynamical information are presented, focusing on hydrogen plasmas relevant to the Jupiter atmosphere. Examples of numerical experiments are given, emphasizing the relevance of the adopted state-to-state approach in reproducing the onset of non-equilibrium internal distributions governing the plasma system evolution. © Springer-Verlag 2011.

The space exploration is nowadays assisted by realisticmodeling of re-entry conditions of space vehicles inplanetary atmospheres, for design of thermal protection systems.The detailed kinetic modeling relies on the accuratedescription of elementary process dynamics, including therole of the excitation of the internal degrees of freedom ofchemical species. Efforts in the construction of a completeand consistent dynamical information are presented, focusingon hydrogen plasmas relevant to the Jupiter atmosphere.Examples of numerical experiments are given, emphasizingthe relevance of the adopted state-to-state approach inreproducing the onset of non-equilibrium internal distributionsgoverning the plasma-system evolution.

A state-to-state model of H-2/He plasmas coupling the master equations for internal distributions of heavy species with the transport equation for the free electrons has been used as a basis for implementing a multi-temperature kinetic model. in the multi-temperature model internal distributions of heavy particles are Boltzmann, the electron energy distribution function is Maxwell, and the rate coefficients of the elementary processes become a function of local temperatures associated to the relevant equilibrium distributions. The slatedo-state and multi-temperature models have been compared in the case of a homogenous recombining plasma, reproducing the conditions met during supersonic expansion though converging-diverging nozzles.

The role of vibrational excitation in affecting the dissociation under discharge conditions characterized by reduced electric field E/N ? 80 Td has been investigated in N2. The kinetic calculations have been performed using a self-consistent approach, solving at the same time the master equation for the composition and the distribution of internal states (vibrational and electronic) and the Boltzmann equation for the electron energy distribution function. The results show that vibrational mechanisms involving heavy particle excited states dominate electron impact dissociation mechanisms involving the whole vibrational ladder for E/N < 50 Td, the two mechanisms being competitive for E/N > 50 Td.

The formation of the electron energy distribution function in nanosecond atmospheric nitrogen discharges is investigated by means of self-consistent solution of the chemical kinetics and the Boltzmann equation for free electrons. The post-discharge phase is followed to few microseconds. The model is formulated in order to investigate the role of the cross section set, focusing on the vibrational-excitation by electron-impact through resonant channel. Four different cross section sets are considered, one based on internally consistent vibrational-excitation calculations which extend to the whole vibrational ladder, and the others obtained by applying commonly used scaling-laws.

This paper deals with the measurements performed to characterize the jet produced by the plasma wind tunnel SCIROCCO. The measurements are aimed to determine the vibrational temperature and the electron density of the plasma flow. A numerical rebuilding of the expansion trough the nozzle has then been performed. The work is part of an experimental activity funded by the European Space Agency and by the Italian Space Agency in the framework of a conjunct research project on the MHD interaction in an unseeded hypersonic air flow. © 2012 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

State-to-state non-equilibrium plasma kinetics is widely used to characterize cold molecular and reentry plasmas. The approach requires a high level of dynamical information, and demands a large effort in the creation of complete databases of state-resolved cross sections and rate coefficients. Recent results, emphasizing the dependence of elementary process probability on both the vibrational and rotational energy content of the H2 molecule, are presented for those channels governing the microscopic collisional dynamics in non-equilibrium plasmas, i.e. electron-impact induced resonant processes, vibrational deactivation and dissociation in atom-diatom collisions and atomic recombination at the surface. Results for H2 plasmas, i.e. negative ion sources for neutral beam injection in fusion reactors, RF parallel-plate reactors for microelectronics, atmospheric discharges and the shock wave formed in the hypersonic entry of vehicles in planetary atmosphere for aerothermodynamics, are discussed.

The paper will present a brief overview of the applications of sate-to-state kinetics in modeling fluid dynamics. The research activities ranges from hypersonic entry (boundary layer, shock wave) to ground test facilities, from MHD interaction to DBD flow control. The state-to-state model in fluid dynamics in the last years is rapidly diffusing, promising new interesting developments in the next future.

Thermal and chemical nonequilibrium effects are investigated in hypersonic nozzle expanding flows by means of vibrational collisional models. The rate coefficients for rovibrational dissociation and excitation are provided by two chemical databases for the N+N 2 system recently developed at NASA Ames Research Center and the University of Bari. Vibrationally averaged rate coefficients for N + N 2 collisions are computed based on the hypothesis of equilibrium between translational and rotational modes. N2+N 2 collisions are also considered based on literature data. Inviscid and quasi 1D governing equations are discretized in space by means of a finite volume method. A fully implicit time integration method is applied to obtain steady state solutions. Results show that, for both N + N 2 and N 2 + N 2 collision dominated flows, the populations of vibrational levels deviate from a Boltzmann distribution. An accurate investigation of vibrational level dynamics shows the different behavior of low and high-lying states. Comparison against experimental data acquired at the EAST facility of NASA Ames Research Center demonstrate good agreement between the computed and experimental results.

In this paper, the absorption coefficient and emissivity of non-equilibrium atomic hydrogen plasma have been calculated in the case of a steady state shock wave. For this purpose, the atomic level population profiles along the shock wave have been calculated using a collisional-radiative model coupled with the electron Boltzmann equation. The spectral coefficients are in turn the input for solving a one-dimensional radiative transfer equation, which allows to calculate the radiation intensity and radiative flux in the plasma slab. © 2011 American Institute of Physics.

The paper presents radiation models developed to investigate radiation in entry in Earth, Mars and Jupiteratmospheres. The capacity of ASTEROID computing code to simulate elementary radiative processes, calculate spectraland groups optical properties, and also solve simple radiative heat transfer problems is presented for Earth entry. Thelarge number of radiative processes involved in the radiative flux is put forward. The contributions of the differentradiative processes encountered in Mars entry are studied using the HTGR spectroscopic database. The validity of thisdatabase with respect to diatomic molecules systems and CO2 infrared radiation is illustrated through experimentalvalidations. The accuracy of statistical narrow-band model to predict radiative flux is illustrated for an afterbody. Finallyrecent improvements of the model developed for the calculation of radiative properties of high-temperature H2/Hemixtures representative of Jupiter atmosphere is presented. The model takes into account the most important radiativeprocesses.

The possibility of using reduced model, that account for non-Boltzmann vibrational distributions for nitrogen monoxide kinetics has been explored. The basic idea is that the rate coefficients, which are proportional to the tail of the vibrational distribution function, are strictly correlated to reactant density rather than to vibrational temperature, which depend on the low energy distribution. The model consider the rate coefficients as a function of the population of the last vibrational level of the relevant species, which evolution is calculated with a proper kinetic equation. © 2011 American Institute of Physics.

Four different types of macroscopic models developed for the vibration-chemistry coupling in nonequilibriumflows for re-entry applications are presented. First, using an approach based on nonequilibrium thermodynamics, globalrate coefficients of dissociation of N2 and O2 under parent molecular or atomic impact and backward molecularrecombination are determined. Then a Two-Level Distribution (TLD) model is developed, in which a relaxation equationfor vibrational temperature is solved as in the case of multi-temperature models but with the simultaneous solution of akinetic equation, as in the case of state-to-state models, but only for the last vibrational level. In a third approach, a multiinternaltemperature model is presented to describe accurately the vibrational distribution function in using several groupsof levels, within which the levels are assumed to follow a Boltzmann distribution at an internal temperature of the group.This multi-internal temperature model allows us to describe accurately the vibrational energy relaxation and dissociationprocesses behind a strong shock wave. Finally, a rovibrational collisional coarse-grain model is developed to reduce adetailed rovibrational mechanism for the internal energy excitation and dissociation processes behind a strong shock wavein a nitrogen flow.

A collisional-radiative model for hydrogen atom, coupled self-consistently with the Boltzmann equation for free electrons, has been applied to model a shock tube. The kinetic model has been completed considering atom-atom collisions and the vibrational kinetics of the ground state of hydrogen molecules. The atomic level kinetics has been also coupled with a radiative transport equation to determine the effective adsorption and emission coefficients and non-local energy transfer. © 2011 Elsevier B.V. All rights reserved.

In this paper, a supersonic flow of an argon plasma around a cylinder has been investigated comparing shock fitting and shock capturing techniques. Shock-capturing codes are algorithmically simple, but are plagued by a number of numerical troubles, particularly evident when the shocks are strong and the grids unstructured. On the other hand, shock-fitting algorithms allow to accurately compute solutions on coarse meshes, but tend to be algorithmically complex. The kinetic scheme adopted includes the argon metastable state as an independent species and takes into account for electron-atom and atom-atom processes. Electron density distributions have been reported.

In this paper we study non equilibrium level kineticsin a steady shock wave propagating in pure hydrogenplasma. The hydrodynamic description of the shock waveis achieved using the steady state continuity equationstaking into account radiative losses into the energy equation.Spectral properties of the (H, H+, e?) plasmahave been evaluated using a recently developed numericalmodel from the level population output of an advancedcollisional-radiative model which solves a Boltzmannequation for the non-equilibrium EEDF.

A simple equation describing the formation of plateaux induced by superelastic collisions in the electron energy distribution function (EEDF) of low temperature and afterglow plasmas is derived. The EEDFs predicted from this equation are in good agreement with those obtained from the numerical solution of the full Boltzmann equation in the presence of excited states.

A collisional-radiative model for the H2/He plasma, coupled to a Boltzmann solver for the free electron kinetics is used to investigate the non-equilibrium conditions created in the expansion of an high-temperature plasma flow through a converging-diverging nozzle, starting from the steady state composition at T 0 = 10 000 K and p 0 = 1 atm in the reservoir. It is shown that the plasma optical thickness plays a major role on the evolution of macroscopic quantities and internal distributions along the nozzle axis. Structured electron energy distribution functions, characterized by long plateaux and humps, are created due to superelastic collisions of cold electrons and electronically excited atomic hydrogen. The magnitudes of the plateaux are orders of magnitude higher in an optically thick plasma compared with a thin plasma, while the electron-electron collisions play a role in smoothing the peaks created by superelastic collisions between cold electrons and H (n > 2).

New calculated thermodynamic properties and transport coefficients of high temperature air are presented. The calculations, which assume local thermodynamic equilibrium, are performed for different pressures (from 0.1 to 1000 atm) in the temperature range from 50 to 30000 K. The results have been obtained by means of the perturbative Chapman-Enskog method, after an appropriate selection of the collision integrals [1]. The calculations include viscosity, total thermal conductivity and electric conductivity. The collision integrals used in calculating the transport coefficients are significantly more accurate than values used in previous theoretical studies. In particular, accurate collision integrals, carried out by Mason [2, 3], for interactions between charged species were calculated using the attractive and repulsive screened Coulomb potentials.

Transport properties of high-temperature helium and hydrogen plasmas as well as Jupiter atmosphere have been calculated for equilibrium and nonequilibrium conditions using higher approximations of the Chapman-Enskog method. A complete database of transport cross sections for relevant interactions has been derived, including minority species, by using both ab initio and phenomenological potentials Inelastic collision integrals terms, due to resonant charge-exchange channels, have been also considered.

Different mechanisms of CO<inf>2</inf> dissociation, in discharge and post-discharge conditions, have been computed by performing a parametric numerical solution of the electron Boltzmann equation as a function of the electric field, the ionization degree and the vibrational temperatures and by considering elastic, inelastic, superelastic and electron electron collisions. Emphasis is given to the role of superelastic electronic and vibrational collisions in affecting the electron energy distribution function and relevant rates. The results show that, at low E/N values, the dissociation rates from pure vibrational mechanism can overcome the corresponding rates of electron impact dissociation. In any case, the electron impact dissociation rates are largely dependent on the transitions from excited vibrational levels.