Non-equilibrium Vibrational Kinetics Research Articles

Low temperature state-to-state vibrational kinetics of O + N2(v) and N + O2(v) collisions

Starting from an equilibrium initial condition at 3000 K, the non-equilibrium vibrational kinetics of a 500 K atmospheric pressure N2/N/O2/O/NO mixture is investigated with a zero-dimensional time-dependent numerical solver. Attention is devoted to the O + N2(v) and N + O2(v) collisions, thanks to new QCT state-to-state rates from the literature. The Zeldovich and the dissociation–recombination reactions are considered; for the N + O2(v) collisions the inelastic vT processes are considered too. Interpolation formulae of the corresponding rates are proposed.The mixture behaviour depends on the combined effects of the different processes, however under the conditions adopted the forward second Zeldovich reaction switches on the kinetics towards a new equilibrium.The aim of the present study is to open the door to more complex applications of plasmas in the fields of the plasma medicine, the fertilizers production and, more in general, of the nitrogen fixation.

Coupling plasma physics and chemistry in the PIC model of electric propulsion: Application to an air-breathing, low-power Hall thruster

This work represents a first attempt to include the complex variety of electron-molecule processes in a full kinetic particle-in-cell/test particle Monte Carlo model for the plasma and neutral gas phase in a Hall thruster. Particular emphasis has been placed on Earth’s atmosphere species for the air-breathing concept. The coupling between the plasma and the gas phase is self-consistently captured by assuming the cold gas approximation and considering gas-wall and gas recycling from the walls due to ion neutralization. The results showed that, with air molecular propellants, all the most relevant thruster performance figures degraded relative to the nominal case using Xe propellant. The main reasons can be ascribed to a reduced ionization cross-section, a larger gas ionization mean free path due to lighter mass air species, and additional electron collisional power losses. While vibrational excitations power losses are negligible, dissociation and electronic excitations compete with the ionization channel. In addition, for molecular oxygen, the large dissociation leads to even faster atoms, further reducing their transit time inside the discharge channel. Future studies are needed to investigate the role of non-equilibrium vibrational kinetics and metastable states for stepwise ionization.

Neural network approach in modelling vibrational kinetics of carbon dioxide

The study is devoted to modeling nonequilibrium vibrational kinetics of carbon dioxide taking into account complex mechanisms of relaxation and intermode energy exchanges. The possibilities of using machine learning methods to improve the performance of numerical simulation of non-equilibrium carbon dioxide flows are studied. Various strategies for increasing the efficiency of the hybrid four-temperature model of CO2 kinetics are considered. The neural network approach proposed by the authors to calculate the rate of vibrational relaxation in each mode turned out to be the most promising. For the problem of spatially homogeneous relaxation, estimates of the error and computational costs of the developed algorithm are carried out, and its high accuracy and efficiency are demonstrated. For the first time, the carbon dioxide flow behind a plane shock wave was simulated in a full state-to-state approximation. A comparison with the results obtained in the framework of the hybrid four-temperature approach is carried out, and the equivalence of the approaches is shown. This makes it possible to recommend developed multitemperature approxima tions as the main tool for solving problems of nonequilibrium kinetics and gas dynamics. The hybrid four-temperature approach using the neural network method for calculating relaxation terms showed the acceleration of numerical simulation in time by more than an order of magnitude, while maintaining accuracy. This technique can be recommended for solving complex multidimensional problems of nonequilibrium gas dynamics, including state-to-state chemical reactions.

Past and present aspects of Italian plasma chemistry

The linking between the initial activities of the Rome–Bari group to their present activities is discussed in different fields of plasma chemical-physics. Several topics are presented including (1) plasma catalysis, (2) the interaction of alumina particles with thermal plasmas and its linking with the thermodynamics and transport properties of plasmas, and (3) non-equilibrium vibrational kinetics coupled with the Boltzmann equation for the electron energy distribution functions (eedf) in aerospace and cold plasma applications. The old activities in plasma catalysis pointed out the importance of atomic species affecting catalytic reactions opening also to the possibility of non-equilibrium vibrational distributions on the chemisorbed ad-atoms. This last aspect is discussed also taking into account recent developments. The study of the interaction of alumina particles with thermal plasmas was rationalized assuming that the step controlling the reaction could be the heat transfer plasma-particle. The model used a simplified fluid dynamic approach with the insertion of accurate values of thermodynamic and transport properties of thermal plasmas. This kind of activity can be considered precursor on the intense work in the field with particular attention on the importance of electronic excited states in affecting thermodynamics and transport of plasmas. Moreover, the plasma-particle interactions can be recovered to a given extent in the modern aspects of hypersonics in the boundary layer of re-entering vehicles as well as in the nozzle flow expansion. In both cases, we underline the existence of vibrational distributions (vdf) far from the Boltzmann behaviour and rates presenting an anti-Arrhenius trend as a function of the inverse of gas temperature. Concerning the non-equilibrium vibrational kinetics, we discuss two case studies. The first one deals with the behaviour of cold nitrogen plasmas pointing out the role of superelastic vibrational and electronic collisions on vdf and eedf. In this case, we discuss also the same case study comparing the results obtained by a complete set of electron molecule cross-sections acting on the whole vibrational ladder with the corresponding ones which consider transitions starting and arriving to the vibrational ground state of the molecule. The last case study concerns the dissociation kinetics of CO2 in cold plasmas, a topic largely studied in the past to emphasize the role of vibrational excitation in CO2 destruction. Recent results obtained using a sophisticated model based on the coupling of Boltzmann equation for the eedf and a state-to-state vibrational kinetics of the asymmetric ladder of CO2 are reported. The interplay between dissociation process by direct electron impact collision and by heavy particle collisions with vibrationally excited CO2 molecules is discussed.

Non-equilibrium vibrational and chemical kinetics in air flows in nozzles

Non-equilibrium vibrational and chemical kinetics in air flows in nozzles

Gas phase Boudouard reactions involving singlet–singlet and singlet–triplet CO vibrationally excited states: implications for the non-equilibrium vibrational kinetics of CO/CO2 plasmas

Rate constants for the Boudouard reactions: CO + CO → CO2 + C and CO + CO → C2O + O, involving ground and vibrationally excited states for both singlet–singlet and singlet–triplet reactant CO molecules, have been obtained by using the transition-state theory on an ab initio generated potential energy surface. The dependence of the activation energies for the different processes on the vibrational energy of reactants has been estimated through a parametrization that accounts for the utilization of vibrational energy and is calculated by the forward and backward ab initio activation energies of the relevant processes at zero vibrational energy. The results and their comparison with available experimental reaction rates demonstrate the importance of vibrational excitation not only for the singlet–singlet reactions, but also for the singlet–triplet ones, which are here investigated for the first time. Finally, the implications of the present results on the kinetics of CO/CO2 cold plasmas are discussed: for their modeling the temperature dependence of the obtained rates for singlet–singlet and singlet–triplet reactants in the ground vibrational states have been represented by both Arrhenius and deformed Arrhenius equations.

Time-dependent coupling of electron energy distribution function, vibrational kinetics of the asymmetric mode of CO2 and dissociation, ionization and electronic excitation kinetics under discharge and post-discharge conditions

A time-dependent self-consistent model based on the coupling of the Boltzmann equation for the electron energy distribution function (EEDF) with the non-equilibrium vibrational kinetics of the asymmetric mode, as well as a simplified global model, have been implemented for a pure CO2 plasma. The simplified time-dependent global model takes into account dissociation and ionization as well as the reverse of these processes. It also takes into account the excitation/de-excitation of an electronic excited state at 10.5 eV. The model has been applied to describe the discharge and post-discharge conditions typically met in an atmospheric-pressure dielectric barrier discharge (DBD) and in a moderate-pressure microwave discharge. The reported results show the strong coupling between the excited state and the electron energy distribution kinetics due to superelastic (vibrational and electronic) collisions. Moreover, the dissociation rate from a pure vibrational mechanism can become competitive with the corresponding rate from the direct electron impact mechanism at high values of vibrational temperature.

Excited-state kinetics and radiation transport in low-temperature plasmas

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.

Surface vibrational relaxation of N2 studied by CO2 titration with time-resolved quantum cascade laser absorption spectroscopy

A new method for determination of the wall de-excitation probability of vibrationally excited N2 on different surfaces exposed to low-pressure plasmas has been developed. A short dc discharge pulse of only a few milliseconds was applied to a mixture containing 0.05–1% of CO2 in N2 at a pressure of 133 Pa. Due to a nearly resonant fast vibrational transfer between N2(v) and the asymmetric ν3 mode of CO2 the vibrational excitation of these titrating molecules is an image of the degree of vibrational excitation of N2. In the afterglow, the vibrational relaxation of CO2 was monitored in situ using quantum cascade laser absorption spectroscopy. The experimental results were interpreted in terms of a numerical model of non-equilibrium vibrational kinetics in CO2–N2 mixtures. Heterogeneous relaxation was the main quenching process of N2(v) under the conditions of this study, which allowed determination of the value of from the best agreement between the experiment and the model. The new method is suitable for determination in a single plasma pulse with the discharge tube surface pretreated by a low-pressure plasma. The relaxation probability of the first vibrational level of nitrogen γ1 = (1.1 ± 0.15) × 10−3 found for Pyrex and silica is in reasonable agreement with the literature data. Using the new technique the N2(v = 1) quenching probability was measured on TiO2 surface, γ1 = (9 ± 1) × 10−3. A linear enhancement of the N2(v) wall deactivation probability with an increase in the admixture of CO2 was observed for all studied materials. In order to explain this effect, a vibrational energy transfer mechanism between N2(v) and adsorbed CO2 is proposed.

Comparison of different models for non-equilibrium CO2 flows in a shock layer near a blunt body

The paper presents results of a numerical simulation of a supersonic two-dimensional (2D) viscous flow containing CO2 molecules near a spacecraft entering the Mars atmosphere. The gas–dynamic equations in the shock layer are coupled to the equations of non-equilibrium vibrational and chemical kinetics in the five-component mixture CO2/CO/O2/C/O. Transport and relaxation processes in the flow are studied on the basis of the rigorous kinetic theory methods; the developed transport algorithms are incorporated in the numerical scheme. The influence of the vibrational excitation of CO2 and chemical reactions on the gas flow parameters and heat transfer is analyzed. The obtained results are compared with those found using two simplified models based on the two-temperature and one-temperature vibrational distributions in CO2. The accuracy of the simplified models and the limits of their validity within the shock layer are evaluated. The effect of bulk viscosity in a flow near a re-entry body is discussed. The role of different diffusion processes, chemical reactions, and surface catalytic properties in a flow of the considered mixture in the shock layer is estimated.

International Space Station Ku-Band Communications Antenna Blockage Analysis

5Fertig, M., Fruhauf, H. H., and Auweter-Kurtz, M., “Modelling of Reactive Processes at SiC Surfaces in Rarefied Nonequilibrium Airflows,” AIAA Paper 2002-3102, June 2002. 6Armenise, I., Capitelli, M., Colonna, G., Koudriavtsev, N., and Smetanin, V., “Nonequilibrium Vibrational Kinetics During Hypersonic Flow of a Solid Body in Nitrogen and Its Influence on the Surface Heat Flux,” Plasma Chemistry and Plasma Processing, Vol. 15, No. 3, 1995, pp. 501–528. 7Capitelli, M., Armenise, I., and Gorse, C., “State-to-State Approach in the Kinetics of Air Components Under Re-Entry Conditions,” Journal of Thermophysics and Heat Transfer, Vol. 11, No. 4, 1997, pp. 570–578.

Vibrational non-equilibrium and `hot atoms' in the oxidation of carbon monoxide on catalytic surfaces

Non-equilibrium vibrational kinetics, as recently developed for adlayers, is applied to the catalytic oxidation of CO by either molecular or atomic oxygen. This model allows one to fit experimental distribution functions of the product CO 2(g) molecules leaving the surface with hyperthermal energies. An LH * mechanism involving non-equilibrium vibrational distribution functions (vdfs) of the relevant adspecies is presented showing the basic consequences of non-equilibrium at the catalytic surface. In this picture `hot atoms' are seen as mobile, vibrationally excited adspecies with their vibrational ladders populated according to non-equilibrium Treanor distribution functions.

Non-equilibrium vibrational kinetics and `hot atom' models in the recombination of hydrogen atoms on surfaces

Non-equilibrium vibrational kinetics as recently developed for adlayers is applied to experimental data on H-atom recombination and abstraction at solid surfaces. This model allows one to fit vibrational and translational energy distribution functions of the excited diatoms leaving the surface. Eley–Rideal and Langmuir–Hinshelwood mechanisms involving vibrationally excited adatoms are presented together with a criterion for establishing their relative contribution to the total reaction rate. Analogies of this multilevel `hot atom' (HA) model with recently employed two and three levels HA kinetic schemes are presented and discussed.

Nonequilibrium Vibrational Kinetics of Air Hitting a Catalytic SiO Surface

The effects of a SiO2 partially catalytic surface on the nonequilibrium chemical and vibrational kinetics of a Ž ve-species (N, N2, O, O2 , NO) air mixture in the boundary layer of hypersonic reentry vehicles have been investigated. To this aim, boundary-layerequationscoupled to vibrationalmaster equations have been solved. The surface atomic recombination reactions have been considered as pumping the last bound vibrational level of N2 and O2 molecules. The results show a combined in uence of gas-phase and surface reactions on NO formation.

Time-resolved Fourier transform infrared spectroscopy of optically pumped carbon monoxide

The paper discusses measurements of vibration-to-vibration (V–V) energy transfer rates for CO–CO using time-resolved step-scan Fourier transform infrared spectroscopy of optically pumped carbon monoxide. In the experiments, time evolution of all vibrational states of carbon monoxide excited by a CO laser and populated by V–V processes (up to v∼40) is monitored simultaneously. The V–V rates are inferred from these data using a kinetic model that incorporates spatial power distribution of the focused laser beam, transport processes, and multi-quantum V–V processes. Although the model predictions agree well with the time-dependent step-scan relaxation data, there is variance between the model predictions and the up-pumping data, however. Comparison of calculations using two different sets of V–V rates with experimental spectra showed that the use of the semi-empirical V–V rates of DeLeon and Rich provides better agreement with experiment. It is also shown that the multi-quantum V–V rates among high vibrational quantum numbers, calculated by Cacciatore and Billing, are substantially overpredicted. The results provide some new insight into nonequilibrium vibrational kinetics, and also demonstrate the capabilities of the step-scan Fourier transform spectroscopy for time-resolved studies of molecular energy transfer processes and validation of theoretical rate models.

Nonequilibrium Vibrational Kinetics of an O/O Mixture Hitting a Catalytic Surface

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Non-equilibrium vibrational kinetics in adlayers: outline of an alternative approach to catalytic processes

It is suggested that catalytic processes at solid surfaces should be treated according to non-equilibrium vibrational kinetics as opposed to current Boltzmann equilibrium assumptions. Vibrational non-equilibrium in adlayers can be established as a result of competition between processes leading to disposal of vibrational energy to the solid and processes of anharmonic vibration–vibration up-pumping in the adlayer, regarded as a two-dimensional gas. The chemisorption kinetics presented leads to quasi-steady-state conditions defined by non-equilibrium Treanor-like vibrational distribution functions exhibiting an overpopulation of upper vibrational levels of surface species with respect to corresponding Boltzmann values. It is shown that the activation entropy of a catalytic isotope exchange reaction can be taken as a measure of this overpopulation. Experimental rates of heterogeneous isotope exchange reactions and connected chemisorption data are presented supporting this point of view, which provides, in particular, a straightforward interpretation of the long debated `compensation effect' in heterogeneous catalysis.

State-to-state nonequilibrium reaction rates

The paper studies the strongly nonequilibrium vibrational and chemical kinetics in a reacting gas flow in the state-to-state approach. Considered are exchange reactions, dissociation and recombination. The algorithms for calculation of reaction rate coefficients, depending on vibrational levels of components are developed on the basis of the kinetic theory. Formulas for reaction rate coefficients are obtained taking into account non-maxwellian velocity distributions.

Nonequilibrium Vibrational Distributions of N in Radio-Frequency Parallel-Plate Reactors

A self-consistent code has been realized to describe and simultaneously interrelate the nonequilibrium molecular vibrational kinetics and the plasma dynamics in a parallel-plate radio frequency discharge in pure nitrogen. The code is based on a one-dimensional in space and two-dimensional in space velocity, particle-in-cell with Monte Carlo collisions model of the plasma dynamics coupled to a set of one-dimensional diffusion-reaction equations for the population of vibrational states of nitrogen molecules in the electronic ground state N 2 (X, v) and for the density of nitrogen atoms, with appropriate catalytic boundary conditions. The code gives information about the plasma dynamics (electron and ion density, mean energy, drift velocity, electric field in the discharge, etc.), the vibrational distribution function, the electron energy distribution function, and the atomic concentration in the discharge. It is shown that a self-consistent approach is essential to accurately calculate the discharge properties.

Measured Shock-Layer Vibrational Populations and Temperatures in Arcjet Nitrogen Flow

Radiation is analyzed from a highly nonequilibrium shock layer produced by a blunt body in a low-density arcjet now of nitrogen. Populations of vibrational states are obtained at several locations in the shock layer through fits of basis spectra to measured spectra. Several techniques determine the rotational and vibrational temperature corresponding to Boltzmann fits to low vibrational state populations for N 2 and N + 2 molecules. These techniques include correlations of ratios of intensity integrals, fits of calculated vibrational basis sets to measurements, and minimization of the deviation between calculated and measured spectra. Analyses of basis set fits yield vibrational populations that deviate from a Boltzmann distribution at vibrational quantum numbers greater than about 6-8. Differences in rotational and vibrational temperatures are found, together with temperature differences between the neutral molecule and the ion. Temperature profiles and non-Boltzmann vibrational populations indicate the nonequilibrium character of the layer. Experimentally determined population distributions should interest anyone modeling nonequilibrium vibrational kinetics. These distributions, up to v' = 20, should be of interest, and temperature profiles generally should be useful when validating the gas models used for high-enthalpy nonequilibrium nitrogen flows.