Transport coefficients of argon,nitrogen, oxygen,argon-nitrogen,and argon-oxygen plasmas

Calculated values of the viscosity, thermal conductivity, and electrical conductivity of argon, nitrogen, and oxygen plasmas, and mixtures of argon anti nitrogen and of argon anti oxygen, are presented. In addition, combined ordinary, pressure, and thermal diffusion coefficients are given for the gas mixtures. These three combined diffusion coefficients fully describe di fusion of the two gases, irrespective of their degree of dissociation or ionizati on. The calculations, which assume local thermodynamic equilibrium, are performed! for atmospheric-pressure plasmas in the temperature range /torn 300 to 30,000 K. A number of the collision integrals used in calculating the transport coefficients are significantly more accurate than values used in previous theoretical studies, resulting in more reliable values of the transport coefficients. The results are compared with those of published theoretical and experimental studies.     

Transport Coefficients of Hydrogen and Argon–Hydrogen Plasmas

Calculated values of the viscosity, thermal conductivity, and electrical conductivity of hydrogen and mixtures of argon and hydrogen at high temperatures are presented. Combined ordinary, pressure, temperature, and electric field diffusion coefficients are also given for the mixtures. The calculations, which assume local thermodynamic equilibrium, are performed for atmospheric pressure plasmas in the temperature range from 300 to 30,000 K. The results are compared with those of previously published studies. Generally, the agreement is reasonable; those discrepancies that exist are attributed to the improved values of some of the collision integrals used here in calculating the transport coefficients.     

Transport Coefficients of Two-temperature Lithium Plasma for Space Propulsion Applications

Lithium has been proposed as an attractive metal propellant for advanced electric propulsion. In our current work, transport coefficients including the viscosity, thermal conductivity, and electrical conductivity of lithium plasma under both the equilibrium and non-equilibrium conditions are calculated based on a two-temperature model. The collision integrals used in calculating the transport coefficients are significantly more accurate than values used in previous theoretical studies, resulting in more reliable values of the transport coefficients. Results are computed for different degrees of thermal non-equilibrium, i.e. the ratio of electron to heavy particle temperatures, from 1 to 15, with the electron temperature ranging from 300 to 60,000 K in a wide pressure range from 0.0001 to 100 atm. We compare our calculated results with existing published results and discrepancies are found and explained.     

Influence of the Excited States of Atomic Nitrogen N(<Superscript>2</Superscript>D) and N(<Superscript>2</Superscript>P) on the Transport Properties of Nitrogen. Part I: Atomic Nitrogen Properties

In this paper, calculated values of the viscosity and thermal conductivity of atomic nitrogen, taking into account three species (the ground and two excited states), are presented. The calculations, which assume that the temperature dependent probability of occupation of the states is given by the Boltzmann factor, are performed for atmospheric-pressure in the temperature range from 1,000 to 20,000 K. Six collision integrals are used in calculating the transport coefficients and we have introduced new averaged collision integrals where the weight associated at each interacting species pair is the probable collision frequency. The influence of the collision integral values and energy transfer between two different species is studied. These results are compared which those of published theoretical studies.     

Thermodynamic Properties and Transport Coefficients of CO<Subscript>2</Subscript>–Cu Thermal Plasmas

This paper presents the calculated values of equilibrium compositions, thermodynamic properties and transport coefficients (viscosity, electrical conductivity and thermal conductivity) for CO₂–Cu thermal plasmas. With several copper mass proportions, the calculation is performed at temperatures 2000–30,000 K and various pressures 0.1–16 bar. Gibbs free energy minimization is used to determine species compositions and thermodynamic properties and the well-known Chapman–Enskog method is applied to calculating transport properties. Furthermore, great attention is paid to cope with the interactions between all the particles in the determination of collision integrals. The results are illustrated indicating the effect of the copper proportions and pressure on the fundamental properties of CO₂–Cu thermal plasmas. It can be found that a small quantity of copper (less than 10 %) can significantly modify the charged species densities and electrical conductivity especially at low temperature. While for other properties, the influences can be noticeable only when the copper proportion is above 10 %.     

Influence of the Excited States of Atomic Nitrogen N(<Superscript>2</Superscript>D), N(<Superscript>2</Superscript>P) and N(R) on the Transport Properties of Nitrogen. Part II: Nitrogen Plasma Properties

In this paper, the calculated values of the viscosity and thermal conductivity of nitrogen plasma are presented taking into account five (e, N, N⁺, N₂ and N₂⁺) or eight (e, N(⁴S), N(²P), N(²D), N(R), N⁺, N₂ and N₂⁺) species. The calculations are based on the supposition that the temperature dependent probability of occupation of the states is given by the Boltzmann factor. The domain for which the calculations are performed, is for p = 1 and 10 atm in the temperature range from 5,000 K to 15,000 K. Classical collision integrals are used in calculating the transport coefficients and we have introduced new averaged collision integrals where the weight associated at each interacting species pair is the probable collision frequency. The influence of the collision integral values and energy transfer between two different species is studied. These results are compared which those of published theoretical studies.     

Influence of Partition Function and Interaction Potential on Transport Properties of Thermal Plasmas

This paper, divided into two parts, is devoted to the transport properties at local thermodynamic equilibrium: the first part shows the influences of partition functions through the plasma composition and the second part the influence of interaction potentials. In the first part, for complex chemical mixtures the determination of the partition functions of different species is considered: monatomic, diatomic and polyatomic. In the plasmas the monatomic species are important; we study thoroughly the partition functions of monatomic neutrals and ions. We introduce two cut-off criteria. We test the influence of the two criteria on the partition functions and consequently onto the plasma composition and transport properties. We applied the study to Ar–Cu mixtures. In the second part, an historic study shows that the collision integrals used in calculating the transport properties become more accurate leading to more reliable values of the transport coefficients: application to N₂ plasma. Now we have to calculate transport properties of complex mixtures and in these cases, for numerous interactions, a lack of data means that model potentials have to be used to determine collision integrals. In this paper, we have used two potential models: the first, for neutral–neutral and ion–neutral interactions, is an improvement of the Lennard-Jones function and the second is developed, from Stockmayer potential, for polar gases. We compare, for the collision integrals, the results obtained by these two models with those determined with more accurate potentials: applications to CO₂ plasma and H₂–N₂ mixtures.     

Transport Coefficients of High Temperature SF6–He Mixtures Used in Switching Applications as an Alternative to Pure SF6

Sulfur hexafluoride (SF₆) gas has a quite high global warming potential and hence it is required that applying any substitute for SF₆ gas. Much interest in the use of a mixture of helium and SF₆ as arc quenching medium were investigated indicating a high performance of arc interruption. The calculated values of transport coefficients of mixtures of SF₆–He mixtures, at high temperatures are presented in this paper: to the knowledge of the authors, related data have not been reported in the literature. The species composition and thermodynamic properties are determined by the method of Gibbs free energy minimization, using standard thermodynamic tables. The transport properties including electron diffusion coefficients, viscosity, thermal conductivity and electrical conductivity, are evaluated by using the Chapman–Enskog method expanded up to the third-order approximation (second-order for viscosity). Particular attention is paid to the collision integral database by the use of the most accurate and recent cross-sections or interaction potentials available in the literature. The calculations, which assume local thermodynamic equilibrium, are performed in the temperature range from 300 to 30,000 K for different pressures between 0.1 and 16 atm. An evaluation of the current interruption performance by adding He into SF₆ is discussed from a microscopic point of view. The properties with regard to SF₆–He mixtures calculated here are expected to be reliable because of the improved collision integrals employed.     

Thermophysical Properties of High Temperature Reacting Mixtures of Carbon and Water in the Range 400–30,000?K and 0.1–10?atm. Part 2: Transport Coefficients

The present contribution is continuation of Part 1: Equilibrium composition and thermodynamic properties. This paper is devoted to the calculation of transport properties of mixtures of water and carbon at high temperature. The transport properties, including electron diffusion coefficient, viscosity, thermal conductivity, and electrical conductivity are obtained by using the Chapman?CEnskog method expanded to the third-order approximation (second-order for viscosity), taking only elastic processes into account. The calculations, which assume local thermodynamic equilibrium, are performed for atmospheric pressure plasmas in the temperature range from 400 to 30,000?K for pressures of 0. 10, 1.0, 3.0, 5.0 and 10.0?atm. with the results obtained are compared to those of previously published studies, and the reasons for discrepancies are analyzed. The results provide reliable reference data for simulation of plasmas in mixtures of carbon and water.     

Calculation of transport properties and intermolecular potential energy function of the binary mixtures of H2 with Ne,Ar, Kr and Xe by a semi-empirical inversion method

The present paper contains inspection of the improved corresponding states principle for transport properties of hydrogen and the binary mixtures of hydrogen with Ne, Ar, Kr and Xe. The set of corresponding states parameters has been defined by a complex numerical analysis of a carefully selected body of experimental data. The obtained correlations for the reduced orientation-averaged diffusion and viscosity collision integrals are restricted to low densities in a temperature range from T = ?/k to the onset of ionization. These equations have been inverted directly to give the isotropic and effective intermolecular potential energy curve for binary mixtures of H₂ with Ne, Ar, Kr and Xe corresponding to the viscosity collision integrals. The results are then used to obtain the best Morse-Spline-Van der Waals (MSV) potential parameters. Our inverted potential energies have been compared with experimental intermolecular potentials that were obtained by molecular beam scattering and infrared spectroscopic measurements. In this research, the Chapman–Enskog and Wang Chang-Uhlenbeck-de Boer (WCUB) version of kinetic theory have been used in conjunction with our inverted potential energies to reproduce viscosity, diffusion, thermal conductivity and thermal diffusion factor of binary mixtures of H₂ with Ne, Ar, Kr and Xe in a wide temperature range for equimolar composition. As the deviation plots illustrate, our obtained intermolecular potential energies (on the basis of the algorithm presented in the inversion process) represent the low-density transport properties of binary mixtures of H₂ with Ne, Ar, Kr and Xe within their expected experimental uncertainties. Close agreement between the predicted values and the literature results of transport properties demonstrates the predictive power of the inversion scheme.     

Thermophysical Properties of H<Subscript>2</Subscript>O–Ar Plasmas at Temperatures 400–50,000 K and Pressure 0.1 MPa

The article presents the calculation of thermophysical properties of the mixture water steam–argon which has been used to further enhance the characteristics of plasma torches stabilized by the water wortex. The calculations were performed at the temperatures 400–50,000 K and at 0.1 MPa. First, the composition and thermodynamic properties are determined by classical methods. Further the calculations of viscosity, electrical conductivity and thermal conductivity of the mixture are computed in the 4th approximation of the Chapman–Enskog method. The computation of collision integrals is described with special respect to the interactions of charged particles where the necessary calculations for the Coulomb potential screened at the Debye length were enlarged to cover the 4th approximation. Then the formulae describing the method based on the variational principle of solving the system of Boltzmann integrodifferential equations are shortly introduced and the transport coefficients are presented.     

Calculation of transport coefficients of air plasmas

This paper is devoted to results of calculation of the main transport coefficients of air plasmas: electrical and thermal conductivities and viscosity. These calculations are performed for pressures between 1 and 200 atm and for temperatures varying from 1000 to 30,000 K. The computational methods proposed by Devoto from the classical formalism described by Hirchfelder et al. are used. Collision integrals for interactions between charged particles are calculated using the formalism of Mason et al. to account for the fact that, in most of the situations considered here, the number of charged particles in the Debye sphere is weak.     

Thermodynamic and Transport Properties of Two-temperature Oxygen Plasmas

Thermodynamic and transport properties of two-temperature oxygen plasmas are presented. Variation of species densities, mass densities, specific heat, enthalpy, viscosity, thermal conductivity, collision frequency and electrical conductivity as a function of temperature, pressure and different degree of temperature non-equilibrium are computed. Reactional, electronic and heavy particle components of the total thermal conductivity are discussed. To meet practical needs of fluid-dynamic simulations, temperatures included in the computation range from 300 K to 45,000 K, the ratio of electron temperature (T _e) to the heavy particle temperature (T _h) ranges from 1 to 30 and the pressure ranges from 0.1 to 7 atmospheres. Results obtained for thermodynamic equilibrium (T _e = T _h) under atmospheric pressure are compared with published results obtained for similar conditions. Observed overall agreement is reasonable. Slight deviations in some properties may be attributed to the values used for collision integral data and for the two temperature formulations used. An approach for computing properties under chemical non-equilibrium and associated deviations from two-temperature results under similar conditions are discussed.     

Transport properties of methane,ethane, propane, <Emphasis Type="Italic">iso</Emphasis>-butane and <Emphasis Type="Italic">neo</Emphasis>-pentane from ab initio potential energy surfaces

In this work, the potential energy surfaces for methane, ethane, propane, iso-butane and neo-pentane, obtained from the ab initio calculations via different levels of electron-correlation, were used in the framework of the kinetic theory to calculate the transport collision integrals and their corresponding low-density transport coefficients. The theoretical results are compared with the available experimental data and the effective scaling potential parameters of methane, ethane, propane, iso-butane and neo-pentane along with the kinetic theory collision integrals and higher order correction factors were obtained. Relation between different potentials and kinetic theory collision integrals are discussed and it was shown that the Mason–Monchick approach is a reliable approximation in the calculation of diffusion coefficients and shear viscosities of chain alkanes, whereas the full predictive Boltzmann weighting method is successful only for lighter alkanes, such as methane and ethane.     

Computation of some thermodynamic properties of nitrogen using a new intermolecular potential from molecular dynamics simulation

A new pair-potential energy function of nitrogen has been determined via the inversion of reduced viscosity collision integrals and fitted to obtain an analytical potential form. The pair-potential reproduces the second virial coefficient, viscosity, thermal conductivity, self-diffusion coefficient, and thermal diffusion factor of nitrogen in a good accordance with experimental data over wide ranges of temperatures and densities. We have also performed the molecular dynamics simulation to obtain pressure, internal energy, heat capacity at constant volume, and self-diffusion coefficient of nitrogen at different temperatures and densities using our calculated pair-potential and some other potentials. The molecular dynamics of the nitrogen molecules has been also used to determine nitrogen equation of state in two (low and high) pressure ranges. Our results are in a good agreement with experiment and literature values.     

A compact formulation for multi-component transport coefficients in gas mixtures

A linearly independent set of generalized cross-sections and their ratios is identified to describe all the elements of the system matrices needed to evaluate transport coefficients in dilute, field-free, gas mixtures with an arbitrary number of polyatomic species. The cross-section ratios are also defined in terms of more customary collision integrals and are related to a number of macroscopic observables. The practical advantages of the proposed formulation when performing calculations of transport coefficients for computationally demanding flow simulations are discussed.     

Transport properties of high temperature air components: A review

The methods for the calculation of the transport properties of high temperature gases are reviewed from the points of view of both kinetic theory and transport cross sections. Particular emphasis is given to the poor convergence of the Chapman-Enskog method for calculating the thermal conductivity of free electrons and of the possible sources of errors when applying well known simplified formulae for calculating the translational thermal conductivity of heavy components and the viscosity of partially ionized gases. The transport cross sections (collision integrals) of high temperature air components are then discussed by comparing old and new calculations particularly emphasizing atom-atom, atom-molecule and atom-ion interactions. Special consideration is dedicated to the knowledge of transport cross sections of electronically excited states. The role of inelastic processes in affecting the transport cross sections is also briefly discussed. Finally the possibility to extend the results to non equilibrium situations is analysed.     

Hard-wall potential function for transport properties of alkali metal vapors

This study demonstrates that the transport properties of alkali metals are determined principally by the repulsive wall of the pair interaction potential function. The (hard-wall) Lennard-Jones (LJ) (15-6) effective pair potential function is used to calculate the transport collision integrals. Accordingly, reduced collision integrals of K, Rb, and Cs metal vapors are obtained from the Chapman-Enskog solution of the Boltzmann equation. The law of corresponding states based on the experimental transport reduced collision integral is used to verify the validity of a LJ(15-6) hybrid potential in describing the transport properties. LJ(8.5-4) potential function and a simple thermodynamic argument with the input PVT data of liquid metals provide the required molecular potential parameters. Values of the predicted viscosity of monatomic alkali metal vapor are in agreement with typical experimental data with average absolute deviations of 2.97% for K in the range of 700-1500 K, 1.69% for Rb, and 1.75% for Cs in the range of 700-2000 K. In the same way, the values of predicted thermal conductivity are in agreement with experiment within 2.78%, 3.25%, and 3.63% for K, Rb, and Cs, respectively. The LJ(15-6) hybrid potential with a hard-wall repulsion character conclusively predicts the best transport properties of the three alkali metal vapors.     

Computation of some thermodynamics, transport, structural properties, and new equation of state for fluid neon using a new intermolecular potential from molecular dynamics simulation

A new pair potential energy function of neon has been determined via the inversion of reduced viscosity collision integrals at zero pressure and fitted to obtain an analytical potential form. The pair potential reproduces the second virial coefficient, viscosity, thermal conductivity, and self-diffusion coefficient of neon in a good accordance with experimental data over wide ranges of temperature and density. We have also performed molecular dynamics simulation to obtain some thermodynamics, transport, and structural properties of fluid neon at different temperatures and densities using our calculated pair potential supplemented by quantum corrections following the Feynman–Hibbs approach. The significance of this work is that the three-body expression of Wang and Sadus (J Chem Phys 125:144509–1, 2006) can be used to improve the prediction of the pressures of neon without requiring an expensive three-body calculation. The molecular dynamics simulation of neon has been also used to determine a new equation of state for neon. Our results are in a good agreement with experiment and literature values.     

Modelling investigation on the thermal conductivity of pure liquid,vapour, and supercritical refrigerants and their mixtures by using Heyen EOS

This work presents a literature survey of the available data regarding the thermal conductivity of refrigerants. About 31 pure refrigerants that contain 7127 data points are selected for the temperature range of 91.35–580.00 K, a pressure range of (0.000111-500) bar, and thermal conductivity range of (0.007–0.27) W m^?1 K^?1 containing liquid, vapour, and supercritical phases. Seven binary and three ternary mixtures are also collected both in liquid and vapour phases with an overall of 803 data points. Based on the similarity between the pressure-volume-temperature and Tλ (thermal conductivity) P diagrams, the thermal conductivity model based on Heyen equation of state has been developed for pure refrigerants and their mixtures. The genetic algorithm is used to determine the adjustable parameters of the model. The calculation results prove that this proposed model can reproduce and predict thermal conductivity of refrigerants with good accuracy (overall AAD = 6.85% for pure compounds, AAD = 6.14% for binary mixtures and AAD = 9.32% for ternary mixtures).