Polyatomic Gas Mixtures Research Articles

Acoustic attenuation in three-component gas mixtures--theory.

Vibrational relaxation accounts for absorption and dispersion of acoustic waves in gases that can be significantly greater than the classical absorption mechanisms related to shear viscosity and heat conduction. This vibrational relaxation results from retarded energy exchange between translational and intramolecular vibrational degrees of freedom. Theoretical calculation of the vibrational relaxation time of gases based on the theory of Landau and Teller [Phys. Z. Sovjetunion 10, 34 (1936); 1, 88 (1932): 2, 46 (1932)] and Schwartz et al. [J. Chem. Phys. 20, 1591 (1952)] has been applied at room temperature to ternary mixtures of polyatomic gases containing nitrogen, water vapor, and methane. Due to vibrational-translational and vibrational-vibrational coupling between all three components in ternary mixtures, multiple relaxation processes produce effective relaxation frequencies affecting the attenuation of sound. The dependence of effective relaxation frequencies and the attenuation on mole fractions of the constituents was investigated. The acoustic attenuation in a mixture that is primarily nitrogen is strongly dependent on the concentrations of methane and water vapor that are present. However, the attenuation in a mixture that is primarily methane is only weakly dependent on the concentrations of nitrogen and water vapor. The theory developed in this paper is applicable to other multicomponent mixtures.

Thermal conductivity of polyatomic dilute gas mixtures

Thermal conductivity of polyatomic dilute gas mixtures

Burnett's equations for multicomponent mixtures of polyatomic gases

Burnett's equations for a multicomponent gas mixture when there are external forces present which do not depend on the velocities and internal energies of the molecules are obtained using the system of kinetic equations in the quasiclassical spherically symmetrical approximation for the case of light exchanges of translational and internal energies of the molecules in the single-liquid approximation, when the system of gas-dynamic equations consists of equations for the concentration of the chemical components, the mean-mass velocity and the mean temperature. Exact and approximate formulae are obtained for the Burnett transport coefficients. Special cases, including the question of the general equations of thermal-stress and concentration-stress convection are considered.

Multitemperature kinetic model for heat transfer in reacting gas mixture flows

Heat transfer in a high temperature reacting gas flow is investigated taking into account the influence of strong vibrational and chemical nonequilibrium. Rapid and slow vibrational energy exchanges in a mixture of molecular gases with realistic molecular spectra are taken into account and the deviation from the Boltzmann distribution over vibrational levels is studied. A kinetic theory approach is developed for the modeling of transport properties of a reacting mixture of polyatomic gases and a generalized multitemperature model is given. This theoretical model is applied for the analysis of the heat transfer and diffusion behind a strong shock wave propagating in air. The heat conductivity, diffusion coefficients, and heat flux are calculated on the basis of this model and compared to the one-temperature approach. The influence of anharmonicity of molecular vibrations is evaluated.

Gas flow and dust acceleration in a cometary Knudsen layer

An analytical model of the innermost gas–dust coma region is proposed. The kinetic Knudsen layer adjacent to the surface of the cometary nucleus, where the initially non-equilibrium velocity distribution function of gas molecules relaxes to Maxwell equilibrium distribution function and, as a result, the macro-characteristics of gas and dust flows vary several-fold, is considered. The gas phase model is based on the equations for mass, momentum and energy flux conservation, and is a natural development of the Anisimov, 1968 and Cercignani, 1981 approaches. The analytical relations between the characteristics of the gas flow on the boundaries of the non-equilibrium layer and the characteristics of the returning gas flow adsorbed by the surface are determined. These values form a consistent basis both for hydrodynamic models of the inner coma and for jet force models. Three particular models are presented: (1) sublimation of a polyatomic one-component gas; (2) sublimation of a two-component polyatomic gas mixture, in both cases from a plane surface; and (3) sublimation of water ice through a porous dust mantle. We conclude that the characteristics of the gas flow emerging from the Knudsen layer over a porous dust mantle is not very sensitive to the structure of the mantle.We also treat the expansion of dust into the coma, concentrating on the interaction between a non-equilibrium gas flow and a test particle. The dynamics of a grain of idealized shape is explored by using several simplifying assumptions for the variation of the drag force. The velocity of a particle at the exterior boundary of the Knudsen layer is thus estimated. Examining various model behaviours of the drag force inside the Knudsen layer, we show that the dust velocity is not sensitive to these variations.

Working gases in thermoacoustic engines.

The best working gases for thermoacoustic refrigeration have high ratios of specific heats and low Prandtl numbers. These properties can be optimized by the use of a mixture of light and heavy noble gases. In this paper it is shown that light noble gas-heavy polyatomic gas mixtures can result in useful working gases. In addition, it is demonstrated that the onset temperature of a heat driven prime mover can be minimized with a gas with large Prandtl number and small ratio of specific heats. The gas properties must be optimized for the particular application of thermoacoustics; it cannot be assumed that high specific heat ratio and low Prandtl number are always desirable.

The local Cauchy problem for multicomponent reactive flows in full vibrational non-equilibrium

We consider reactive mixtures of dilute polyatomic gases in full vibrational non-equilibrium. The governing equations are derived from the kinetic theory and possesses an entropy. We recast this system of conservation laws into a symmetric conservative form by using entropic variables. Following a formalism developed by the authors in a previous paper, the system is then rewritten into a normal form, that is, in the form of a quasilinear symmetric hyperbolic-parabolic system. Using a result of Vol'pert and Hudjaev, we prove local existence and uniqueness of a bounded smooth solution to the Cauchy problem.

ASYMPTOTIC STABILITY OF EQUILIBRIUM STATES FOR MULTICOMPONENT REACTIVE FLOWS

We consider the equations governing multicomponent reactive flows derived from the kinetic theory of dilute polyatomic reactive gas mixtures. Using an entropy function, we derive a symmetric conservative form of the system. In the framework of Kawashima and Shizuta's theory, we recast the resulting system into a normal form, that is, in the form of a symmetric hyperbolic–parabolic composite system. We also characterize all normal forms for symmetric systems of conservation laws such that the null space associated with dissipation matrices is invariant. We then investigate an abstract second-order quasilinear system with a source term, around a constant equilibrium state. Assuming the existence of a generalized entropy function, the invariance of the null space naturally associated with dissipation matrices, stability conditions for the source term, and a dissipative structure for the linearized equations, we establish global existence and asymptotic stability around the constant equilibrium state in all space dimensions and we obtain decay estimates. These results are then applied to multicomponent reactive flows using a normal form and the properties of Maxwellian chemical source terms.

Transport properties in reacting mixture of polyatomic gases

The mathematical modeling of transport properties in reacting gases on the basis of kinetic equations for the distribution functions is given in this paper. Thermal and chemical nonequilibrium conditions are considered. The influence of rotational and vibrational excitation and chemical reactions on the pressure tensor, heat flux and diffusion velocity is investigated. The generalization of the Chapman-Enskog method is used at the different levels of the strong nonequilibrium mixture description. Three nonequilibrium models are presented: the level approach, the generalized multi-temperature approach and the one-temperature approach. The macroscopic equations for macroparameters are derived from the kinetic theory treatment, and the expressions for the pressure tensor, diffusion velocity and heat flux as well as for the transport coefficients are given. The role of the different rates of the various energy exchanges, the anharmonism of molecular vibrations and chemical reactions in the transport properties of reacting mixtures is discussed.

Thermal conductivity of multicomponent polyatomic dilute gas mixtures

A new expression for the thermal conductivity of anN-component polyatomic gas mixture in the dilute-gas limit has been derived, based on the Thijsse approximation. The results are presented in terms of experimentally accessible quantities to allow for easier calculation of the thermal conductivity and easier interpretation of the experimentally available data. The resulting expression are much simpler than other formulae hitherto available. An additional new expression for the thermal conductivity of anN-component polyatomic gas mixture has been derived by replacing the effective cross-section by their spherical limits. These results are cast in a form which is analogous with, and no more complicated than, the corresponding expressions for purely monatomic mixtures.

Kinetic theory of dilute gas mixtures with independent internal energy modes near equilibrium

We extend the kinetic theory of dilute polyatomic gas mixtures to the case where the particles have various internal energy modes. The present theory is valid when the inernal energy modes are mechanically independent and when the various degrees of freedom of the molecules are at zeroth order equilibrium. In this case, we derive new transport linear systems with which to evaluate all the transport coefficients of the mixture. These linear systems are given explicitly in terms of various collision integrals and provide expressions for the volume viscosity, the shear viscosity, the species diffusion coefficients, the thermal diffusion coefficients, and the partial thermal conductivity.

Fast and Accurate Multicomponent Transport Property Evaluation

We investigate iterative methods for solving linear systems arising from the kinetic theory and providing transport coefficients of dilute polyatomic gas mixtures. These linear systems are obtained in their naturally constrained, singular, and symmetric form, using the formalism of Waldmann and Trübenbacher. The transport coefficients associated with the systems obtained by Monchick, Yun, and Mason are also recovered, if two misprints are corrected in the work of these authors. Using the recent theory of Ern and Giovangigli, all the transport coefficients are expressed as convergent series. By truncating these series, new, accurate, approximate expressions are obtained for all the transport coefficients. Finally, the computational efficiency of the present transport algorithms in multicomponent flow applications is illustrated with several numerical experiments.

Transport properties of nonequilibrium polyatomic gas mixtures

It is shown that the well-known Hirschfelder-Euken correction to the thermal conductivity of a polyatomic gas mixture given by the first approximation in Sonine polynomials can be less than the corresponding exact value (for a Lorentz mixture of light and heavy molecules interacting in accordance with Coulomb's law) by a factor of 3.4. Fairly high accuracy is achieved in the second approximation in Sonine polynomials. Within the framework of the latter, similar corrections to the nonequilibrium heat and diffusion fluxes are found. On the basis of the generalized Chapman-Enskog method a more general case is studied. In this case some of the nonelastic collision integrals is also taken into account in calculating the transport coefficients. The transport coefficients are either represented in terms of the well-known formulas for fast and retarded internal molecular energy exchange or convenient approximate expressions are obtained.

Thermal conduction and thermal diffusion in dilute polyatomic gas mixtures

A novel theoretical basis for the evaluation of the thermal conductivity and the thermal diffusion ratios of dilute polyatomic gas mixtures is derived within the semi-classical isotropic kinetic theory. New expressions for species diffusion coefficients, thermal diffusion coefficients, and thermal diffusion ratios are also obtained by using an expansion vector based upon the total energy of the molecules. Finally, practical and accurate expressions for the thermal conductivity and the thermal diffusion ratios are derived by using the recent theory of iterative transport algorithms, as developed by the authors. The resulting expressions can be used in either theoretical calculations or computational models of multicomponent flows.

Practical, accurate expressions for the thermal conductivity of atom-diatom gas mixtures

The use of an expansion vector based upon the total energy flux has led to a considerable simplification of the kinetic theory results for the thermal conductivity of a polyatomic gas mixture. In this paper the simplification process is taken further in order to provide expressions for the thermal conductivity of a mixture of atomic and diatomic species that are both accurate and practical for the interpretation of experimental data. In particular, the thermal conductivity of the mixture can be cast in a form that is analogous to, and no more complicated than, the corresponding expression for entirely monatomic systems. The accuracy of the resulting expression is demonstrated with the aid of new calculations of the relevant kinetic cross sections for realistic potential models.

Kinetic theory for binary mixtures of monatomic and polyatomic gases

A kinetic theory is developed for binary mixtures of a monotomic gas (consisting of perfectly smooth, elastic, and rigid spherical particles) and a polyatomic gas (consisting of perfectly rough, elastic, and rigid spherical molecules). A macroscopic state of the mixture is characterized by 29 scalar fields of partial mass densities, partial velocities, partial pressure tensors, partial translational heat fluxes, and partial rotational heat flux. By using the field equations of the 29-field theory and an iterative scheme akin to the Maxwellian procedure, the generalized laws of Fick, Fourier, and Navier-Stokes are obtained. The results of this theory are applied to specific binary mixtures of monatomic gases (He, Ne, Ar, Kr, and Xe) and polyatomic gases (CH 4, and CF 4, and compared with experimental data.

Wall jumps in temperature, partial pressures and populations of multicomponent mixtures of nonequilibrium polyatomic gases

The Maxwell-Loyalka method is used to derive formulas for the jumps in the macroparameters of a multicomponent nonequilibrium gas mixture. It is assumed that within the kinetic (Knudsen) wall layer one group of internal states of the molecules is close to equilibrium at the translational temperature, while another group and homogeneous chemical reactions are excited fairly slowly, so that they may be considered to be frozen and the corresponding inelastic collision integrals in the kinetic equations can be neglected. However, at the wall different groups of internal states of the molecules may be excited and chemical reactions may take place. The final calculation formulas are obtained under a series of simplifying assumptions in accordance with the recommendations made in [1, 2].

Modification of the first approximation of the Chapman-Enskog method for a gas mixture

The authors propose a transformation of the equations of the first approximation of the Chapman-Enskog method for a gas mixture with frozen internal degrees of freedom. As a result, the solution for the perturbation of the distribution functions can be written in terms of the diffusion velocities and temperature gradient, and the derivation of the Stefan-Maxwell relations and the heat flux calculations can be much simplified. The transformations are extended to a mixture of polyatomic gases with nonequilibrium excitation of the internal degrees of freedom of the molecules. The modification of the first approximation of the Chapman-Enskog method does not affect the relations used for calculating the viscosity of the mixture. Accordingly, that part of the solution is not considered.

Alternative expressions for the thermal conductivity of dilute gas mixtures

Abstract New expressions for the thermal conductivity of a multicomponent mixture of polyatomic gases have been derived within the semi-classical Wang Chang-Uhlenbeck kinetic theory. Using the Wang Chang-Uhlenbeck formulation of the solution of the kinetic equations, the thermal conductivity is written explicitly, to an arbitrary order of approximation, in terms of a series of effective cross-sections for the first time and in a form suitable for computer implementation. In the alternative formulation of Thijsse, 't Hooft, Combe, Knaap and Beenakker, the thermal conductivity of the mixture is also written explicitly in terms of the effective cross-section. The resulting expression proves to be much simpler than hitherto available.

Composition dependence of the thermal conductivity of low-density polyatomic gas mixtures

We present a predictive scheme for the composition dependence of the thermal conductivity of mixtures containing polyatomic gases at zero density. This supplements earlier work which developed a method to interpolate for the composition dependence of dense gas mixtures, as well as an earlier procedure to calculate the thermal conductivity of mixtures of monatomic gases. In all cases, the algorithm makes use of accurately measured values of the thermal conductivity of pure gases and is validated with the aid of almost equal accurately measured values of selected binary mixtures. Such accurate data have been obtained mostly in transient hot-wire instruments. The formulae proposed for the calculations use the Monchick-Pereira-Mason kinetic-theory analysis as a starting point but contain a number of detailed improvements. The present algorithm is tested by comparison with measurements on 22 mixtures, which show absolute average deviations from the predictions ranging from 0.7 to 2.7%, with one unexplained case, that of CF4-He mixtures, which show deviations reaching as much as 7%. We estimate that the algorithm predicts the zerodensity thermal conductivity of binary mixtures, containing at least one polyatomic component, with a probable error in the order of 2%.