Polyatomic Gas Mixtures Research Articles

On the Chapman-Enskog asymptotics for a mixture of monoatomic and polyatomic rarefied gases

In this paper, we propose a formal derivation of the Chapman-Enskog asymptotics for a mixture of monoatomic and polyatomic gases. We use a direct extension of the model devised in [8,16] for treating the internal energy with only one continuous parameter. This model is based on the Borgnakke-Larsen procedure [6]. We detail the dissipative terms related to the interaction between the gradients of temperature and the gradients of concentrations (Dufour and Soret effects), and present a complete explicit computation in one case when such a computation is possible, that is when all cross sections in the Boltzmann equation are constants.

Kinetic theory of two-temperature polyatomic plasmas

We investigate the kinetic theory of two-temperature plasmas for reactive polyatomic gas mixtures. The Knudsen number is taken proportional to the square root of the mass ratio between electrons and heavy-species, and thermal non-equilibrium between electrons and heavy species is allowed. The kinetic non-equilibrium framework also requires a weak coupling between electrons and internal energy modes of heavy species. The zeroth-order and first-order fluid equations are derived by using a generalized Chapman–Enskog method. Expressions for transport fluxes are obtained in terms of macroscopic variable gradients and the corresponding transport coefficients are expressed as bracket products of species perturbed distribution functions. The theory derived in this paper provides a consistent fluid model for non-thermal multicomponent plasmas.

Relaxation Time Coupling Method for Ultrasonic Sensor Design

In our previous work [Sens. Actuator B: Chem. 203 1-8 (2014)], a ultrasonic sensor has been proposed to detect gas compositions by the acoustic spectral peak location. However, the effective relaxation area constructed by existing theoretical model cannot match the detection method when there are more than one strong relaxational components in gas mixture. A method that calculates the relaxation time of a multi-component relaxation process is presented. Based on acquirement of decoupled relaxation times and their corresponding effective specific heat values, it calculates the whole relaxation time of a multi-component relaxation process. The method is based on the fact that for a multi-component gas mixture, such as occurs in many polyatomic gas mixtures, the relaxation process should be considered as a whole rather than being decoupled as some single relaxation processes. Acquiring relaxation time provides the approach to obtain the acoustic absorption spectral peak value directly.

A BGK relaxation model for polyatomic gas mixtures

A BGK relaxation model for polyatomic gas mixtures

The gas dynamics equations of slow flows of polyatomic gas mixtures, non-uniform in temperature and concentrations

The formulation of the system of equations of the mechanics of a gas as a continuous medium is completed. This describes the non-stationary slow laminar flow of a mixture of gases (the Mach number being much less than unity), for a Reynolds number and relative drops in temperature and molar fractions of the order of unity. The distribution with respect to the internal energies of the molecules is close to Boltzmann (the case of rapid exchanges of translational and internal energies of the molecules). The difference from the similar system of equations in the Navier–Stokes approximation is the fact that in the equation of motion the Burnett stresses, expressed in terms of the second differential and paired products of the first derivatives with respect to the temperature and molar fractions (concentrations) are taken into account. A consequence of the action of these stresses is thermal-stress and concentration-stress convection. Special cases and possible extensions are considered.

Multicomponent transport in laminar flames

The transport fluxes and transport coefficients derived from the kinetic theory of polyatomic gas mixtures are discussed. The mathematical structure of transport linear systems and numerical algorithms for fast evaluation of accurate transport coefficients are presented. The impact of thermal diffusion and volume viscosity on flame structures and of thermodynamic nonidealities on cold mixing layers are investigated.

Prediction of Thermal Conductivity of Pure Gases and Mixtures

Inter relation between the various transport properties of gases have been presented which enable to compute and predict the thermal conductivity of pure monoatomic as well as polyatomic gases. Similar relations are also presented for multicomponent mixture of monoatomic and polyatomic gases. Many calculations have been performed to have a critical assessment of such approaches and for which this work reveals a very good promise. This has encouraged us to predict thermal conductivity of pure gases and mixtures under conditions where the experiments have not been performed but the data are needed in a variety of important applied problems.

Calculation of Thermal Conductivity of Polyatomic Gas Mixtures at high Temperatures

Reliable methods for prediction of thermal conductivity at high temperature are very useful for a variety of important practical needs. Three different methods (i) approximate (ii) semitheoretical and (iii) empirical have been investigated. The success of these procedures is demonstrated by actual computation for a large number of systems at temperature and compositions where direct meaurements are available. These procedures are valuable as the rigorous theory being complicated requires a large amount of input information and even then leads to unreliable values.

Analytical model for acoustic multi-relaxation spectrum in gas mixtures

To identify the correlation between sound propagation and molecular multimode vibrational relaxation in polyatomic gas mixture, an analytical model that constructs acoustic multi-relaxation spectrum is presented. The frequency-dependent effective specific heat of gas is formulated from the micro view of vibrational mode energy transfer as well as the macro view of relaxation process due to vibrational-vibrational mode energy coupling. With the aid of the general relaxation equations of multimode vibrational energy transfer, the analytical expressions to calculate acoustic relaxation absorption and dispersion, which reflect both primary and secondary relaxation processes, are developed from the effective specific heat. The constructed absorption spectra of various gas mixtures, consisting of carbon dioxide, methane, nitrogen, and oxygen, accord with the experimental data very well. Especially, the peak errors of those results are less than 1%. Moreover, the simulation results illustrate that less than two single processes with higher strength appear generally in a multi-relaxation absorption spectrum. Compared with the existing models, the analytical model can directly obtain the analytical expressions of characteristic points in the relaxation spectrum of gas mixtures, which makes it advantageous to analyze the spectral characteristics qualitatively and quantitatively. Consequently, the model provides an effective approach to analyzing the relationship between sound propagation and molecular vibrational relaxation of gas mixtures.

On the steady flow of a multicomponent, compressible, chemically reacting gas

We consider the system of equations governing the steady flow of a polyatomic isothermal reactive gas mixture. The model covers situations when the pressure depends on species concentration and when the diffusion coefficients of each of the species are density-dependent. It is shown that this problem admits a weak solution provided the adiabatic exponent for the mixture γ is greater than .

Reconstruction algorithm of relaxation attenuation spectrum in polyatomic gas

A reconstruction algorithm that synthesizes the relaxation attenuation spectrum in a wide frequency range is presented. And the effective relaxation time of gas can be estimated by two approaches, which are base on SSH theory and experimental data, respectively. The acoustic attenuation spectra of various polyatomic gas mixtures, consisting of nitrogen, methane, oxygen, carbon dioxide and water, were estimated by the reconstruction algorithm. The sound frequency rang of interest is from 1 Hz to 10 GHz. Comparing with the results of the relaxation attenuation based on the DL model, the estimations of relaxation attenuation of the reconstruction algorithm agreed with the latter. The precision of the reconstruction algorithm depends upon the knowledge of the physical mechanism of molecular relaxation processes. In addition, the reconstruction algorithm was applied to quantitatively determining the concentrations of water and carbon dioxide in some polyatomic gas mixtures. The results show that the relaxation attenuation can be used as a quantitative probe of the composition of polyatomic gas mixtures. And this could lead to the development of smart acoustic gas sensors capable of determining the precise compositions of gas mixtures.

Transformations of the equations of the first approximation of Chapman–Enskog methods and vector transport relations for mixtures of polyatomic gases

Transformations of the systems of equations of the first approximation of the classical and generalized Chapman–Enskog methods are proposed for those terms of the distribution functions by means of which one can calculate the vector transport relations for mixtures of polyatomic gases, connecting the diffusion and heat fluxes and gradients of the scalar gas-dynamic variables. The solutions of the transformed systems are expressed in terms of diffusion rates and gradients of the macroparameters. The derivation and formulae for the coefficients of the Stefan–Maxwell relations and their generalizations are simplified, and rigorous results for the matrices of the transport coefficients are established. Approximate vector transport relations are given for mixtures of non-equilibrium reacting polyatomic gases.

Fine-tuning molecular acoustic models: sensitivity of the predicted attenuation to the Lennard–Jones parameters

In a previous paper [Y. Dain and R. M. Lueptow, J. Acoust. Soc. Am. 109, 1955 (2001)], a model of acoustic attenuation due to vibration-translation and vibration-vibration relaxation in multiple polyatomic gas mixtures was developed. In this paper, the model is improved by treating binary molecular collisions via fully pairwise vibrational transition probabilities. The sensitivity of the model to small variations in the Lennard-Jones parameters--collision diameter (sigma) and potential depth (epsilon)--is investigated for nitrogen-water-methane mixtures. For a N2(98.97%)-H2O(338 ppm)-CH4(1%) test mixture, the transition probabilities and acoustic absorption curves are much more sensitive to sigma than they are to epsilon. Additionally, when the 1% methane is replaced by nitrogen, the resulting mixture [N2(99.97%)-H2O(338 ppm)] becomes considerably more sensitive to changes of sigma(water). The current model minimizes the underprediction of the acoustic absorption peak magnitudes reported by S. G. Ejakov et al. [J. Acoust. Soc. Am. 113, 1871 (2003)].

The impact of the Lennard-Jones parameter choice on theoretical acoustic absorption and dispersion curves

The acoustic vibrational relaxation in polyatomic gas mixtures is modeled based on binary collisions treated via pairwise transition probabilities. The sensitivity of the model to the values of the Lennard-Jones parameters (potential well depth and collision diameter) is investigated for nitrogen–water–methane mixtures. The choice of the collision diameter has a far greater effect on the transition probabilities and subsequently on the acoustic absorption than that of the Lennard-Jones potential depth. In addition, the sensitivity of the acoustic relaxation model to the choice of an LJ parameter (the collision diameter for water, for the mixture considered) is itself sensitive to the mixture composition. Thus, a binary mixture of moist nitrogen with 338 ppm water is considerably more sensitive to changes of the water collision diameter than is a mixture of nitrogen, 338 ppm water and 1% methane. [Work supported by NASA.]

New Approximate Formulas for Viscosity and Thermal Conductivity of Dilute Gas Mixtures

New approximate formulas are developed for accurately estimating the viscosity and thermal conductivity of dilute, polyatomic gas mixtures, which may include polar and nonpolar species. For the viscosity and the translational energy contribution to the thermal conductivity, the new formulas use well-known approximations for the required collision integrals in an analytic formula obtained from a single iteration of the preconditioned conjugate-gradient method for solving the linear transport equations. Unlike many approximate formulas, they are derived from a manifestly multicomponent solution of the transport equations and include, to lowest order, contributions from the off-diagonal elements of the transport property matrix. For polyatomic mixtures, the internal energy contribution to the thermal conductivity is obtained using the Hirschfelder ‐Eucken formalism or the Thijsse total-energy formalism. The new rules require the pure species viscosity, conductivity, molecular weight, specie c heats, and the Lennard ‐Jones or Stockmayer potential parameters and are easy to numerically evaluate.Bytheuseofalargeexperimentalviscosityandconductivitydatabasecoveringabroadrangeofmolecular weights, gas temperatures, and molar compositions, these rules were tested, and their predictions compared with those of the Wilke and Brokaw rules for viscosity and conductivity and the Mason ‐Saxena rule for conductivity. Thenewrulesperformbetterthan theWilkerules, havecomparableperformanceto theBrokawrulesand Mason ‐ Saxena conductivity rule for binary mixture data, and outperform the Wilke, Brokaw, and Mason ‐Saxena rules for multicomponent mixture data.

Kinetic Theory of Reactive Gas Mixtures with Application to Combustion

We consider a generalized Boltzmann equation valid for dilute, isotropic, polyatomic gas mixtures with chemical reactions. Depending on the ratio of characteristic times between reactive and inert collisions, various chemical regimes are obtained in the first order Enskog expansion and their compatibility with the Boltzmann H-theorem is investigated. We then review the mathematical structure of the transport linear systems resulting from a Galerkin approximation of the integral equations satisfied the species perturbed distribution functions. The multicomponent transport coefficients are written as convergent series and accurate approximate expressions are obtained by truncation. Numerical results are presented for combustion applications including laminar flame propagation, counterflow flame extinction and multidimensional Bunsen flames.

Thermal Conductivity of Nitrogen-Methane Mixtures at Temperatures Between 300 and 425 K and at Pressures Up to 16 MPa

The thermal conductivities of nitrogen and three mixtures of nitrogen and methane at six nominal temperatures between 300 and 425 K have been measured as a function of pressure up to 16 MPa. The relative uncertainty of the thermal conductivity measurements at a 95% confidence level is estimated to be less then 1%. The data obtained and the results of the low-density analysis were used to test two prediction methods for the thermal conductivity of gas mixtures under pressure and for the thermal conductivity of dilute polyatomic gas mixtures. Reasonable agreement was found with expressions for predicting thermal conductivity of nonpolar mixtures in a dilute-gas limit developed by Schreiber et al. The scheme underestimates the experimental thermal conductivity with deviations not exceeding 3%. The prediction scheme for the thermal conductivity of gas mixtures under pressure suggested by Mason et al. and improved by Vesovic and Wakeham underestimates the experimental thermal conductivities throughout, likely due to its use of the Hirchsfelder–Eucken equation at the low-density limit.

On Dissipative Fluxes in a Mixture of Polyatomic Gases

From the system of linearized kinetic equations, the diffusion and heat fluxes and the stress tensor for slow steady-state flows of a mixture of polyatomic gases are obtained and the transfer coefficients are found.

Calculation of Heat Transfer and Drag in Tubes under Conditions of Laminar Flow of Gases with Varying Properties

A numerical investigation is performed of the problem on heat transfer and hydraulic drag in the hydrodynamic and thermal initial sections of a round tube heated by the qw = const law, under conditions of laminar flow of gases with varying physical properties. Monatomic, diatomic, and polyatomic gases and gas mixtures are treated, as well as the range of heat loads Q+in up to 20. The obtained results are used to analyze disagreement between the available literature data; methods are suggested for improving the engineering procedure of thermohydraulic design under laminar flow of gases and the known model of stabilized flow and heat transfer.

The transport properties of gases in Burnett's approximation

The relations necessary to calculate Burnett's corrections to the distribution functions of the molecules of multicomponent mixtures of polyatomic gases are derived. Effective expressions for the transport properties and “working” formulae for the transport coefficients of a binary mixture of monatomic gases and a polyatomic gas in Burnett's approximation ignoring external forces are obtained. The transient equations of thermal stress convection of a polyatomic gas are considered and estimates of the effect of the rotational degrees of freedom of the molecules on the coefficients of these equations are given.