The influence of vibrational state-resolved transport coefficients on the wave propagation in diatomic gases. (English) Zbl 1514.76078
Summary: A detailed kinetic-theory model for the vibrationally state-resolved transport coefficients is developed taking into account the dependence of the collision cross section on the size of vibrationally excited molecule. Algorithms for the calculation of shear and bulk viscosity, thermal conductivity, thermal diffusion and diffusion coefficients for vibrational states are proposed. The transport coefficients are evaluated for single-component diatomic gases \(\mathrm{N}_2\), \(\mathrm{O}_2\), NO, \(\mathrm{H}_2\), \(\mathrm{Cl}_2\) in the wide range of temperature, and the effects of molecular diameters and the number of accounted states are discussed. The developed model is applied to study wave propagation in diatomic gases. For the case of initial Boltzmann distribution, the influence of vibrational excitation on the phase velocity and attenuation coefficient is found to be weak. We expect more significant effect in the case of initial thermal non-equilibrium, for instance in gases with optically pumped selected vibrational states.
MSC:
| 76P05 | Rarefied gas flows, Boltzmann equation in fluid mechanics |
| 82C40 | Kinetic theory of gases in time-dependent statistical mechanics |
Software:
CHEMKINReferences:
| [1] | Montroll, E.; Shuler, K., Studies in nonequilibrium rate processes. I. The relaxation of a system of harmonic oscillators, J. Chem. Phys., 26, 3, 454-464 (1957) |
| [2] | Lordet, F.; Meolans, J.; Chauvin, A.; Brun, R., Nonequilibrium vibration-dissociation phenomena behind a propagating shock wave: vibrational population calculation, Shock Waves, 4, 299-312 (1995) · Zbl 0840.76089 |
| [3] | Adamovich, I.; Macheret, S.; Rich, J.; Treanor, C., Vibrational energy transfer rates using a forced harmonic oscillator model, J. Thermophys. Heat Transfer, 12, 1, 57-65 (1998) |
| [4] | Colonna, G.; Capitelli, M.; Tuttafesta, M.; Giordano, D., Non-arrhenius NO formation rate in one-dimensional nozzle airflow, J. Thermophys. Heat Transfer, 13, 3, 372-375 (1999) |
| [5] | Kustova, E.; Nagnibeda, E., Transport properties of a reacting gas mixture with strong vibrational and chemical nonequilibrium, Chem. Phys., 233, 57-75 (1998) |
| [6] | Kustova, E., On the simplified state-to-state transport coefficients, Chem. Phys., 270, 1, 177-195 (2001) |
| [7] | Kustova, E.; Nagnibeda, E.; Chauvin, A., State-to-state nonequilibrium reaction rates, Chem. Phys., 248, 2-3, 221-232 (1999) |
| [8] | Kustova, E.; Kremer, G. M., Chemical reaction rates and non-equilibrium pressure of reacting gas mixtures in the state-to-state approach, Chem. Phys., 445, 82-94 (2014) |
| [9] | Armenise, I.; Capitelli, M.; Kustova, E.; Nagnibeda, E., The influence of nonequilibrium kinetics on the heat transfer and diffusion near re-entering body, J. Thermophys. Heat Transfer, 13, 2, 210-218 (1999) |
| [10] | Kustova, E.; Nagnibeda, E.; Armenise, I.; Capitelli, M., Non-equilibrium kinetics and heat transfer in \(O{}_2/O\) mixtures near catalytic surfaces, J. Thermophys. Heat Transfer, 16, 2, 238-244 (2002) |
| [11] | Kustova, E.; Nagnibeda, E.; Alexandrova, T.; Chikhaoui, A., On the non-equilibrium kinetics and heat transfer in nozzle flows, Chem. Phys., 276, 2, 139-154 (2002) |
| [12] | Nagnibeda, E.; Kustova, E., Nonequilibrium Reacting Gas Flows. Kinetic Theory of Transport and Relaxation Processes (2009), Springer-Verlag: Springer-Verlag Berlin, Heidelberg · Zbl 1186.82003 |
| [13] | E. Josyula, J. Burt, E. Kustova, P. Vedula, M. Mekhonoshina, State-to-state kinetic modeling of dissociating and radiating hypersonic flows, AIAA Paper 2015-0475, http://dx.doi.org/10.2514/6.2015-0475. |
| [14] | Kunova, O.; Kustova, E.; Mekhonoshina, M.; Nagnibeda, E., Non-equilibrium kinetics, diffusion and heat transfer in shock heated flows of n \({}_2\)/n and \(O{}_2/O\) mixtures, Chem. Phys., 463, 70-81 (2015) |
| [15] | Armenise, I.; Kustova, E., On different contributions to the heat flux and diffusion in non-equilibrium flows, Chem. Phys., 428, 90-104 (2014) |
| [16] | Armenise, I.; Reynier, P.; Kustova, E., Advanced models for vibrational and chemical kinetics applied to mars entry aerothermodynamics, J. Thermophys. Heat Transfer, 30, 4 (2016) |
| [17] | Kang, S.; Kunc, J., Molecular diameters in high-temperature gases, J. Phys. Chem., 95, 6971-6973 (1991) |
| [18] | Gorbachev, Y.; Gordillo-Vazquez, F.; Kunc, J., Diameters of rotationally and vibrationally excited diatomic molecules, Physica A, 247, 108-120 (1997) |
| [19] | Kunc, J.; Gordillo-Vazquez, F., Rotational-vibrational levels of diatomic molecules represented by the Tietz-Hua rotating oscillator, J. Phys. Chem., 101, 1595-1602 (1997) |
| [20] | Hirschfelder, J., Heat conductivity in polyatomic or electrically excited gases, J. Chem. Phys., 26, 282-285 (1957) |
| [21] | Capitelli, M.; Bruno, D.; Laricchiuta, A., Fundamental Aspects of Plasma Chemical Physics: Transport (2013), Springer Verlag: Springer Verlag Berlin |
| [22] | Istomin, V. A.; Kustova, E. V.; Mekhonoshina, M. A., Eucken correction in high-temperature gases with electronic excitation, J. Chem. Phys., 140, 184311 (2014) |
| [23] | Istomin, V.; Kustova, E., State-specific transport properties of partially ionized flows of electronically excited atomic gases, Chem. Phys., 485-486, 125-139 (2017) |
| [24] | Wysong, I. J., Molecular collision models for reacting flows: should molecular diameters which depend on internal energy state be incorporated in DSMC simulations?, (Brun, R.; Campargue, R.; Gatignol, R.; Lengrand, J.-C., Rarefied Gas Dynamics 21, Vol. 2 (1999), CEPADUES: CEPADUES Toulouse, France), 3-14 |
| [25] | Kustova, E.; Kremer, G. M., Effect of molecular diameters on state-to-state transport properties: the shear viscosity coefficient, Chem. Phys. Lett., 636, 84-89 (2015) |
| [26] | Kustova, E. V.; Kremer, G. M., Influence of state-to-state vibrational distributions on transport coefficients of a single gas, AIP Conference Proceedings, 1786, 1, 070002 (2016), URL http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4967578 |
| [27] | Kornienko, O. V.; Kustova, E. V., Influence of variable molecular diameter on the viscosity coefficient in the state-to-state approach, Vestnik of Saint Petersburg University. Series 1, Mathematics. Mechanics. Astronomy 3, 61, 3, 457-467 (2016) |
| [28] | Huber, K. P.; Herzberg, G., Molecular Spectra and Molecular Structure. IV. Constants of Diatomic Molecules (1979), Van Nostrand: Van Nostrand New York |
| [29] | Kremer, G. M., An Introduction To the Boltzmann Equation and Transport Processes in Gases (2010), Springer: Springer Berlin · Zbl 1317.82002 |
| [30] | Parker, J., Rotational and vibrational relaxation in diatomic gases, Phys. Fluids, 2, 449 (1959) |
| [31] | Kee, R.; Miller, J.; Jefferson, T., Chemkin: A General-Purpose, Problem-Independent, Transportable, Fortran Chemical Kinetics Code Package, SAND80-8003 (1980), Sandia National Laboratories |
| [32] | Damyanova, M.; Zarkova, L.; Hohm, U., Effective intermolecular interaction potentials of gaseous fluorine, chlorine, bromine, and iodine, Int. J. Thermophys., 30, 4, 1165-1178 (2009) |
| [33] | Brau, C.; Johnkman, R., Classical theory of rotational relaxation in diatomic gases, J. Chem. Phys., 52, 477 (1970) |
| [34] | Chapman, S.; Cowling, T., The Mathematical Theory of Non-Uniform Gases (1970), Cambridge University Press: Cambridge University Press Cambridge |
| [35] | Schwartz, R.; Slawsky, Z.; Herzfeld, K., Calculation of vibrational relaxation times in gases, J. Chem. Phys., 20, 1591 (1952) |
| [36] | Bray, K., Vibrational relaxation of anharmonic oscillator molecules: relaxation under isothermal conditions, J. Phys. B. (Proc. Phys. Soc. ), 1, 2, 705 (1968) |
| [37] | Herzfeld, K.; Litovitz, T., Absorption and Dispersion of Ultrasonic Waves (1959), Academic Press: Academic Press New York |
| [38] | Brun, R.; Zappoli, B., Model equations for a vibrationally relaxing gas, Phys. Fluids, 20, 9, 1441-1448 (1977) · Zbl 0368.76070 |
| [39] | Kustova, E.; Oblapenko, G., Reaction and internal energy relaxation rates in viscous thermochemically non-equilibrium gas flows, Phys. Fluids, 27, 016102 (2015) · Zbl 1326.76107 |
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