Using thermal nonequilibrium physicochemical kinetics models, allowing to numerically study the reacting gas flows with allowance for the processes of vibrational and electronic-translational relaxation and exchange as well as chemical and plasma-chemical reactions based on the data on electrical properties (polarizability, dipole moment) of neutral and charged gaseous species in their ground and excited electronic states, the profiles of the Gladstone – Dale constant and refractive index are calculated for two model problems: relaxation of air behind the shock wave front and expansion of hydrogen and syngas combustion products in a supersonic nozzle. For each of the problems, the analysis of accuracy of different approximations in calculation of the gas optical properties is carried out.
Учет влияния термической неравновесности и ионизации на показатель преломления реагирующего газа: атмосферный воздух и продукты сгорания
С использованием термически-неравновесных моделей физико-химической кинетики, позволяющих численно исследовать течения реагирующего газа с учетом про-цессов колебательно- и электронно-поступательной релаксации и обмена, а также химических и плазмо-химических реакций на основе данных об электрических свойствах (поляризуемость, дипольный момент) нейтральных и заряженных компонентов газа в основном и возбужденных состояниях рассчитаны профили константы Гладстона – Дейла и показателя преломления для двух модельных задач: релаксация воздуха за фронтом ударной волны и расширение продуктов сгорания водорода и синтез-газа в сверхзвуковом сопле. Для каждой из задач проведен анализ точности различных приближений при расчете оптических свойств газа.
1. Kharitonov A.I., Khoroshko K.S., Shkadova V.P. Temperature dependence of air refraction at high temperature // Fluid Dyn., 1974, Vol. 9, pp. 851-853. 2. Osipov A.I., Uvarov A.V. Kinetic and gasdynamic processes in nonequilibrium molecular physics // Sov. Phys. Usp., 1992, Vol. 35, pp. 903-923. 3. Sharipov A.S., Loukhovitski B.I., Starik A.M. Influence of Vibrations and Rotations of Diatomic Molecules on Their Physical Properties: II. Refractive Index, Diffusion Coefficients, Reactivity // J. Phys. B: At. Mol. Opt. Phys., 2016, Vol. 49, No. 125103. 4. Sharipov A.S., Loukhovitski B.I., Loukhovitskaya E.E. Influence of Internal Degrees of Freedom on Electric and Related Molecular Properties, Maroulis, G. (ed.); Springer International Publishing, 2022. 5. Lukhovitskii B.I., Sharipov A.S.; Arsent'ev I.V., Kuzmitskii, V.V., Penyazkov O. G. On the refractive index of a gas under high-thermal-nonequilibrium conditions // J. Eng. Phys. Thermophys., 2020, Vol. 93, pp. 850-857. 6. Osipov A.I., Panchenko V.Y., Filippov A.A. Refractive index of a vibrationally excited gas // Sov. J. Quant. Electron., 1984, Vol. 14, pp. 1259-1260. 7. Bishop D.M. Molecular vibrational and rotational motion in static and dynamic electric fields // Rev. Mod. Phys., 1990, Vol. 62, pp. 343-374. 8. Tropina A.A., Wu Y., Limbach C.M., Miles R.B. Influence of vibrational non-equilibrium on the polarizability and refraction index in air: computational study // J. Phys. D: Appl. Phys., 2019, Vol. 53, No. 105201. 9. Sharipov A.S., Pelevkin A.V., Loukhovitski B.I. A simple semiempirical model for the static polarizability of electronically excited atoms and molecules // Chin. Phys. B, 2023, Vol. 32, No. 043301. 10. Cvetanovic R.J. Excited State Chemistry in the Stratosphere // Can. J. Chem., 1974, Vol. 52, pp. 1452-1464. 11. Capitelli M., Ferreira C.M., Gordiets B.F., Osipov A.I. Plasma Kinetics in Atmospheric Gases, Springer-Verlag, Berlin, 2000. 12. Fridman A. Plasma Chemistry, Cambridge University Press, Cambridge, UK, 2008. 13. Krasnopolsky V.A. Atmospheric chemistry on Venus, Earth, and Mars: Main features and comparison // Planet. Space Sci., 2011, Vol. 59, pp. 952-964. 14. Shang J.S., Surzhikov S.T. Nonequilibrium radiative hypersonic flow simulation // Prog. Aerosp. Sci., 2012, Vol. 53, pp. 46-65. 15. Sharipov A.S., Loukhovitski B.I., Pelevkin A.V., Kobtsev V.D., Kozlov D.N. Polarizability of Electronically Excited Molecular Oxygen: Theory and Experiment // J. Phys. B: At. Mol. Opt. Phys., 2019, Vol. 52, No. 045101. 16. Arsentiev I.V. On the influence of discharge parameters on the kinetics of plasma-assisted combustion of synthesis gas in air // Physical-Chemical Kinetics in Gas Dynamics, 2021, Vol. 22, http://chemphys.edu.ru/issues/2021-22-5/articles/953 (in Russian, English abstract) 17. Kadochnikov I.N. Modelling of syngas/air laser-induced ignition with the state-to-state vibrational kinetics taken into consideration // Physical-Chemical Kinetics in Gas Dynamics, 2021, Vol. 22, http://chemphys.edu.ru/issues/2021-22-6/articles/961 (in Russian, English abstract) 18. Kadochnikov I.N., Arsentiev I.V., Loukhovitski B.I., Sharipov A.S. State-to-state vibrational kinetics of diatomic molecules in laser-induced ignition of a syngas-air mixture: modeling study // Chem. Phys., 2022, Vol. 562, No. 111669. 19. Yun-yun C., Zhen-hua L., Yang S., An-zhi H. Extension of the Gladstone-Dale equation for flame flow field diagnosis by optical computerized tomography // Appl. Opt., 2009, Vol. 48, pp. 2485-2490. 20. Wang M., Mani A., Gordeyev S. Physics and Computation of Aero-Optics // Annu. Rev. Fluid Mech., 2012, Vol. 44, pp. 299-321. 21. Sharma S.P., Ruffin S.M., Meyer S.A., Gillespie W.D., Yates L.A. Density Measurements in an Expanding Flow Using Holographic Interferometry // J. Thermophys. Heat Transfer, 1993, Vol. 7, pp. 261-268. 22. Kuzmitskiy V.V., Penyazkov O.G., Buganov O.V. Visualization of nonequilibrium gas flows by schlieren technique with a double-pulse femtosecond laser a source of optical radiation // Nonequilibrium processes. Vol. 1. Kinetics and plasma / [Edited by S.M. Frolov and A.I. Lanshin], Moscow: Torus Press, 2019, pp. 162-171. 23. Tropina A.A., Wu Y., Limbach C.M., Miles R.B. Aero-optical effects in non-equilibrium air // AIAA paper, 2018, No. 3904. 24. Alpher R.A., White D.R. Optical Refractivity of High Temperature Gases. I. Effects Resulting from Dissociation of Diatomic Gases // Phys. Fluids, 1959, Vol. 2, pp. 153-161. 25. Byron S. Shock-Tube Measurement of the Rate of Dissociation of Nitrogen // J. Chem. Phys., 1966, Vol. 44, pp. 1378-1388. 26. Kiefer J.H., Sathyanarayana R. Vibrational relaxation and dissociation in the perfluoromethyl halides, CF3Cl, CF3Br, and CF3I // Int. J. Chem. Kinet., 1997, Vol. 29, pp. 705-716. 27. Mackey L.E., Boyd I.D. Assesment of hypersonic flow physics on aero-optics // AIAA J., 2019, Vol. 57, pp. 3885-3897. 28. Craig J.E., Azzazy M., Poon C.C. Resonant Holographic Detection of Hydroxyl Radicals in Reacting Flows // AIAA J., 1986, Vol. 24, pp. 74-81. 29. White D.R. Optical Refractivity of High Temperature Gases. III. The Hydroxyl Radical // Phys. Fluids, 1961, Vol. 4, pp. 40-45. 30. Zuev A.P., Negodyaev S.S., Tkachenko B.K. Laser schlieren measurement of vibrational relaxation times for N2O in mixtures containing CO, N2, and Ar behind a shock wave // Sov. Phys. J., 1984, Vol. 27, pp. 911-914. 31. Kiefer J., Buzyna L., Dib A., Sundaram S. Observation and analysis of nonlinear vibrational relaxation of large molecules in shock waves // J. Chem. Phys., 2000, Vol. 113, pp. 48-58. 32. Saxena S., Kiefer J.H., Tranter R.S. Relaxation, Incubation, and Dissociation in CO2 // J. Phys. Chem. A, 2007, Vol. 111, pp. 3884-3890. 33. Alpher R.A., White D.R. Optical Refractivity of High Temperature Gases. II. Effects Resulting from Ionization of Monatomic Gases // Phys. Fluids, 1959, Vol. 2, pp. 162-169. 34. van der Veek B., Chintalapati S., Kirk D.R., Gutierrez H. Modeling and Validation of Ku-Band Signal Attenuation Through Rocket Plumes // J. Spacecraft Rockets, 2013, Vol. 50, pp. 992-1001. 35. Golubkov G.V., Golubkov M.G., Manzhelii M.I. Rydberg States in the D Layer of the Atmosphere and the GPS Positioning Errors // Russ. J. Phys. Chem. B, 2014, Vol. 8, pp. 103-115. 36. Takahashi Y., Yamada K., Abe T. Prediction Performance of Blackout and Plasma Attenuation in Atmospheric Reentry Demonstrator Mission // J. Spacecraft Rockets, 2014, Vol. 51, pp. 1954-1964. 37. Takahashi Y., Nakasato R., Oshima N. Analysis of Radio Frequency Blackout for a Blunt-Body Capsule in Atmospheric Reentry Missions // Aerospace, 2016, Vol. 3, No. 2. 38. Liang Y., Wu J., Li H., Tian R., Yuan C., Wang Y., Kudryavtsev A.A., Zhou Z., Tian H. A kinetic model for investigating the dielectric properties of rocket exhaust dusty plasmas // Phys. Plasmas, 2019, Vol. 26, No. 043704. 39. Gladkov S.M., Koroteev N.I. Quasiresonant nonlinear optical processes involving excited and ionized atoms // Sov. Phys. Usp., 1990, Vol. 33, pp. 554-575. 40. Cao S.Q., Su M.G., Jiao Z.H., Min Q., Sun D.X., Ma P.P., Wang K.P., Dong C.Z. Dynamics and density distribution of laser-produced plasma using optical interferometry // Phys. Plasmas, 2018, Vol. 25, No. 063302. 41. Zimakov V.P., Lavrentyev S.Y., Solovyov N.G., Shemyakin A.N., Yakimov M.Y. Spatial and Temporal Instabilities of Optical Discharges // Physical-Chemical Kinetics in Gas Dynamics, 2018, Vol. 19, http://chemphys.edu.ru/issues/2018-19-4/articles/754/ (in Russian, English abstract) 42. Egan P.F., Stone J.A., Scherschligt J.K., Harvey A.H. Measured relationship between thermodynamic pressure and refractivity for six candidate gases in laser barometry // J. Vac. Sci. Technol. A, 2019, Vol. 37, No. 031603. 43. Rourke P.M.C., Gaiser C., Gao B., Ripa D.M., Moldover M.R., Pitre L., Underwood R. Refractive-index gas thermometry // Metrologia, 2019, Vol. 56, No. 032001. 44. Gaiser C., Fellmuth B., Sabuga W. Primary gas-pressure standard from electrical measurements and thermophysical ab initio calculations // Nature Physics, 2020, Vol. 16, pp. 177-180. 45. Gardiner Jr. W.C., Hidaka Y., Tanzawa T. Refractivity of Combustion Gases // Combust. Flame, 1981, Vol. 40, pp. 213-219. 46. Bel'skii V.M., Mikhailov A.L., Rodionov A.V., Sedov A.A. Microwave Diagnostics of Shock-Wave and Detonation Processes // Combust. Expl. Shock Waves, 2011, Vol. 47, pp. 639-650. 47. Meidanshahi F. S., Madanipour K., Shokri B. Investigation of first and second ionization on optical properties of atmospheric plasmas // Opt. Commun., 2012, Vol. 285, pp. 453-458. 48. Wu Y., Tropina A.A., Miles R.B., Limbach C.M. Measurements of N2 refractive index and scalar polarizability in a pulsed nanosecond non-equilibrium discharge by Mach-Zehnder interferometry and spontaneous Raman scattering // J. Phys. D: Appl. Phys., 2020, Vol. 53, No. 485203. 49. Loukhovitski B.I., Sharipov A.S., Starik A.M. Influence of vibrations and rotations of diatomic molecules on their physical properties: I. Dipole moment and static dipole polarizability // J. Phys. B: At. Mol. Opt. Phys., 2016, Vol. 49, No. 125102. 50. Sharipov A.S., Loukhovitski B.I., Starik A.M. Influence of Vibrations of Polyatomic Molecules on Dipole Moment and Static Dipole Polarizability: Theoretical Study // J. Phys. B: At. Mol. Opt. Phys., 2017, Vol. 50, No. 165101. 51. Sharipov A.S., Loukhovitski B.I. A simple semiempirical model for the static polarizability of ions // Chin. Phys. B, 2023 (in press). DOI: 10.1088/1674-1056/acd2b2 52. Kadochnikov I.N., Arsentiev I.V. Kinetics of Nonequilibrium Processes in Air Plasma Formed behind Shock Waves: State-to-State Consideration // J. Phys. D: Appl. Phys., 2018, Vol. 51, No. 374001. 53. Kadochnikov I.N., Arsentiev I.V. Modelling of vibrational nonequilibrium effects on the H2-air mixture ignition under shock wave conditions in the state-to-state and mode approximations // Shock Waves, 2020, Vol. 30, pp. 491-504. 54. Nelson Jr. R.D., Lide Jr. D.R., Maryott A.A. Selected values of electric dipole moments for molecules in the gas phase // National Standard Reference Data Series, National Bureau of Standards 10, 1967. 55. Teuff Y.H.L., Millar T.J., Markwick A.J. The UMIST database for astrochemistry 1999 // Astron. Astrophys. Suppl. Ser., 2000, Vol. 146, pp. 157-168. 56. Lide D.R. (ed.) CRC Handbook of Chemistry and Physics, 90th Edition, CRC press, 2010. 57. Hohm U. Experimental Static Dipole-Dipole Polarizabilities of Molecules // J. Mol. Struct., 2013, Vol. 1054-1055, pp. 282-292. 58. Schwerdtfeger P., Nagle J.K. 2018 Table of static dipole polarizabilities of the neutral elements in the periodic table // Mol. Phys., 2019, Vol. 117, pp. 1200-1225. 59. Johnson III R.D. 2010 NIST computational chemistry comparison and benchmark database, NIST standard reference database number 101 release 15a. 60. Lie G.C., Hinze J., Liu B. Valence excited states of CH. II. Properties // J. Chem. Phys., 1973, Vol. 59, pp. 1887-1898. 61. Adamowicz L. Numerical multiconfiguration self-consistent field study of the total (electronic and nuclear) parallel polarizability and hyperpolarizability for the OH, OH+, OH- // J. Chem. Phys. 1988, Vol. 89, pp. 6305-6309. 62. Andersson K., Sadlej A.J. Electric dipole polarizabilities of atomic valence states // Phys. Rev. A, 1992, Vol. 46, pp. 2356-2362. 63. Éhn L., Černušak I. Atomic and ionic polarizabilities of B, C, N, O, and F // Int. J. Quantum Chem., 2020, Vol. 121, No. e26467. 64. Wang K., Wang X., Fan Z., Zhao H.-Y., Miao L., Yin G.-J., Moro R., Ma L. Static dipole polarizabilities of atoms and ions from Z=1 to 20 calculated within a single theoretical scheme // Eur. Phys. J. D, 2021, Vol. 75, No. 46. 65. Sharipov A., Loukhovitski B., Pelevkin A. Diffusion Coefficients of Electronically Excited Molecules // Physical-Chemical Kinetics in Gas Dynamics, 2021, Vol. 22, http://chemphys.edu.ru/issues/2021-22-1/articles/913/ (in Russian, English abstract) 66. Weck G., Milet A., Moszynski R., Kochanski E. Analysis of accuracy in ab initio calculations of the static dipole polarizability components. Examples of the water molecule and hydroxide ion // J. Comput. Methods Sci. Eng., 2004, Vol. 4, pp. 501-516. 67. Kerl K., Hohm U., Varchmin H. Polarizability α(ω, T, ρ) of Small Molecules in the Gas Phase // Ber. Bunsenges. Phys. Chem., 1992, Vol. 96, pp. 728-733. 68. Nagnibeda E. A., Papina K.V. Chemical Kinetics in Air Flows in Nozzles // Physical-Chemical Kinetics in Gas Dynamics, 2016, Vol. 17, http://chemphys.edu.ru/issues/2016-17-2/articles/635/ (in Russian, English abstract) 69. Starik A.M., Kozlov V. E., Titova N.S. On the Influence of Singlet Oxygen Molecules on Characteristics of HCCI Combustion: A Numerical Study // Combust. Theory Model., 2013, Vol. 17, pp. 579-609. 70. Knyazkov D.A., Bolshova T.A., Dmitriev A.M., Shmakov A.G., Korobeinichev O. P. Experimental and Numerical Investigation of the Chemical Reaction Kinetics in H2/CO Syngas Flame at a Pressure of 1–10 atm // Combust. Expl. Shock Waves, 2017, Vol. 53, pp. 388-397. 71. Belhi M., Han J., Casey T.F., Chen J.-Y., Im H.G., Sarathy S.M., Bisetti F. Analysis of the current-voltage curves and saturation currents in burner-stabilised premixed flames with detailed ion chemistry and transport models // Combust. Theor. Model. 2018, Vol. 22, pp. 939-972.