Nonlinear Dynamics of Acoustic Instability in a Vibrationally Excited Gas: Influence of Heating and Cooling


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The dynamics of unstable sound waves in a nonequilibrium vibrationally excited gas is considered, taking into account viscosity and thermal conductivity. A numerical model has been constructed and a computational tool has been developed to study the linear and nonlinear stages of the development of acoustic instability in a nonequilibrium gas with different models of relaxation, heating and cooling times. The numerical model has high spatial resolution and second order accuracy. It is shown that at the initial stage, small disturbances generated by a sound source grow exponentially in accordance with the conclusions of linear theory. At the nonlinear stage of development of acoustic instability, a sawtooth system of weak shock waves is first formed, and then, due to the interaction (merger) of shock waves, a quasi-stationary system of high-intensity shock wave pulses is formed.

nonequilibrium gas, vibrational relaxation, instability of sound waves, shock waves, numerical methods CSPH-TVD and MUSCL

DOI: http://doi.org/10.33257/PhChGD.24.6.1059


Volume 24, issue 6, 2023 year


Нелинейная динамика акустической неустойчивости в колебательно-возбужденном газе: влияние нагрева и охлаждения

Рассмотрена динамика неустойчивых звуковых волн в неравновесном колебательно-возбужденном газе с учетом вязкости и теплопроводности. Построена численная модель и разработан вычислительный инструмент для исследования линейной и нелинейной стадии развития акустической неустойчивости в неравновесном газе с различными моделями времени релаксации, нагрева и охлаждения. Численная модель обладает высоким пространственным разрешением и имеет второй порядок точности. Показано, что на начальной стадии малые возмущения, генерируемые источником звука, нарастают по экспоненциальному закону в соответствии с выводами линейной теории. На нелинейной стадии развития акустической неустойчивости сначала формируется пилообразная система слабых ударных волн, а затем из-за взаимодействия (слияния) ударных волн образуется квазистационарная система ударно-волновых импульсов высокой интенсивности.

неравновесный газ, колебательная релаксация, неустойчивость звуковых волн, ударные волны, численные методы CSPH-TVD и MUSCL

DOI: http://doi.org/10.33257/PhChGD.24.6.1059


Volume 24, issue 6, 2023 year



Анимация динамики акустической неустойчивости (работает только в Acrobat Reader)

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1. Kogan E.Y., Molevich N.E. Sound waves in a nonequilibrium molecular gas // Soviet Physics Journal. 1986. V. 29. P. 547–551.
2. Molevich N.E., Oraevsky A.N. Sound viscosity in media in thermodynamic disequilibrium // Soviet Physics - JETP. 1988. V. 67. № 3. P. 504¬–508.
3. Osipov A.I., Uvarov A.V. Kinetic and gasdynamic processes in nonequilibrium molecular physics // Sov. Phys. Usp. 1992. V. 35 № 11. P. 903–923.
4. Molevich N.E. Sound velocity dispersion and second viscosity in media with nonequilibrium chemical reactions // Acoustical Physics. 2003. V. 49. № 2. P. 189–192.
5. Zavershinskii D., Molevich N., Belov S., Riashchikov D. Overstability of acoustic waves in heat-releasing gaseous media // AIP Conference Proceedings. 2020. V. 2304, issue 1, article id.020028. DOI: 10.1063/5.0034849
6. Napalkov O., Kustova E., Saifutdinov A. I. Study of microwave discharges in air on the basis of extended fluid-dynamic model // Physical-Chemical Kinetics in Gas Dynamics. 2023. V.24, iss. 5. http://chemphys.edu.ru/issues/2023-24-5/articles/1063/
7. Surzhikov S. Application of Quasi-Stationary eRC Models for the Calculation of Non-Equilibrium Radiation of Shock Waves at Velocity about 10 km/s//Physical-Chemical Kinetics in Gas Dynamics. 2022. V.23, iss. 4. http://chemphys.edu.ru/issues/2022-23-4/articles/1015/
8. Litvintsev A. S., Molchanova A. N., Vashchenkov P. V., Kashkovsky A. V., Bondar Y. A. Influence of surface chemical reactions on high-altitude aerothermodynamics of a model capsule // Physical-Chemical Kinetics in Gas Dynamics. 2023. V.24, iss. 2. http://chemphys.edu.ru/issues/2023-24-2/articles/1035/
9. Shoev G.V., Bondar Y.A., Oblapenko G.P., Kustova E.V. Development and testing of a numerical simulation method for thermally nonequilibrium dissociating flows in ANSYS Fluent // Thermophysics and Aeromechanics. 2016. Т. 23. № 2. С. 151-163.
10. Osipov A.I., Uvarov A.V. Stability problems in a nonequilibrium gas // Physics-Uspekhi. 1996. V. 39. № 6. P. 597–608.
11. Makarian V., Molevich N. Структура слабых ударных волн в стационарно неравновесной среде // Physical-Chemical Kinetics in Gas Dynamics. 2005. V.3. http://chemphys.edu.ru/issues/2005-3/articles/84/
12. Makaryan V.G., Molevich N.E. Weak shock waves in negative-dispersion nonequilibrium media // Technical Physics. 2005. V. 50. № 6. P. 685–691.
13. Makaryan V.G., Molevich N.E. Stationary shock waves in nonequilibrium media // Plasma Sources Science and Technology. 2007. V. 16. № 1. P. 124–131.
14. Molevich N.E., Galimov R.N., Makaryan V.G., Zavershinskii D.I. General nonlinear acoustical equation of relaxing media and its stationary solutions // J. Acoust. Soc. Am. 2013. V. 133. № 5. P. 3555–3563.
15. Nelson D., Springel V., Pillepich A. et al. The IllustrisTNG simulations: public data release // Comput. Astrophys. 2019. V. 6. № 2. P. 1–29.
16. Crain R.A., van de Voort F. Hydrodynamical Simulations of the Galaxy Population: Enduring Successes and Outstanding Challenges // Annual Review of Astronomy and Astrophysics. 2023. V. 61. P. 473–515.
17. Elizarova T.G., Istomina M.A., Zlotnik A.A. Hydrodynamical aspects of the formation of spiral–vortical structures in rotating gaseous disks // Astronomy Reports. 2018. V. 62. № 1. P. 9–18.
18. Khoperskov S., Zinchenko I., Avramov B., Khrapov S., Berczik P., Saburova A., Ishchenko M., Khoperskov A., Pulsoni C., Venichenko Yu., Bizyaev D., Moiseev A. Extreme kinematic misalignment in IllustrisTNG galaxies: the origin, structure, and internal dynamics of galaxies with a large-scale counterrotation // Monthly Notices of the Royal Astronomical Society. 2021. V. 500. № 3. P. 3870–3888.
19. Khoperskov S., Haywood M., Snaith O., Di Matteo P., Lehnert M., Vasiliev E., Naroenkov S., Berczik P. Bimodality of [αFe]-[Fe/H] distributions is a natural outcome of dissipative collapse and disc growth in Milky Way-type galaxies // Monthly Notices of the Royal Astronomical Society 2021. V. 501. P. 5176–5196.
20. Butenko M.A., Belikova I.V., Kuzmin N.M., Khokhlova S.S., Ivanchenko G.S., Ten A.V., Kudina I.G. Numerical simulation of the galaxies outer spiral structure: the influence of the dark halo non-axisymmetry on the gaseous disk shape // Mathematical Physics and Computer Simulation. 2022. V. 25. № 3. P. 73–83.
21. Panasenko A. Calculation of Shock Wave Formation in a Shock Tube with a Different Method of Initial Gas Outflow // Physical-Chemical Kinetics in Gas Dynamics. 2023. V.24, iss. 3. http://chemphys.edu.ru/issues/2023-24-3/articles/1045/
22. Khoperskov A.V., Khrapov S.S., Nedugova E.A. Dissipative-Acoustic Instability in Accretion Disks at a Nonlinear Stage // Astronomy Letters. 2003. V. 29. № 4. P. 246–257.
23. Afanasiev V.L., Dodonov S.N., Khrapov S.S., Mustsevoi V.V., Moiseev A.V. Formation of ionization-cone structures in active galactic nuclei: II. Nonlinear hydrodynamic modelling // Astrophysical Bulletin. 2007. V. 62. № 1. P. 15–25.
24. Khrapov S., Khoperskov A. Dynamics of unstable sound waves in a non-equilibrium medium at the nonlinear stage // Journal of Physics: Conference Series. 2018. V. 973. id. 012007. P.1–11. DOI: 10.1088/1742-6596/973/1/012007
25. Khrapov S., Khoperskov A., Khoperskov S. Lagrange-Eulerian method for numerical integration of the gas dynamics equations: parallel implementation on GPUs // Journal of Physics: Conference Series. 2019. V. 1392. id. 012041. DOI: 10.1088/1742-6596/1392/1/012041
26. van Leer B. Towards the Ultimate Conservation Difference Scheme V. A Second Order Sequel to Godunov’s Method // J. Comput. Phys. 1979. V. 32. P. 101–136.
27. Khoperskov S.A., Vasiliev E.O., Sobolev A.M., Khoperskov A.V. The simulation of molecular clouds formation in the Milky Way // Monthly Notices of the Royal Astronomical Society. 2013. V. 428. P. 2311–2320.
28. Landau L., Teller E. Theory of sound dispersion // Physik Zeitschrift der Sowjetunion. 1936. V. 10. P. 34–43.
29. Kosareva A.A., Nagnibeda E.A. Dissociation and vibrational relaxation in a spatially homogeneous mixture CO2/CO/O. // Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy. 2016. № 3. P. 468–480.
30. Millikan R.C., White D.R. Systematics of vibrational relaxation // J. Chem. Phys. 1963. V. 39. P. 3209–3213.
31. Kustova E., Oblapenko G., Sharafutdinov I. Vibrational relaxation models for non-equilibrium multi-temperature flows//Physical-Chemical Kinetics in Gas Dynamics. 2015. V.16, iss. 2. http://chemphys.edu.ru/issues/2015-16-2/articles/536/
32. Gordiets B.F., Osipov A.I., Stupochenko E.V., Shelepin L.A. Vibrational relaxation in gases and molecular lasers // Sov. Phys. Usp. 1973. V. 15. P. 759–785.
33. Park C. Nonequilibrium Hypersonic Aerothermodynamics. J.Wiley and Sons, New York, Chichester, Brisbane, Toronto, Singapore, 1990.
34. Kovach E., Losev S., Sergievskaya A., Khrapak N. Catalogue of models of physical and chemical processes. Part 2. Vibrational energy exchange processes // Physical-Chemical Kinetics in Gas Dynamics. 2010. V.10. http://chemphys.edu.ru/issues/2010-10/articles/332/
35. Alemasov V.E., Dregalin A.F., Tishin A.P., Khudyakov V.A., Kostin V.N. Thermodynamic and thermophysical properties of combustion products. M.: VINITI, USSR Academy of Sciences. 1980. T. 10. No. 1. 379 p.
36. Khrapov S.S., Ivanchenko G.S., Radchenko V.P., Titov A.V. Numerical Simulation of Acoustic Instability in a Nonequilibrium Vibrationally Excited Gas // Journal of Technical Physics. 2023. V. 93. Issue. 12. P.1727-1731.
37. Khrapov S.S., Ivanchenko G.S., Radchenko V.P., Makoveev I.S. Dynamics of Small Disturbances in a Nonequilibrium Vibrationally Excited Gas // Mathematical physics and computer modeling. 2023. V. 26. No. 4. P. 83-105.
38. Harten A., Lax P., van Leer B. On upstream differencing and Godunov type methods for hyperbolic conservation laws // SIAM review. 1983. V. 25. P. 35-61.
39. Toro E.F., Spruce M., Speares W. Restoration of the Contact Surface in the HLL-Riemann Solver // Shock Waves. 1994. V. 4. № 1. P. 25–34.
40. Harten A. High Resolution Schemes for Hyperbolic Conservation Laws // J. Comput. Phys. 1983. V. 49. P. 357-393.
41. Monaghan J.J. Smoothed Particle Hydrodynamics // Annu. Rev. Astron. Astrophys. 1992. V. 30. P. 543–574.
42. Galkin V., Losev S. Equations of relaxation gasdynamics / /Physical-Chemical Kinetics in Gas Dynamics. 2008. V.6. http://chemphys.edu.ru/issues/2008-6/articles/288/
43. Shapiro S.A., Tyukolski S.A. Black holes, white dwarfs and neutron stars. Part 2. M.: Mir, 1985. 400 p.
44. Vasiliev E.O. Non-equilibrium ionization states and cooling rates of photoionized enriched gas // Monthly Notices of the RoyalAstronomical Society. 2011. V. 414. P. 3145–3157.
45. Kusov A., Kozlov P., Bykova N., Zabelinskii I., Gerasimov G., Levashov V. Direct statistical simulation of oxygen radiation behind shock wave // Physical-Chemical Kinetics in Gas Dynamics. 2022. V.23, iss. 3. http://chemphys.edu.ru/issues/2022-23-3/articles/1000/
46. Kusov A., Bykova N., Gerasimov G., Zabelinskii I., Kozlov P., Levashov V. Direct Statistical Simulation of Radiation Behind the Shock Wave Front in CO2 and N2 Mixture//Physical-Chemical Kinetics in Gas Dynamics. 2023. V.24, iss. 2. http://chemphys.edu.ru/issues/2023-24-2/articles/1038/