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Simulation of wave processes in a vapor-liquid medium

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Abstract

Numerical methods for the simulation of nonlinear wave processes in a vapor-liquid medium with a model two-phase spherical symmetric cell, with a pressure jump at its external boundary are considered. The viscosity and compressibility of the liquid, as well as the space variation of pressure in the vapor, are neglected. The problem is described by the heat equations in the vapor and liquid, and by a system of ODEs for the velocity, pressure, and radius at the bubble boundary. The equations are discretized in space by an implicit finite-volume scheme on a dynamic adaptive grid with grid refinement near the bubble boundary. The total time derivative is approximated by a method of backward characteristics. “Nonlinear” iterations are implemented at each time step to provide a specified high accuracy. The results of numerical experiments are presented and discussed for the critical thermodynamic parameters of water, for some initial values of the bubble radius and pressure jump.

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References

  1. Nigmatulin, R.I., Osnovy mekhaniki geterogennykh sred (The Fundamentals of Mechanics of HeterogeneousMedia), part 1, Moscow: Nauka, 1987.

    Google Scholar 

  2. Nakoryakov, V.E., Pokusaev, B.G., and Shreiber, I.R., Volnovaya dinamika gazo-i parozhidkostnykh sred (Wave Dynamics of Gas- and Vapor-LiquidMedia), Moscow: Energoatomizdat, 1990.

    MATH  Google Scholar 

  3. Nakoryakov, V.E. and Gorin, A.V., Teplomassoperenos v dvukhfaznykh sistemakh (Heat-and-Mass Transfer in Two-Phase Systems), Novosibirsk: Institute of Thermophysics SB RAS, 1994.

    Google Scholar 

  4. Kedrinskii, V.K., Shokin, Yu.I., Vshivkov, V.A., Dudnikova, G.I., and Lazareva, G.G., Generation of Shock Waves in a Liquid by Spherical Bubble Clusters, Dokl. Ross. Akad. Nauk, 2001, vol. 381, no. 6, pp. 773–776.

    Google Scholar 

  5. Gimaltdinov, I.K., Nigmatulin, R.I., and Shagapov, V.Sh., Evolution of Pressure Waves in a Liquid Containing a Liquid Zone with Bubbles, Izv. Ross. Akad. Nauk, Mekh. Zhidkosti Gaza, 2001, no. 3, pp. 133–142.

  6. Teshukov, V.M., A Kinetic Model of Bubble Flow, Prikl. Mekh. Tekhn. Fiz., 2000, vol. 41, no. 5, pp. 129–139.

    Google Scholar 

  7. Aganin, A.A., Khalitova, T.F., and Khismatullina, N.A., Calculation of Strong Compression of a Spherical Vapor-Gas Bubble in a Liquid, Vych. Tekhnol., 2008, vol. 13, no. 6, pp. 17–27.

    MATH  Google Scholar 

  8. Aleksandrov, A.A. and Grigor’ev, B.A., Tablitsy teplofizicheskikh svoistv vody i vodyanogo para (Tables of Thermophysical Properties of Water and Water Vapor), Moscow: Moscow Power Engineering Institute, 1999.

    Google Scholar 

  9. Il’in, V.P.,Metody konechnykh raznostei i konechnykh ob’yomov dlya ellipticheskikh uravnenii (Finite Difference and Finite Volume Methods for Elliptic Equations), Novosibirsk: Inst. Comp. Math. Math. Geophys. SB RAS, 2001.

  10. Il’in, V.P., Chislennyi analiz (Numerical Analysis), part 1, Novosibirsk: Inst. Comp. Math. Math. Geophys. SB RAS, 2004.

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Authors and Affiliations

  1. Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Lavrent’eva 1, Novosibirsk, 630090, Russia

    V. G. Gasenko

  2. Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Lavrent’eva 6, Novosibirsk, 630090, Russia

    G. V. Demidov, V. P. Il’in & I. A. Shmakov

Authors
  1. V. G. Gasenko
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  2. G. V. Demidov
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  3. V. P. Il’in
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  4. I. A. Shmakov
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Correspondence to V. G. Gasenko.

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Original Russian Text © V.G. Gasenko, G.V. Demidov, V.P. Il’in, I.A. Shmakov, 2012, published in Sibirskii Zhurnal Vychislitel’noi Matematiki, 2012, Vol. 15, No. 3, pp. 261–270.

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Gasenko, V.G., Demidov, G.V., Il’in, V.P. et al. Simulation of wave processes in a vapor-liquid medium. Numer. Analys. Appl. 5, 213–221 (2012). https://doi.org/10.1134/S1995423912030032

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  • DOI: https://doi.org/10.1134/S1995423912030032

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