High Temperature

, Volume 57, Issue 3, pp 398–406 | Cite as

Dynamics of a Polydisperse Vapor Mixture Taking into Account Crushing, Coagulation, Evaporation of Drops, and Condensation of Vapor

  • A. L. TukmakovEmail author
  • N. A. TukmakovaEmail author


A numeric model of a hydro- and thermodynamics of polydisperse vapor–droplet mixture was constructed. It takes into account the processes of the crushing, coagulation, and evaporation of droplets and vapor condensation. The dynamics of the carrier medium is described by a set of motion equations for a viscous, compressible, heat-conducting gas that takes into account the mass, impulse, and energy exchange with fractions of disperse phase. Each disperse fraction of droplets is described by a set of equations including the continuity equation for the average density, the equation for the conservation of impulse components, and the heat energy conservation equation. These take into account the interphase mass, impulse, and energy exchange with the carrier medium. Numerical solution of the equation set for motion of the carrier medium and fractions of disperse phase by the explicit McCormack method with splitting of the spatial operator by directions and with the scheme of nonlinear correction at each time step represents the main part of the computation algorithm, which is supplemented by models of the crushing, coagulation, and evaporation of droplets and vapor condensation with further correction of the hydro- and thermodynamic parameters of mixture. A software package was developed based on the presented model, and an example of the computation of polydisperse vapor–droplet mixture flow with the coagulation, crushing, and evaporation of droplets and vapor condensation in a channel composed of coaxial cylinders was shown.



This study was supported by the Russian Foundation for Basic Research and the government of the Republic of Tatarstan, project no. 18-48-160017, and state task of the Ministry of Education and Science of the Russian Federation for universities, project no. 9.5542.2017/6.7.


  1. 1.
    Serazetdinov, B.F., Serazetdinov, F.Sh., and Tonkonog, V.G., RF Patent 2467260, 2012.Google Scholar
  2. 2.
    Nigmatulin, R.I., Dinamika mnogofaznykh sred (Dynamics of Multiphase Media), Moscow: Nauka, 1987, part 1.Google Scholar
  3. 3.
    Kutushev, A.G., Matematicheskoe modelirovanie volnovykh protsessov v aerodispersnykh i poroshkoobraznykh sredakh (Mathematical Simulation of Wave Processes in Aerodispersed and Powdered Media), St. Petersburg: Nedra, 2003.Google Scholar
  4. 4.
    Arefyev, K.Yu. and Voronetsky, A.V., Theromophys. Aeromech., 2015, vol. 22, no. 5, p. 585.ADSCrossRefGoogle Scholar
  5. 5.
    Bayanov, I.M., Khamidullin, I.R., and Shagapov, V.Sh., High Temp., 2007, vol. 45, no. 5, p. 688.CrossRefGoogle Scholar
  6. 6.
    Alemasov, V.E., Dregalin, A.F., Tishin, A.P., and Khudyakov, V.A., Metody rascheta (Calculation Methods), vol. 1 of Termodinamicheskie i teplofizicheskie svoistva produktov sgoraniya. Spravochnik (Thermodynamic and Thermophysical Properties of Combustion Products: A Handbook), 5 vols., Moscow: Vseross. Inst. Nauchn. Tekh. Inf. Ross. Akad. Nauk, 1971.Google Scholar
  7. 7.
    Tukmakov, A.L., Tonkonog, V.G., and Arslanova, S.N., Acoust. Phys., 2016, vol. 62, no. 1, p. 125.ADSCrossRefGoogle Scholar
  8. 8.
    Samoilovich, G.S., Gidrogazodinamika (Fluid and Gas Dynamics), Moscow: Mashinostroenie, 1990.Google Scholar
  9. 9.
    Fletcher, C.A.J., Computational Techniques for Fluid Dynamics, 2 vols., Berlin: Springer, 1988.CrossRefzbMATHGoogle Scholar
  10. 10.
    Steger, J.L., AIAA J., 1978, vol. 16, no. 7, p. 679.ADSCrossRefGoogle Scholar
  11. 11.
    Read, R., Prausnitz, J., and Sherwood, T., The Properties of Gases and Liquids, New York: McGraw-Hill, 1977.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Kazan National Research Technical University named after A.N. Tupolev–KAIKazanRussia
  2. 2.Institute of Mechanics and Engineering, Subdivision of the Federal State Budgetary Institution of Science, Kazan Scientific Center of the Russian Academy of Sciences (IME, Subdivision of FIC, KazanSC of RAS)KazanRussia

Personalised recommendations