Calculation of Heat-Conducting Vapor–Gas–Drop Mixture Flows


A characteristic analysis of the equations of a single-velocity heat-conducting vapor–gas–drop mixture with interfractional heat transfer is carried out. The equations are shown to be hyperbolic. Calculation formulas for a Godunov-type method with a linearized Riemann solver are presented. These formulas are used to calculate some mixture flows.

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  1. 1

    Murrone, A. and Guillard, H., A Five Equation Reduced Model for Compressible Two Phase Flow Problems, J. Comput. Phys., 2005, vol. 202, iss. 2, pp. 664–698.

  2. 2

    Wackers, J. and Koren, B., A Fully Conservative Model for Compressible Two-Fluid Flow, J. Num. Meth. Fluids, 2005, vol. 47, nos. 10/11, pp. 1337–1343.

  3. 3

    Kreeft, J.J. and Koren, B., A New Formulation of Kapila’s Five-Equation Model for Compressible Two-Fluid Flow, and Its Numerical Treatment, J. Comput. Phys., 2010, vol. 229, iss. 18, pp. 6220–6242.

  4. 4

    Surov, V.S., One-Velocity Model of Heterogeneous Media,Mat. Model., 2001, vol. 13, no. 10, pp. 27–42.

  5. 5

    Surov, V.S., One-Velocity Model of a Heterogeneous Medium with a Hyperbolic Adiabatic Kernel, Comput. Math. Math. Phys., 2008, vol. 48, no. 6, pp. 1048–1062.

  6. 6

    Surov, V.S., Reflection of an Air Shock Wave from a Foam Layer,High Temp., 2000, vol. 38, no. 1, pp. 97–105.

  7. 7

    Surov, V.S., Calculation of the Interaction of an Air Shock Wave with a Porous Material, Chelyabinsk Fiz.-Mat. Zh., 1997, vol. 6, no. 1, pp. 124–134.

  8. 8

    Surov, V.S., Analysis of Wave Phenomena in Gas-Liquid Media,High Temp., 1998, vol. 36, no. 4, pp. 600–606.

  9. 9

    Saurel, R., Boivin, P., and Lemetayer, O., A General Formulation for Cavitating, Boiling and Evaporating Flows, Comp. Fluids, 2016, vol. 128, pp. 53–64.

  10. 10

    Kapila, A.K., Schwendeman, D.W., Gambino, J.R., and Henshaw, W.D., A Numerical Study of the Dynamics of Detonation Initiated by Cavity Collapse, Shock Waves, 2015, vol. 25, iss. 6, pp. 545–572.

  11. 11

    Surov, V.S., On Localization of Contact Surfaces in Multifluid Hydrodynamics, J. Engin. Phys. Thermophys., 2010, vol. 83, no. 3, pp. 549–559.

  12. 12

    Surov, V.S., A Hyperbolic Model of One-Velocity Multicomponent Heat-Conducting Medium, High Temp., 2009, vol. 47, no. 6, pp. 870–878.

  13. 13

    Cattaneo, C., A Form of Heat Conduction Equation which Eliminates the Paradox of Instantaneous Propagation, Compt. Rend. Acad. Sci. Paris, 1958, vol. 247, pp. 431–433.

  14. 14

    Godunov, S.K., Zabrodin, A.V., Ivanov, M.Ya., Kraiko, A.N., and Prokopov, G.P., Chislennoe reshenie mnogomernykh zadach gazovoi dinamiki (Numerical Solution of Multidimensional Problems of Gas Dynamics), Moscow: Nauka, 1976.

  15. 15

    Kulikovskii, A.G., Pogorelov, N.V., and Semenov, A.Yu.,Matematicheskie voprosy chislennogo resheniya giperbolicheskikh sistem uravnenii (Mathematical Problems of Numerical Solutions of Hyperbolic Equation Systems), Moscow: Fizmatlit, 2012.

  16. 16

    Toro, E.F., Riemann Solvers with Evolved Initial Condition,Int. J. Num. Meth. Fluids, 2006, vol. 52, pp. 433–453.

  17. 17

    Wallis, G., Odnomernye dvukhfaznye techeniya (One-Dimensional Two-Phase Flow), Moscow: Mir, 1972.

  18. 18

    Surov, V.S., The Godunov Method for Calculating Multidimensional Flows of a One-Velocity Multicomponent Mixture,J. Engin. Phys. Thermophys., 2016, vol. 89, no. 5, pp. 1227–1240.

  19. 19

    Surov, V.S., The Riemann Problem for One-Velocity Model of Multicomponent Mixture, High Temp., 2009, vol. 47, no. 2, pp. 263–271.

  20. 20

    Surov, V.S., On a Method of Approximate Solution of the Riemann Problem for a One-Velocity Flow of a Multicomponent Mixture,J. Engin. Phys. Thermophys., 2010, vol. 83, no. 2, pp. 373–379.

  21. 21

    Surov, V.S., One-Velocity Model of a Multicomponent Heat-Conducting Medium, J. Engin. Phys. Thermophys., 2010, vol. 83, no. 1, pp. 146–157.

  22. 22

    Surov, V.S., Numerical Simulation of the Interaction of an Air Shock Wave with a Surface Gas–Dust Layer, J. Engin. Phys. Thermophys., 2018, vol. 91, no. 2, pp. 370–376.

  23. 23

    Surov, V.S., Hyperbolic Models in the Mechanics of Heterogeneous Media, Comput. Math. Math. Phys., 2014, vol. 54, no. 1, pp. 148–157.

  24. 24

    Surov, V.S., Diffraction of a Shock Wave on a Wedge in a Dusty Gas, J. Engin. Phys. Thermophys., 2017, vol. 90, no. 5, pp. 1170–1177.

  25. 25

    Surov, V.S., Interaction of Shock Waves with Bubble-Liquid Drops, Techn. Phys., 2001, vol. 46, no. 6, pp. 662–667.

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Surov, V.S. Calculation of Heat-Conducting Vapor–Gas–Drop Mixture Flows. Numer. Analys. Appl. 13, 165–179 (2020).

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  • hyperbolic model of a heat–conducting vapor–gas–drop mixture
  • interfractional heat transfer
  • Godunov’s method
  • linearized Riemann solver