Skip to main content
SpringerLink
Log in

Numerical and Analytical Approaches to Modeling Critical Two-Phase Flow with Granular Layer

  • Published:
Journal of Engineering Thermophysics Aims and scope

Abstract

Based on data obtained in the previous experimental study conducted by the authors, two approaches are proposed for analytical and numerical modeling of a critical two-phase flow in a pipe with a granular layer. An analytical approach is based on a polytrophic model, while a numerical approach was developed using a smoothed particle hydrodynamics method. A model of isenthalpic flow of vapor–water mixture in a fixed bed of solid particles is considered is this study. The mixture expansion process is considered to be polytropic. Similarly to the known problem of gas dynamics of a granular bed, an analytical relationship for calculation of a critical mass velocity was obtained. The results of the calculation based on the analytical and numerical models were compared with the experimental data and agreement between analytical and numerical data and the experiment was observed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Tairov, E.A., Pokusaev, B.G., and Bykova, S.M., Vapor–Liquid Critical Flow through a Layer of Spherical Particles, High Temp., 2016, vol. 54, pp. 262–270.

    Article  Google Scholar 

  2. Goldstick, M.A., Protsessy perenosa v zernistomsloe (TransferProcesses inGranular Layer), Novosibirsk: Inst. of Thermophysics SB RAS, 2005.

    Google Scholar 

  3. Kim, S., Mudawar, I., and Int, J., Review of Flow Boiling and Critical Heat Flux in Microgravity, Heat Mass Tranfer, 2015, vol. 87, pp. 470–497.

    Google Scholar 

  4. Henry, R.E. and Fauske, H.K., The Two-Phase Critical Flow of One-Component Mixtures in Nozzles, Orifices, and Short Tubes, Heat Transfer, 1971, vol. 93, pp. 179–188.

    Article  Google Scholar 

  5. Avdeev, A.A. and Soziev, R.I., Hydrodynamic Drag of a Flow of Steam-Water Mixture in a Pebble Bed, High Temp., 2008, vol. 46, pp. 251–256.

    Article  Google Scholar 

  6. Avdeev, A.A., Balunov, B.F., Rybin, R.A., et al., Critical Flow of Steam-Water in a Packed Bed, High Temp., 2033, vol. 41, pp. 259–267.

    Google Scholar 

  7. Kontsyrev, B.L., Kroshilin, A.E., and Nigmatulin, B.I., Nonstationary Thermodynamic Equilibrium Flow of BoilingWater Vessel with Faucets, High Temp., 1985, vol. 23, pp. 1125–1130.

    Google Scholar 

  8. Nigmatulin, R.I., Dinamika mnogofaznykh sred, tt. 1, 2 (Multiphase Medium Dynamics, vols. 1, 2), Moscow: Nauka, 1987.

    Google Scholar 

  9. Melikhov, B.I., Melikhov, O.I., and Parfenov, U.V., Analysis of Sensitivity of Computational Results Based on Code ATHLET of Experimental Regime with Big Leakage of Heat Carrier on a Stand BK B-213, Higher Ed. Inst. Lett., Nuclear Energy, 2007, pp. 91–98.

    Google Scholar 

  10. Jeong, J.H., Jhona, M.S., Halowb, J.S., and Osdol, J., Smoothed Particle Hydrodynamics. Applications to Heat Conduction, Comp. Phys. Comm., 2003, vol. 153, pp. 71–84.

    Article  ADS  Google Scholar 

  11. Drew, D.A., Mathematical Modeling of Two-Phase Flow, Ann. Rev. Fluid. Mech., 1983, vol. 15, pp. 261–291.

    Article  ADS  MATH  Google Scholar 

  12. Flesch, B. and Cochet, D., Leak-before-Break in Steam Generator Tubes, Int. J. Press. Vess. Piping, 1990, vol. 43, pp. 165–179.

    Article  Google Scholar 

  13. John, H., Reimann, J., Westphal, F., and Friedel, L. Critical Two-Phase Flow through Rough Slits, Int. J. Multiphase Flow, 1988, vol. 14, pp. 155–174.

    Article  Google Scholar 

  14. Hu, X.Y. and Adams, N.A., A Multi-Phase SPH Method forMacroscopic and Mesoscopic Flows, J. Comp. Phys., 2006, vol. 213, pp. 844–861.

    Article  ADS  MATH  Google Scholar 

  15. Yang, X. and Kong, S., A Smoothed Particle Hydrodynamics Method for Evaporating Multiphase Flows, Phys. Rev. E, 2017, vol. 96, 033309.

    Article  ADS  Google Scholar 

  16. Grenier, N., A Hamiltonian Interface SPH Formulation for Multi-Fluid and Free Surface Flows, J. Comp. Phys., 2009, vol. 228, pp. 8380–8393.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. Monaghan, J.J., Smoothed Particle Hydrodynamics, Rep. Prog. Phys., 2005, vol. 68, pp. 1703–1759.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. Pokusaev, B.G., Tairov, E.A., and Vasilev, S.A., Speed of Low-Frequency PressureWaves in Vapor–Liquid Medium with Static Layer of Spherical Particles, Akust. Zh., 2010, vol. 56, no. 3, pp. 341–347.

    Google Scholar 

  19. Gubaidullin, D.A., Nikiforov, A.A., and Gafiatov R.N., AcousticWaves in Two Fraction Bubbly Liquids with Phase Transitions, High Temp., 2012, vol. 50, pp. 269–275.

    Google Scholar 

  20. Gasenko, V.G., Gorelik, R.S., Nakoryakov, V.E., and Timkin, L.S., Measurement of Acoustic Wave Phase Velocity by FourierMethod in Gas–LiquidMedium, J. Eng. Therm., 2015, vol. 24, pp. 330–334.

    Article  Google Scholar 

  21. Tairov, E. and Khan, P.V., A Polytropic Model of a Critical Two-Phase Flow in a Bed of Spherical Particles, MATEC Web Conf., 2017, 115:05007, DOI: 10.1051/matecconf/201711505007.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow Polytechnic Institute, ul. B. Semyonovskaya 38, Moscow, 107023, Russia

    B. G. Pokusaev & D. P. Khramtsov

  2. Melentiev Energy Systems Institute, Siberian Branch, Russian Academy of Sciences, ul. Lermontova 130, Irkutsk, 664033, Russia

    E. A. Tairov & P. V. Khan

Authors
  1. B. G. Pokusaev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. A. Tairov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. V. Khan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. D. P. Khramtsov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. G. Pokusaev.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pokusaev, B.G., Tairov, E.A., Khan, P.V. et al. Numerical and Analytical Approaches to Modeling Critical Two-Phase Flow with Granular Layer. J. Engin. Thermophys. 27, 20–29 (2018). https://doi.org/10.1134/S1810232818010022

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1810232818010022

Search

Navigation