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Numerical Simulation of Couette–Taylor–Poiseuille Two-Phase Flow

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Abstract

A numerical study of the Couette–Taylor–Poiseuille two-phase flow is presented in this work. The proposed mathematical model takes into account the nonstationarity and three-dimensionality of the process of medium motion and rotation of the surface of the inner cylinder, as well as surface tension and the action of gravity. The developed numerical technique was tested on the solution of the problem of Couette–Taylor single-phase flow, which is the limiting case of a two-phase flow, when the volume concentration of the gas phase is zero. Two regimes of a two-phase flow are obtained. At low Reynolds numbers, a stratified flow regime is observed. In the second regime of two-phase flow, the gas phase is localized along a helical line along the surface of the inner cylinder. It is shown that the dimensionless torque increases when the gas phase is added to the flow.

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REFERENCES

  1. G. I. Taylor, ‘‘Stability of viscous liquid contained between rotating cylinders,’’ Phil. Trans. R. Soc. London, Ser. A 223, 289–343 (1923).

    Article  Google Scholar 

  2. C. D. Andereck, S. S. Liu, and H. L. Swinney, ‘‘Flow regimes in a circular Couette system with independently rotating cylinders,’’ J. Fluid Mech. 164, 155–183 (1985).

    Article  Google Scholar 

  3. D. Coles, ‘‘Transition in circular Couette flow,’’ J. Fluid Mech. 21, 385–425 (1965).

    Article  Google Scholar 

  4. R. J. Donnelly and N. J. Simon, ‘‘An empirical torque relation for supercritical flow between rotating cylinders,’’ J. Fluid Mech. 7, 401–418 (1960).

    Article  Google Scholar 

  5. T. T. Lim and K. S. Tan, ‘‘A note on power-law scaling in a Taylor–Couette flow,’’ Phys. Fluids 16, 140–144 (2004).

    Article  Google Scholar 

  6. I. V. Morenko, ‘‘Numerical simulation of laminar Taylor–Couette flow,’’ Lobachevskii J. Math. 41 (7), 1255–1260 (2020).

    Article  MathSciNet  Google Scholar 

  7. I. V. Morenko, ‘‘Viscous fluid flow in a wide annular gap of two rotating coaxial cylinders,’’ J. Phys.: Conf. Ser. 1588, 012034 (2020).

    Google Scholar 

  8. I. V. Morenko, ‘‘Numerical simulation of the propagation of pressure waves in water during the collapse of a spherical air cavity,’’ Ocean Eng. 215, 107905 (2020).

    Article  Google Scholar 

  9. D. A. Gubaidullin and B. A. Snigerev, ‘‘Numerical simulation of the turbulent upward flow of a gas-liquid bubble mixture in a vertical pipe: Comparison with experimental data,’’ High Temp. 56, 61–69 (2018).

    Article  Google Scholar 

  10. D. A. Gubaidullin and B. A. Snigerev, ‘‘Numerical simulation of heat transfer during boiling flow of cryogenic fluid in vertical tube,’’ Lobachevskii J. Math. 41 (7), 1210–1215 (2020).

    Article  Google Scholar 

  11. A. Y. Varaksin, ‘‘Two-phase flows with solid particles, droplets, and bubbles: Problems and research results (review),’’ High Temp. 58, 595–614 (2020).

    Article  Google Scholar 

  12. D. V. Guzei, A. V. Minakov, M. I. Pryazhnikov, and A. A. Dekterev, ‘‘Numerical modeling of gas-liquid flows in mini- and microchannels,’’ Thermophys. Aeromech. 22, 61–71 (2015).

    Article  Google Scholar 

  13. D. B. Kothe, W. J. Rider, S. J. Mosso, J. S. Brock, and J. I. Hochstein, ‘‘Volume tracing of interfaces having surface tension in two and three dimensions,’’ AIAA Paper № 96-0859 (1999).

  14. C. W. Hirt and B. D. Nichols, ‘‘Volume of Fluid (VOF). Methods for the dynamics of free boundaries,’’ J. Comput. Phys. 39, 201–225 (1981).

    Article  Google Scholar 

  15. I. V. Morenko, ‘‘Numerical simulation of the liquid column collapse in the reservoirs of different shapes,’’ Tomsk. Univ. J. Math. Mech. 60, 119–131 (2019).

    MathSciNet  Google Scholar 

  16. http://www.openfoam.com/.

  17. M. Biage and J. C. C. Campos, ‘‘Visualization study and quantitative velocity measurements in turbulent Taylor-Couette flow tagging: A description of the transition to turbulence,’’ J. Braz. Soc. Mech. Sci. Eng. 25, 378–390 (2003).

    Article  Google Scholar 

  18. E. A. Chinnov and O. A. Kabov, ‘‘Two-phase flows in pipes and capillary channels,’’ High Temp. 44, 773–791 (2006).

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute of Mechanics and Engineering, FRC Kazan Scientific Center, Russian Academy of Sciences, 420111, Kazan, Russia

    I. V. Morenko

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  1. I. V. Morenko
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Correspondence to I. V. Morenko.

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(Submitted by D. A. Gubaidullin)

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Morenko, I.V. Numerical Simulation of Couette–Taylor–Poiseuille Two-Phase Flow. Lobachevskii J Math 42, 2186–2191 (2021). https://doi.org/10.1134/S1995080221090201

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  • DOI: https://doi.org/10.1134/S1995080221090201

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