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Roll waves in channels with an active gas phase

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Journal of Applied Mechanics and Technical Physics Aims and scope

Abstract

A mathematical model of the flow of a thin layer of heavy liquid under an elastic shell filled with gas is constructed. By means of mass exchange with the environment, the gas phase is active and maintains self-organized wave motion in the liquid layer. The conditions under which small perturbations are transformed into quasiperiodic wave packets of finite amplitude which move in the same direction are found. It is shown that the structure of the waves is similar to that of roll waves in open channels.

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References

  1. G. B. Whitham, Linear and Nonlinear Waves (New York, Wiley, 1974).

    MATH  Google Scholar 

  2. R. F. Dressler, “Mathematical Solution of the Problem of Roll-Waves in Inclined Open Channels,” Comm. Pure Appl. Math. 2, 149–194 (1949).

    Article  MATH  MathSciNet  Google Scholar 

  3. A. Dyment and A. Boudlal, “A Theoretical Model for Gas–Liquid Slug Flow in Down Inclined Ducts,” Int. J. Multiphase Flow 30, 521–550 (2004).

    Article  MATH  Google Scholar 

  4. A. Boudlal and V. Yu. Liapidevskii, “Stability of Regular Roll Waves,” Vychisl. Tekhnol. 10 (2), 3–14 (2005).

    MATH  Google Scholar 

  5. D. J. Needham and J. H. Merkin, “On Roll Waves Down an Open Inclined Channel,” Proc. Roy. Soc. London, Ser. A 394, 259–278 (1981).

    Article  ADS  Google Scholar 

  6. C. Kranenburg, “On the Evolution of Roll Waves,” J. Fluid Mech. 245, 249–261 (1992).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  7. G. L. Richard and S. L. Gavrilyuk, “A New Model of Roll Waves: Comparison with Brock’s Experiments,” J. Fluid Mech. 698, 374–405 (2012).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  8. V. Yu. Liapidevskii and A. A. Chesnokov, “Mixing Layer under the Free Surface,” Prikl. Mekh. Tekh. Fiz. 55 (2), 127–140 (2014)

    Google Scholar 

  9. V. Yu. Liapidevskii and A. A. Chesnokov, J. Appl. Mech. Tech. Phys. 55 (2), 299–310 (2014)].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  10. D. Barnea and Y. Taitel, “Interfacial and Structural Stability of Separated Flow,” Int. J. Multiphase Flow 25, 387–414 (1994).

    Article  Google Scholar 

  11. E. Kordyban, “Horizontal Slug Flow: a Comparison of Existing Theories,” Trans. ASME, J. Fluids Eng. 112 74–83 (1990).

    Article  Google Scholar 

  12. V. Yu. Liapidevskii, “Structure of Roll Waves in Two-Layer Flows,” Prikl. Mat. Mekh. 64 (6), 976–982 (2000).

    Google Scholar 

  13. A. Boudlal, “Roll Waves and Plugs in Two-Layer Flows,” Europ. J. Appl. Math. 19, 1–19 (2007).

    MathSciNet  Google Scholar 

  14. V. Yu. Liapidevskii, “Roll Waves in a Gas–Liquid Medium,” Prikl. Mekh. Tekh. Fiz. 43 (2), 39–42 (2002)

    Google Scholar 

  15. V. Yu. Liapidevskii, J. Appl. Mech. Tech. Phys. 43 (2), 204–207 (2002)].

    Article  MathSciNet  ADS  Google Scholar 

  16. V. Yu. Liapidevskii and V. M. Teshukov, Mathematical Models of Propagation of Long Waves in an Inhomogeneous Liquid (Izd. Sib. Otd. Ross. Akad. Nauk, Novosibirsk, 2000) [in Russian].

    Google Scholar 

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Correspondence to A. Boudlal.

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Original Russian Text © A. Boudlal, V.Yu. Liapidevskii.

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 56, No. 4, pp. 3–11, July–August, 2015.

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Boudlal, A., Liapidevskii, V.Y. Roll waves in channels with an active gas phase. J Appl Mech Tech Phy 56, 541–548 (2015). https://doi.org/10.1134/S002189441504001X

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  • DOI: https://doi.org/10.1134/S002189441504001X

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