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Steady-state axisymmetric flows of an incompressible fluid through rotating porous media with regard to the Coriolis force

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Abstract

Exact solutions to the problem of steady-state axisymmetric flow of an incompressible fluid through rotating rigid body with regard to the centrifugal and Coriolis forces are constructed. The case of the locally transversally isotropic porous skeleton and the quadratic resistance force in the law of flow is considered. Estimates of the practical applicability of the solutions obtained are given. An analysis of increase in the length of the trajectory of a liquid particle due to its deviation from the radial direction in the frame of reference connected with the skeleton is carried out. This is of interest for applications related to deep-bed filtration of suspensions.

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References

  1. D.A. Nield, “Spin-up in a Saturated Porous Medium,” Transport in Porous Media 4, 495–497, DOI: 10.1007/BF00179532 (1989).

    Article  Google Scholar 

  2. V.G. Zhukov and V.M. Chesnokov, “Two-Dimensional Problem of Centrifugal Filtration,” Theoretical Foundations of Chemical Engineering 45, No. 4, 386–393, DOI: 10.1134/S0040579511040166 (2011).

    Article  Google Scholar 

  3. P. Vadasz, “Fluid Flow through Heterogeneous Porous Media in a Rotating Square Channel,” Transport in Porous Media 12, No. 1, 43–54, DOI: 10.1007/BF00616361 (1993).

    Article  MathSciNet  Google Scholar 

  4. P. Vadasz, “Flow and Thermal Convection in Rotating Porous Media,” in: K. Vafai (Ed.), Handbook of Porous Media (1st ed., Marcel Dekker, Inc., N.Y., Basel, 2000), P. 395–439.

    Google Scholar 

  5. R.E. Collins, Flow of Fluids through Porous Materials (Reinhold Publishing Corp., N.Y., 1961; Mir, Moscow, 1964).

    Google Scholar 

  6. Yu.I. Sirotin, “Tensor Functions of a Polar and Axial Vector Compatible with Texture Geometry,” Journal of Applied Mathematics and Mechanics 28, No. 4, 804–816, DOI: 10.1016/0021-8928(64)90065-6 (1964).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  7. V.F. Pleshakov and Yu.I. Sirotin, “Anisotropic Vector Functions of a Vector Argument,” Journal of AppliedMathematics and Mechanics 30, No. 2, 301–313, DOI: 10.1016/0021-8928(67)90178-5 (1967).

    ADS  MATH  Google Scholar 

  8. S. Whitaker, The Method of Volume Averaging (Theory and Applications of Transport in Porous Media. Vol. 13, Springer Science+Business Media, Dordrecht, 1999), DOI: 10.1007/978-94-017-3389-2.

    Book  Google Scholar 

  9. N.E. Leont’ev, Fundamentals of the Theory of Flow through Porous Media (Publishing House of the Center of Applied Investigations under the Mechanics and Mathematics Department of Lomonosov Moscow State University, Moscow, 2009) [in Russian].

    Google Scholar 

  10. J.-L. Auriault, C. Geindreau, and P. Royer, “Coriolis Effects on Filtration Law in Rotating Porous Media,” Transport in Porous Media 48, 315–330, DOI: 10.1023/a:1015720529464 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  11. A.N. Kraiko and A.A. Makhmudov, “Solution of the Two-Dimensional Unsteady Problem of Percolation into a Porous Soil within the Framework of the Instantaneous Saturation Model,” Fluid Dynamics 24 (4), 574–581, DOI: 10.1007/BF01052420 (1989).

    Article  ADS  Google Scholar 

  12. M. Vygodsky, Mathematical Handbook. Higher Mathematics (Mir, Moscow, 1971).

    Google Scholar 

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Authors and Affiliations

  1. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Leninskiye Gory 1, Moscow, 119991, Russia

    N. E. Leont’ev & A. V. Smikhovskii

Authors
  1. N. E. Leont’ev
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  2. A. V. Smikhovskii
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Correspondence to N. E. Leont’ev.

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Original Russian Text © N.E. Leont’ev, A.V. Smikhovskii, 2017, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2017, No. 5, pp. 86–89.

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Leont’ev, N.E., Smikhovskii, A.V. Steady-state axisymmetric flows of an incompressible fluid through rotating porous media with regard to the Coriolis force. Fluid Dyn 52, 678–681 (2017). https://doi.org/10.1134/S001546281705009X

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  • DOI: https://doi.org/10.1134/S001546281705009X

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