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Modeling of turbulent annular flows of Hershel-Bulkley fluids with eccentricity and inner cylinder rotation

Abstract

The paper presents results of modeling of Hershel-Bulkley fluid flows through an eccentric cylindrical channel. The effect of inner cylinder rotation and eccentricity on flow characteristics (hydrodynamic channel resistance, flow pattern, stresses, etc.) is studied and it is demonstrated that, for a number of cases, the turbulence caused by the inner cylinder rotation results in reduction of the channel resistance. Moreover, certain relations of axial and rotational Reynolds numbers result in flows, where laminar and turbulent regions are present at the same time.

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References

  1. 1.

    Escudier, M.P., Gouldson, I.W., Oliveira, P.J., and Pinho, F.T., Effects of Inner Cylinder Rotation on Laminar Flow of a Newtonian Fluid through an Eccentric Annulus, Int. J. Heat Fluid Flow, 2000, vol. 21, pp. 92–103.

    Article  Google Scholar 

  2. 2.

    Podryabinkin, E.V. and Rudyak, V.Ya., Moment and Forces Exerted on the Inner Cylinder in Eccentric Annular Flow, J. Eng. Therm., 2011, vol. 20, no. 3, pp. 320–328.

    Article  Google Scholar 

  3. 3.

    Podryabinkin, E.V. and Rudyak, V.Ya., Modeling of Herschel-Bulkley Fluid Flow through Eccentric Annulus, Proc. Russ. Higher Educ. Acad. Sci., 2012, no. 2, pp. 112–122.

    Google Scholar 

  4. 4.

    Nouri, J.M., Umur, H., and Whitelaw, J.H., Flow of Newtonian and Non-Newtonian Fluids in Concentric and Eccentric Annuli, J. Fluid Mech., 1993, no. 253, pp. 617–641.

    Google Scholar 

  5. 5.

    Nouri, J.M. and Whitelaw, J.H., Flow of Newtonian and Non-Newtonian Fluids in an Eccentric Annulus with Rotation of the Inner Cylinder, Int. J. Heat Fluid Flow, 1997, vol. 18, no. 2, pp. 236–246.

    Article  Google Scholar 

  6. 6.

    Fukushima, E., Nuclear Magnetic Resonance as a Tool to Study Flow, Annual Rev. Fluid Mech., 1999, vol. 31, pp. 95–123.

    ADS  Article  Google Scholar 

  7. 7.

    Callaghan, P.T., Rheo-NMR: Nuclear Magnetic Resonance and the Rheology of Complex Fluids, Rep. Prog. Phys., 1999, vol. 62, pp. 599–668.

    ADS  Article  Google Scholar 

  8. 8.

    Ultrasonic Doppler Velocity Profiler for Fluid Flow, Takeda, Ya., Ed., Berlin: Springer, 2012.

    Google Scholar 

  9. 9.

    Escudier, M.P., Gouldson, I.W., and Jones, D.M., Flow of Shear-Thinning Fluids in a Concentric Annulus, Exper. Fluids, 1995, vol. 18, no. 4, pp. 225–238.

    ADS  Article  Google Scholar 

  10. 10.

    Podryabinkin, E.V. and Rudyak, V.Ya., Modeling of Turbulent Flows through the Annular Channel with Eccentricity and Rotating Inner Cylinder, Vestnik NGU, Fiz., 2012, vol. 7, no. 4, pp. 79–86.

    Google Scholar 

  11. 11.

    Pinho, F.T., A GNF Framework for Turbulent Flow Models of Drag Reducing Fluids and Proposal for a k-e Type Closure, J. Non-Newt. Fluid Mech., 2003, vol. 114, pp. 149–184.

    Article  MATH  Google Scholar 

  12. 12.

    Cruz, D.O.A. and Pinho, F.T., Turbulent Pipe Flow Predictions with a Low Reynolds Number k-e Model for Drag Reducing Fluids, J. Non-Newt. Fluid Mech., 2003, vol. 114, pp. 109–148.

    Article  MATH  Google Scholar 

  13. 13.

    Gavrilov, A.A., Minakov, A.V., Dekterev, A.A., and Rudyak, V.Ya., Mathematical Model and Numerical Methodic of Modeling of Fully Developed Turbulent Flow of Non-Newtonian Viscoplastic Fluids, Proc. Int. Conf. on Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment and Practice, 2011; http://conf.nsc.ru/files/conferences/niknik-90/fulltext/39228/47095/Gavrilov_MD_Rudyak.pdf.

    Google Scholar 

  14. 14.

    Gavrilov, A.A., Minakov, A.V., Dekterev, A.A., and Rudyak, V.Ya., Numerical Algorithm for Fully Developed Laminar Flow of a Non-Newtonian Fluid through an Eccentric Annulus, Comput. Technol., 2012, vol. 17, no. 1, pp. 44–57.

    Google Scholar 

  15. 15.

    Gavrilov, A.A., Minakov, A.V., Dekterev, A.A., and Rudyak, V.Ya., A Numerical Algorithm for Modeling Laminar Flows in an Annular Channel with Eccentricity, J. Appl. Indust. Math., 2011, vol. 5, no. 4, pp. 559–568.

    Article  MathSciNet  Google Scholar 

  16. 16.

    Menter, F.R., Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications, AIAA J., 1994, vol. 32, no. 8, pp. 1598–1605.

    ADS  Article  Google Scholar 

  17. 17.

    Papanastasiou, T.C., Flows of Materials with Yield, J. Rheol., 1987, vol. 31, pp. 385–404.

    ADS  Article  MATH  Google Scholar 

  18. 18.

    Gavrilov, A.A., Rudyak, V.Ya., Minakov, A.V., and Dekterev, A.A., Direct Numerical Simulation of the Turbulent Pipe Flow of Power Law Fluids, Proc. 9th European Fluid Mechanics Conference EFMC9, September 9–13, 2012, Rome, Italy, pp. 294–302.

  19. 19.

    Idelchik, I.E., Handbook of Hydraulic Resistance, 3d ed., 2001, p. 672.

    Google Scholar 

  20. 20.

    Haciislamoglu, M. and Cartalos, U., Practical Pressure Loss Predictions in Realistic Annular Geometries, SPE 28304 presented at the SPE Annual Technical Conference and Exhibition, New Orleans, 1994, pp. 25–28.

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Correspondence to E. V. Podryabinkin.

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Podryabinkin, E.V., Rudyak, V.Y. Modeling of turbulent annular flows of Hershel-Bulkley fluids with eccentricity and inner cylinder rotation. J. Engin. Thermophys. 23, 137–147 (2014). https://doi.org/10.1134/S1810232814020064

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Keywords

  • Shear Rate
  • Pressure Drop
  • Strain Rate Tensor
  • Engineer THERMOPHYSICS
  • Turbulent Region