Skip to main content
SpringerLink
Log in

Direct numerical simulation of the turbulent flows of power-law fluids in a circular pipe

  • Published:
Thermophysics and Aeromechanics Aims and scope

Abstract

Fully developed turbulent pipe flows of power-law fluids are studied by means of direct numerical simulation. Two series of calculations at generalised Reynolds numbers of approximately 10000 and 20000 were carried out. Five different power law indexes n from 0.4 to 1 were considered. The distributions of components of Reynolds stress tensor, averaged viscosity, viscosity fluctuations, and measures of turbulent anisotropy are presented. The friction coefficient predicted by the simulations is in a good agreement with the correlation obtained from experiment. Flows of power-law fluids exhibit stronger anisotropy of the Reynolds stress tensor compared with the flow of Newtonian fluid. The turbulence anisotropy becomes more significant with the decreasing flow index n. An increase in apparent viscosity away from the wall leads to the damping of the wall-normal velocity pulsations. The suppression of the turbulent energy redistribution between the Reynolds stress tensor components observed in the simulations leads to a strong domination of the axial velocity pulsations. The damping of wall-normal velocity pulsations leads to a reduction of the fluctuating transport of momentum from the core toward the wall, which explains the effect of drag reduction.

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. D.W. Dodge and A.B. Metzner, Turbulent flow of non-Newtonian system, AIChE J., 1959, Vol. 5, No. 2, P. 189-204.

    Article  Google Scholar 

  2. M.P. Escudier, I.W. Gouldson, and D.M. Jones, Flow of shear-thinning fluids in a concentric annulus, Experiments in Fluids, 1995, Vol. 18, P. 225-238.

    Article  ADS  MATH  Google Scholar 

  3. M.P. Escudier, P.J. Oliveira, and F.T. Pinho, Fully developed laminar flow of purely viscous non-Newtonian liquids through annuli, including the effects of eccentricity and inner-cylinder rotation, Int. J. Heat and Fluid Flow, 2002, Vol. 23, P. 52-73.

    Article  Google Scholar 

  4. E.V. Podryabinkin and V.Ya. Rudyak, Moment and forces exerted on the inner cylinder in eccentric annual flow, J. Engng Thermophys., 2011, Vol. 20, No. 3, P. 320-328.

    Article  Google Scholar 

  5. A.A. Gavrilov, A.V. Minakov, A.A. Dekterev, and V.Ya. Rudyak, Numerical algorithm for fully developed laminar flow of non-Newtonian fluid through an eccentric annulus, Vychislitel’nye tekhnologii, 2012, Vol. 17, No. 1, P. 44-56.

    Google Scholar 

  6. M.R. Malin, Turbulent pipe flow of power-law fluids, Int. Communs. Heat Mass Transfer, 1997, Vol. 24, No. 7, P. 977-988.

    Article  Google Scholar 

  7. F.T. Pinho, A GNF framework for turbulent flow models of drag reducing fluids and proposal for a k-e type closure, J. Non-Newtonian Fluid Mech., 2003, Vol. 114, P. 149-184.

    Article  MATH  Google Scholar 

  8. D.O.A. Cruz and F.T. Pinho, Turbulent pipe flow predictions with a low Reynolds number k-e model for drag reducing fluids, J. Non-Newtonian Fluid Mech., 2003, Vol. 114, P. 109-148.

    Article  MATH  Google Scholar 

  9. A.A. Gavrilov and V.Ya. Rudyak, Modeling the coefficient of molecular viscosity of viscoplastic fluids in turbulent regime, Doklady Academii Nauk Vysshei Shkoly of Russian Federation, 2013, No. 2, P. 69-80.

    Google Scholar 

  10. A.A. Gavrilov and V.Ya. Rudyak, A model of averaged molecular viscosity for turbulent flow of non-Newtonian fluids, J. Siberian Federal University. Mathematics and Physics, 2014, Vol. 7, No. 1, P. 46-57.

    Google Scholar 

  11. M. Rudman, H.M. Blackburn, L.J.W. Graham, and L. Pullum, Turbulent pipe flow of shear-thinning fluids, J. Non-Newtonian Fluid Mech., 2004, Vol. 118, P. 33-48.

    Article  MATH  Google Scholar 

  12. M. Rudman and H.M. Blackburn, Direct numerical simulation of turbulent non-Newtonian flow using a spectral element method, Appl. Math. Modelling, 2006, Vol. 30, P. 1229-1248.

    Article  MATH  Google Scholar 

  13. R. Guang, M. Rudman, A. Chryss, P. Slatter, and S. Bhattacharya, A DNS investigation of the effect of yield stress for turbulent non-Newtonian suspension flow in open channels, Particulate Sci. and Technology: An Int. J., 2011, Vol. 29, No. 3, P. 209-228.

    Article  Google Scholar 

  14. X. Wu and P. Moin, A direct numerical simulation study on the mean velocity characteristics in turbulent pipe flow, J. Fluid Mech., 2008, Vol. 608, P. 81-112.

    Article  ADS  MATH  Google Scholar 

  15. N.V. Nikitin, Direct numerical modeling of three-dimensional turbulent flows in pipes of circular cross section, Fluid Dyn., 1994, Vol. 29, No. 6, P. 749-758.

    Article  ADS  Google Scholar 

  16. N.V. Nikitin, Statistical characteristics of wall turbulence, Fluid Dyn., 1996, Vol. 31, No. 3, P. 361-370.

    Article  ADS  MATH  Google Scholar 

  17. V.Ya. Rudyak, A.V. Minakov, A.A. Gavrilov, and A.A. Dekterev, Application of new numerical algorithm for solving the Navier-Stokes equations for modelling the work of a viscometer of the physical pendulum type, Thermophysics and Aeromechanics, 2008, Vol. 15, No. 2, P. 333-345.

    Article  ADS  Google Scholar 

  18. A.A. Gavrilov, A.V. Minakov, A.A. Dekterev, and V.Ya. Rudyak, Numerical algorithm for modeling laminar flows in an annular channel with eccentricity, J. Applied and Industr. Math., 2011, Vol. 5, No. 4, P. 559-568.

    Article  MathSciNet  MATH  Google Scholar 

  19. V.Ya. Rudyak, A.V. Minakov, A.A. Gavrilov, and A.A. Dekterev, Modelling of flows in micromixers, Thermophysics and Aeromechanics, 2010, Vol. 17, No. 4, P. 565-576.

    Article  ADS  MATH  Google Scholar 

  20. R. Rossi, Direct numerical simulation of scalar transport using unstructured finite-volume schemes, J. Comput. Phys., 2009, Vol. 228, No. 5, P. 1639-1657.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. J.G.M. Eggels, F. Unger, M.H. Weiss, J. Westerweel, R.J. Adrian, R. Friedrich, and F.T.M. Nieuwstadt, Fully developed turbulent pipe flow: a comparison between direct numerical simulation and experiment, J. Fluid Mech., 1994, Vol. 268, P. 175-181.

    Article  ADS  Google Scholar 

  22. K. Fukagata and N. Kasagi, Highly energy-conservative finite difference method for the cylindrical coordinate system, J. Comput. Phys., 2002, Vol. 181, P. 478-498.

    Article  ADS  MATH  Google Scholar 

  23. A.B. Metzner and J.C. Reed, Flow of non-Newtonian fluids-correlation of the laminar, transition and turbulentflow regions, AIChE J., 1955, Vol. 1, No. 4, P. 434-440.

    Article  Google Scholar 

  24. M.P. Escudier, A.K. Nickson, and R.J. Poole, Turbulent flow of viscoelastic shear-thinning liquids through a rectangular duct: Quantification of turbulence anisotropy, J. Non-Newtonian Fluid Mech., 2009, Vol. 160, P. 2-10.

    Article  Google Scholar 

  25. J.L. Lumley, Computational modeling of turbulent flows, Adv. Appl. Mech., 1978, Vol. 18, P. 123-176.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  26. J.L. Lumley, Drag reduction in two phase and polymer flows, Phys. Fluids, 1977, Vol. 20, P. S64-S65.

    Article  ADS  Google Scholar 

  27. A.B. Metzner, Polymer solution and fiber suspension rheology and their relationship to turbulent drag reduction, Phys. Fluids, 1977, Vol. 20, P. S145-S146.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kutateladze Institute of Thermophysics SB RAS, Novosibirsk, Russia

    A. A. Gavrilov

  2. Novosibirsk State University of Architecture and Civil Engineering, Novosibirsk, Russia

    V. Ya. Rudyak

Authors
  1. A. A. Gavrilov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. Ya. Rudyak
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. Ya. Rudyak.

Additional information

The work was partially supported by the Russian Science Foundation (Grant No. 14-19-00312).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gavrilov, A.A., Rudyak, V.Y. Direct numerical simulation of the turbulent flows of power-law fluids in a circular pipe. Thermophys. Aeromech. 23, 473–486 (2016). https://doi.org/10.1134/S0869864316040016

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0869864316040016

Key words

Search

Navigation