Direct Numerical Simulation of Turbulent Channel Flow of a Viscous Anisotropic Fluid

  • M. Manhart
  • R. Friedrich
Conference paper

Abstract

Direct Numerical Simulations (DNS) of turbulent channel flow axe performed with a viscous anisotropic model to account for the effect of dilute polymer solutions in water. The model is based on the assumption that the polymer molecules behave like rigid elongated rods. In addition it is assumed that the average orientation angle of the molecules is parallel to the instantaneous flow vector. The results of the DNS with two different model parameters show a drag reduction compared to the Newtonian case. The evaluation of the averaged flow variables shows a change in turbulence structure that is in line with published data of turbulent channel or pipe flows of dilute polymer solutions.

Keywords

Turbulent Kinetic Energy Direct Numerical Simulation Drag Reduction Bulk Velocity Extensional Viscosity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Achia, B. U, Thompson, D.W.: Structure of the Turbulent Boundary Layer in Drag Reducing Pipe Flow.J. Fluid Mech. 81 (1977), 439–464CrossRefGoogle Scholar
  2. 2.
    Bird, R.B., Armstrong, R.C., Hassager, O.: Dynamics of Polymeric Liquids, Vol. 1, Fluid Mechanics. John Wiley and Sons, 2nd edition , 1987Google Scholar
  3. 3.
    den Toonder, J.M.J.: Drag Reduction by Polymer Additives in a Turbulent Pipe Flow: Laboratory and Numerical Experiments. PhD thesis, Technische Universiteit Delft, Netherlands, 1995Google Scholar
  4. 4.
    denToonder, J.M.J., Hulsen, M.A., Kuiken, G.D.C., Nieuwstadt, F.T.M.: Drag Reduction by Polymer Additives in a Turbulent Pipe Flow:Numeric al and Laboratory Experiments.J. Fluid Mech. 337 (1997), 193–231CrossRefGoogle Scholar
  5. 5.
    Eggels, J.G.M., Unger, F., Weiss, M.H., Westerweel, J., Adrian, R.J., R. Friedrich, R., Nieuwstadt, F.T.M.: Fully Developed Turbulent Pipe Flow:A Comparison between Direct Numerical Simulation and Experiment.J. Fluid Mech. 268 (1994), 175–209CrossRefGoogle Scholar
  6. 6.
    Ericksen, J.L.: Anisotropic fluids.Arch. Ration. Mech. Anal. 4 (1960), 231–237MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Ericksen, J.L.: Transversely Isotropic Fluids.Kolloid-Z. 173 (1960), 117–122CrossRefGoogle Scholar
  8. 8.
    de Gennes, P.G.: Introduction to Polymer Dynamics. Cambridge University Press, 1990Google Scholar
  9. 9.
    Gyr, A., Bewersdorff, H.-W.: Drag Reduction of turbulent flows by additives, volume 32 of Fluid Mechanics and its Applications.Kluwer Academic Publishers, Dordrecht, 1995Google Scholar
  10. 10.
    Harder, K.J., Tiedermann, W.G.: Drag Reduction and Turbulent Structure in Two-Dimensional Channel Flows.Phil. Trans. R. Soc. Lond. A 336 (1991), 19–34CrossRefGoogle Scholar
  11. 11.
    Jiménez, J., Pinelli, A.:The Autonomous Cycle of Near-Wall Turbulence.J. Fluid Mech. 389 (1999), 335–359MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Joseph, D.D.: Fluid Dynamics of Viscoelastic Liquids. Springer, 1990Google Scholar
  13. 13.
    Kim, J., Moin, P., Moser, R.: Turbulence Statistics in Fully Developed Channel Flow at Low Reynolds Number.J. Fluid Mech. 17 (1987), 133–166CrossRefGoogle Scholar
  14. 14.
    Landahl, M.T.: Drag Reduction by Polymer Addition. In E. Becker and G.K. Mikhailov, editors, Theoretical and Applied Mechanics, Proc. 13th Intl. Congr. Theor. and Appl. Mech., Springer, 1973, 177-199Google Scholar
  15. 15.
    Manhart, M., Deng, G.B., Hüttl, T.J., Tremblay, F., Segal, A., Friedrich, R., Piquet, J., and Wesseling, P.: The Minimal Turbulent Flow Unit as a Test Case for Three Different Computer Codes. In E.H. Hirschel, editor, Vol. 66, Notes on numerical fluid mechanics. Vieweg-Verlag, Braunschweig, 1998Google Scholar
  16. 16.
    Metzner, A.B., and Metzner, A.P.: Stress Levels in Rapid Extensional Flows of Polymeric Fluids.Rheol. Acta, 9 (1970), 174–181CrossRefGoogle Scholar
  17. 17.
    Moin, P., Moser, R.: Characteristic-Eddy Decomposition of Turbulence in a Channel. J. Fluid Mech. 200 (1989), 471–509MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    Orlandi, P.: A Tentative Approach to the Direct Simulation of Drag Reduction by Polymers. J. Non-Newtonian Fluid Mech., 60 (1995), 277–301CrossRefGoogle Scholar
  19. 19.
    Pinho, F.T., Whitelaw, J.H.: Flow of Non-Newtonian Fluids in a Pipe. J. Non-Newtonian Fluid Mech., 34 (1990), 129–144CrossRefGoogle Scholar
  20. 20.
    Robinson, S.K.:Coherent Motions in the Turbulent Boundary Layer.Annu. Rev. Fluid Mech., 23 (1991), 601–639CrossRefGoogle Scholar
  21. 21.
    Rotta, J.: Turbulente Strömungen.Teubner,Stuttgart, 1972MATHGoogle Scholar
  22. 22.
    Schmitt, L., Richter, K., and Friedrich, R.: Large-Eddy Simulation of Turbulent Boundary Layer and Channel Flow at High Reynolds Number. In U. Schumann and R. Friedrich, editors, Direct and Large Eddy Simulation of Turbulence, Vieweg Braunschweig (1986), 161–176Google Scholar
  23. 23.
    Szeri, A.J., Leal, L.G.: A New Computational Method for the Solution of Flow Problems of Microstructured Fluids. Part 1. Theory . J. Fluid Mech., 242 (1992), 549–576MathSciNetMATHCrossRefGoogle Scholar
  24. 24.
    A.J. Szeri, A.J.,Leal, L.G.:A New Computational Method for the Solution of Flow Problems of Microstructured Fluids. Part 2. Inhomogeneous Shear Flow of a Suspension.J. Fluid Mech., 262 (1994), 171–204MATHCrossRefGoogle Scholar
  25. 25.
    Tennekes, H., Lumley, J.L.: A First Course in Turbulence. MIT Press, Cambridge, Massachusetts, 1972Google Scholar
  26. 26.
    Tiedermann, W.G.: The Effect of Dilute Polymer Solutions on Viscous Drag and Turbulence Structure. In A. Gyr, editor, Structure of Turbulence and Drag Reduction, IUTAM Symp., Springer (1990), 187-200Google Scholar
  27. 27.
    Wei, T., and Willmarth, W.W.: Modifying Turbulent Structure with Drag-Reducing Polymer Additives in Turbulent Channel Flows.J. Fluid Mech. 245 (1992), 619–641CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • M. Manhart
    • 1
  • R. Friedrich
    • 1
  1. 1.Lehrstuhl für FluidmechanikTechnische Universität MünchenGarchingGermany

Personalised recommendations