The role of elongational viscosity in the mechanism of drag reduction by polymer additives is investigated qualitatively by means of direct numerical simulations of a turbulent pipe flow. For the polymer solution, a generalised Newtonian constitutive model is utilised in which the viscosity depends on the second and third invariant of the rate-of-strain tensor via an elongation parameter. This elongation parameter is capable of identifying elongational type of regions within the flow. The simulations show that complementary to stretching of the polymers, also compression must be incorporated to have drag reduction, contrary to many suggestions done in the literature on the mechanism which assume that stretching of the polymers is most important.
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Batchelor, G.K., The stress generated in a non-dilute suspension of elongated particles by pure straining motion.J. Fluid Mech. 46 (1971) 813–829.
Berman, N.S. and George, W.K., Jr., Onset of drag reduction in dilute polymer solutions.Phys. Fluids 17 (1974) 250–251.
Berner, C. and Scrivener, O., Drag reduction and structure of turbulence in dilute polymer solutions. In: Hough, G.R. (ed.),Viscous Flow Drag Reduction, American Institute of Aeronautics and Astronautics, New York (1980) pp. 290–299.
Bewersdorff, H.-W., Heterogene Widerstandsverminderung bei turbulenten Rohrströmungen.Rheologica Acta 23 (1984) 522–534.
Bird, R.B., Curtiss, C.F., Armstrong, R.C. and Hassager, O.,Dynamics of Polymeric Liquids, Vol. 2, Kinetic Theory. John Wiley & Sons, New York (1987).
Debbaut, B. and Crochet, M.J., Extensional effects in complex flows.J. non-Newt. Fluid Mech. 30 (1988) 169–184.
Eggels, J.G.M, Pourquié, M.J.B.M. and Nieuwstadt, F.T.M., Large-eddy simulation of turbulent pipe flow. Submitted toTheoretical and Computational Fluid Dynamics (1992).
Eggels, J.G.M., Unger, F., Weiss, M.H., Westerweel, J., Adrian, R.J., Friedrich, R. and Nieuwstadt, F.T.M., Fully developed turbulent pipe flow: a comparison between direct numerical simulation and experiment. Submitted toJournal of Fluid Mechanics (1993).
de Gennes, P.G.,Introduction to Polymer Dynamics. Cambridge University Press, Cambridge (1990).
Harder, K.J. and Tiederman, W.G., Drag reduction and turbulent structure in two-dimensional channel flows.Phil. Trans. R. Soc. Lond. A 336 (1991) 19–34.
Hunt, J.C.R., Wray, A.A. and Moin, P., Eddies, streams and convergence zones in turbulent flows. In:Center for Turbulence Research, Proceedings of the Summer Program 1988 (1988) pp. 193–208.
Lumley, J.L., Drag reduction in turbulent flow by polymer additives.Macromol. Rev. 7 (1973) 263–290.
Lumley, J.L., Drag reduction in two-phase and polymer flows.Phys. Fluids 20 (1977) S64-S71.
McComb, W.D.,The Physics of Fluid Turbulence. Oxford University Press, New York (1991).
McComb, W.D. and Rabie, L.H., Local drag reduction due to injection of polymer solutions into turbulent flow in a pipe.AIChE J. 28 (1982) 547–565.
Maerker, J.M. and Schowalter, W.R., Biaxial extension of an elastic liquid.Rheologica Acta 13 (1974) 627–638.
Metzner, A.B. and Metzner, A.P., Stress levels in rapid extensional flows of polymeric liquids.Rheologica Acta 9 (1970) 174–181.
Mizushina, T. and Usui, H., Reduction of eddy diffusion for momentum and heat in viscoelastic flow in a circular tube.Phys. Fluids 20 (1977) S100-S108.
Schumann, U., Linear stability of finite difference equations for three-dimensional flow problems.J. Comp. Phys. 18 (1975) 465–470.
Tiederman, W.G., The effect of dilute polymer solutions on viscous drag and turbulence structure. In: Gyr, A. (ed.),Structure of Turbulence and Drag Reduction (IUTAM Symp. 1989), Springer-Verlag (1990) pp. 187–200.
den Toonder, J.M.J.,Drag Reduction by Additives: The State-of-the-Art. Internal report Lab. Aero and Hydrodynamics, Delft University of Technology (1992) 101 pp.
Usui, H., Maeguchi, K. and Sano, Y., Drag reduction caused by the injection of polymer thread into a turbulent pipe flow.Phys. Fluids 31 (1988) 2518–2523.
Virk, P.S., Drag reduction fundamentals.AIChE Journal 21 (1975) 625–656.
Virk, P.S. and Wagger, D.L., Aspects of mechanisms in type B drag reduction. In: Gyr A. (ed.),Structure of Turbulence and Drag Reduction (IUTAM Symp. 1989), Springe-Verlag (1990) pp. 201–213.
Westerweel, J.,Digital Particle Image Velocimetry — Theory and Application. Ph.D. thesis, Delft University of Technology (1993).
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den Toonder, J.M.J., Nieuwstadt, F.T.M. & Kuiken, G.D.C. The role of elongational viscosity in the mechanism of drag reduction by polymer additives. Appl. Sci. Res. 54, 95–123 (1995). https://doi.org/10.1007/BF00864368
- direct numerical simulation
- drag reduction
- elongational viscosity
- flow classification
- turbulent pipe flow