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Common features between the Newtonian laminar–turbulent transition and the viscoelastic drag-reducing turbulence

Published online by Cambridge University Press:  27 August 2019

Anselmo S. Pereira Open the ORCID record for Anselmo S. Pereira [Opens in a new window] ,
Roney L. Thompson Open the ORCID record for Roney L. Thompson [Opens in a new window]  and
Gilmar Mompean Open the ORCID record for Gilmar Mompean [Opens in a new window]
Anselmo S. Pereira
Affiliation:
MINES ParisTech, PSL Research University, Centre for Material Forming (CEMEF), CNRS UMR 7635, CS 10207 rue Claude Daunesse, 06904 Sophia-Antipolis CEDEX, France
Roney L. Thompson*
Affiliation:
COPPE, Department of Mechanical Engineering, Universidade Federal do Rio de Janeiro, Centro de Tecnologia, Ilha do Fundão, 21945-970, Rio de Janeiro, RJ, Brazil
Gilmar Mompean
Affiliation:
Université de Lille, Polytech’Lille, and Unité de Mécanique de Lille, UML EA 7512, Cité Scientifique, 59655 Villeneuve d’Ascq, France
*
†Email address for correspondence: rthompson@coppe.ufrj.br
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Abstract

The transition from laminar to turbulent flows has challenged the scientific community since the seminal work of Reynolds (Phil. Trans. R. Soc. Lond. A, vol. 174, 1883, pp. 935–982). Recently, experimental and numerical investigations on this matter have demonstrated that the spatio-temporal dynamics that are associated with transitional flows belong to the directed percolation class. In the present work, we explore the analysis of laminar–turbulent transition from the perspective of the recent theoretical development that concerns viscoelastic turbulence, i.e. the drag-reducing turbulent flow obtained from adding polymers to a Newtonian fluid. We found remarkable fingerprints of the variety of states that are present in both types of flows, as captured by a series of features that are known to be present in drag-reducing viscoelastic turbulence. In particular, when compared to a Newtonian fully turbulent flow, the universal nature of these flows includes: (i) the statistical dynamics of the alternation between active and hibernating turbulence; (ii) the weakening of elliptical and hyperbolic structures; (iii) the existence of high and low drag reduction regimes with the same boundary; (iv) the relative enhancement of the streamwise-normal stress; and (v) the slope of the energy spectrum decay with respect to the wavenumber. The maximum drag reduction profile was attained in a Newtonian flow with a Reynolds number near the boundary of the laminar regime and in a hibernating state. It is generally conjectured that, as the Reynolds number increases, the dynamics of the intermittency that characterises transitional flows migrate from a situation where heteroclinic connections between the upper and the lower branches of solutions are more frequent to another where homoclinic orbits around the upper solution become the general rule.

JFM classification

Flow Control: Drag reduction Non-Newtonian Flows: Viscoelasticity Turbulent Flows: Turbulent transition

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 877 , 25 October 2019 , pp. 405 - 428
Copyright
© 2019 Cambridge University Press 

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References

Alizard, F. & Biau, D. 2019 Restricted nonlinear model for high and low drag events in a plane channel flow. J. Fluid Mech. 864, 221–243.10.1017/jfm.2019.14Google Scholar
Armfield, S. W. & Street, R. L. 2000 Fractional step methods for the Navier–Stokes equations on non-staggered grids. ANZIAM J. 42(E), C134–C156.10.21914/anziamj.v42i0.593Google Scholar
Barkley, D. 2016 Theoretical perspective on the route to turbulence in a pipe. J. Fluid Mech. 803, 1–80.10.1017/jfm.2016.465Google Scholar
Barkley, D., Song, B., Mukund, V., Lemoult, G., Avila, M. & Hof, B. 2015 The rise of fully turbulent flow. Nature 526, 550–564.10.1038/nature15701Google Scholar
Bird, R., Curtiss, C. F., Armstrong, R. & Hassager, O. 1987 Dynamics of Polymeric Liquids. Volume 2: Kinetic Theory. Wiley-Interscience.Google Scholar
Choueiri, G. H., Lopez, J. M. & Hof, B. 2018 Exceeding the asymptotic limit of polymer drag reduction. Phys. Rev. Lett. 120 (124501), 1–5.10.1103/PhysRevLett.120.124501Google Scholar
Dubief, Y., Terrapon, V. E. & Soria, J. 2013 On the mechanism of elasto-inertial turbulence. Phys. Fluids 25, 110817.10.1063/1.4820142Google Scholar
Dubief, Y., Terrapon, V. E., White, C. M., Shaqfeh, E. S. G., Moin, P. & Lele, S. K. 2005 New answers on the interaction between polymers and vortices in turbulent flows. Flow Turbul. Combust. 74, 311–329.10.1007/s10494-005-9002-6Google Scholar
Dubief, Y., White, C. M., Shaqfeh, E. S. G. & Terrapon, V. E.2011 Polymer maximum drag reduction: a unique transitional state. arXiv:1106.4482v1.Google Scholar
Dubief, Y., White, C. M., Terrapon, V. E., Shaqfeh, E. S. G., Moin, P. & Lele, S. K. 2004 On the coherent drag-reducing and turbulence-enhancing behaviour of polymers in wall flows. J. Fluid Mech. 514, 271–280.10.1017/S0022112004000291Google Scholar
Eckert, M. 2010 The troublesome birth of hydrodynamic stability theory: Sommerfeld and the turbulence problem. Eur. Phys. J. H 35, 29–51.10.1140/epjh/e2010-00003-3Google Scholar
Elbing, B. R., Perlin, M., Dowling, D. R. & Ceccio, S. L. 2013 Modification of the mean near-wall velocity profile of a high-Reynolds number turbulent boundary layer with the injection of drag-reducing polymer solutions. Phys. Fluids 25, 085103.10.1063/1.4817073Google Scholar
Fu, Z., Iwaki, Y., Motozawa, M., Tsukara, T. & Kawaguchi, Y. 2015 Characteristic turbulent structure of a modified drag-reduced surfactant solution flow via dosing water from channel wall. Intl J. Heat Fluid Flow 53, 135–145.10.1016/j.ijheatfluidflow.2015.03.006Google Scholar
Graham, M. D. 2014 Drag reduction and the dynamics of turbulence in simple and complex fluids. Phys. Fluids 26 (101301), 1–24.10.1063/1.4895780Google Scholar
Graham, M. D. 2015 Turbulence spreads like wildfire. Nature 526, 508–509.10.1038/526508aGoogle Scholar
Grundestam, O., Wallin, S. & Johansson, A. V. 2008 Direct numerical simulations of rotating turbulent channel flow. J. Fluid Mech. 598, 177–199.10.1017/S0022112007000122Google Scholar
Hansen, R. J. & Little, R. C. 1974 Early turbulence and drag reduction phenomena in larger pipes. Nature 252, 690–690.10.1038/252690a0Google Scholar
Henningson, D. S., Lundbladh, A. & Johansson, A. V. 1993 A mechanism for bypass transition from localized disturbances in wall-bounded shear flows. J. Fluid Mech. 250, 169–207.10.1017/S0022112093001429Google Scholar
Housiadas, K. D. & Beris, A. N. 2013 On the skin friction coefficient in viscoelastic wall-bounded flows. Intl J. Heat Fluid Flow 42, 49–67.10.1016/j.ijheatfluidflow.2012.11.004Google Scholar
Hunt, J. C. R., Wray, A. A. & Moin, P.1988 Eddies, stream, and convergence zones in turbulent flows. Center for Turbulence Research – Proceedings of Summer Program Report CTR-S88, 193–208.Google Scholar
Johansson, A. V., Alfredsson, P. H. & Kim, J. 1991 Evolution and dynamics of shear-layer structures in near-wall turbulence. J. Fluid Mech. 224, 579–599.10.1017/S002211209100188XGoogle Scholar
Kim, K., Li, C.-F., Sureshkumar, R., Balachandar, L. & Adrian, R. J. 2007 Effects of polymer stresses on eddy structures in drag-reduced turbulent channel flow. J. Fluid Mech. 584, 281–299.10.1017/S0022112007006611Google Scholar
Komminaho, J., Lundbladh, A. & Johansson, A. V. 1996 Very large structures in plane turbulent Couette flow. J. Fluid Mech. 320, 259–285.10.1017/S0022112096007537Google Scholar
Lundbladh, A. & Johansson, A. V. 1991 Direct simulation of turbulent spots in plane Couette flow. J. Fluid Mech. 229, 499–516.10.1017/S0022112091003130Google Scholar
Min, T., Yoo, J. Y. & Choi, H. 2003a Maximum drag reduction in a turbulent channel flow by polymer additives. J. Fluid Mech. 492, 91–100.10.1017/S0022112003005597Google Scholar
Min, T., Yoo, J. Y., Choi, H. & Joseph, D. D. 2003b Drag reduction by polymer additives in a turbulent channel flow. J. Fluid Mech. 486, 213–238.10.1017/S0022112003004610Google Scholar
Park, J. S., Shekar, A. & Graham, M. 2018 Bursting and critical layer frequencies in minimal turbulent dynamics and connections to exact coherent states. Phys. Rev. Fluids 3 (014611), 1–18.10.1103/PhysRevFluids.3.014611Google Scholar
Pereira, A. S.2016 Transient aspects of the polymer induced drag reduction phenomenon. PhD thesis, pp. 1–211.Google Scholar
Pereira, A. S., Mompean, G. & Soares, E. J. 2018 Modeling and numerical simulations of polymer degradation in a drag reducing plane Couette flow. J. Non-Newtonian Fluid Mech. 256, 1–7.10.1016/j.jnnfm.2018.03.007Google Scholar
Pereira, A. S., Mompean, G., Thais, L. & Soares, E. J. 2017a Transient aspects of drag reducing plane Couette flows. J. Non-Newtonian Fluid Mech. 241, 60–69.10.1016/j.jnnfm.2017.01.008Google Scholar
Pereira, A. S., Mompean, G., Thais, L., Soares, E. J. & Thompson, R. L. 2017b Active and hibernating turbulence in drag-reducing plane Couette flows. Phys. Rev. Fluids 2 (084605), 1–14.10.1103/PhysRevFluids.2.084605Google Scholar
Pereira, A. S., Mompean, G., Thais, L. & Thompson, R. L. 2017c Statistics and tensor analysis of polymer coil-stretch mechanism in turbulent drag reducing channel flow. J. Fluid Mech. 824, 135–173.10.1017/jfm.2017.332Google Scholar
Pereira, A. S., Mompean, G., Thompson, R. L. & Soares, E. J. 2017d Elliptical, parabolic, and hyperbolic exchanges of energy in drag reducing plane Couette flows. Phys. Fluids 29, 115106.10.1063/1.5010047Google Scholar
Pomeau, Y. 1986 Front motion, metastability and subcritical bifurcations in hydrodynamics. Physica D 23, 3–11.Google Scholar
Pomeau, Y. 2015 The transition to turbulence in parallel flows: a personal view. C. R. Méc. 343, 210–218.10.1016/j.crme.2014.10.002Google Scholar
Reynolds, O. 1883 An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels. Phil. Trans. R. Soc. Lond. A 174, 935–982.Google Scholar
Sano, M. & Tamai, K. 2016 A universal transition to turbulence in channel flow. Nat. Phys. 12, 249–253.10.1038/nphys3659Google Scholar
Shekar, A., McMullen, R. M., Wang, S.-N., McKeon, B. J. & Graham, M. D. 2019 Critical-layer structures and mechanisms in elastoinertial turbulence. Phys. Rev. Lett. 122, 124503.10.1103/PhysRevLett.122.124503Google Scholar
Sid, S., Terrapon, V. E. & Dubief, Y. 2018 Two-dimensional dynamics of elasto-inertial turbulence and its role in polymer drag reduction. Phys. Rev. Fluids 3 (011301), 1–9.10.1103/PhysRevFluids.3.011301Google Scholar
Sureshkumar, R., Beris, A. N. & Handler, R. A. 1997 Direct numerical simulation of the turbulent channel flow of a polymer solution. Phys. Fluids 9, 743–755.10.1063/1.869229Google Scholar
Thais, L., Gatski, T. B. & Mompean, G. 2012 Some dynamical features of the turbulent flow of a viscoelastic fluid for reduced drag. J. Turbul. 13, 1–26.Google Scholar
Thais, L., Gatski, T. B. & Mompean, G. 2013a Analysis of polymer drag reduction mechanisms from energy budgets. Intl J. Heat Fluid Flow 43, 52–61.10.1016/j.ijheatfluidflow.2013.05.016Google Scholar
Thais, L., Gatski, T. B. & Mompean, G. 2013b Spectral analysis of turbulent viscoelastic and newtonian channel flows. J. Non-Newtonian Fluid Mech. 200, 165–176.10.1016/j.jnnfm.2013.04.006Google Scholar
Thais, L., Tejada-Martinez, A., Gatski, T. B. & Mompean, G. 2011 A massively parallel hybrid scheme for direct numerical simulation of turbulent viscoelastic channel flow. Comput. Fluids 43, 134–142.10.1016/j.compfluid.2010.09.025Google Scholar
Toms, B. A. 1948 Some observations on the flow of linear polymer solutions through straight tubes at large Reynolds numbers. In Proceedings of the International Congress of Rheology, Holland, pp. 135–141. North-Holland.Google Scholar
Tuckerman, L. S., Kreilos, T., Schrobsdorff, H., Scneider, T. M. & Gibson, J. F. 2014 Turbulent-laminar patterns in plane poiseuille flow. Phys. Fluids 26 (114103), 1–14.10.1063/1.4900874Google Scholar
Vinogradov, G. V. & Mannin, V. N. 1965 An experimental study of elastic turbulence. Colloid Polym. Sci. 201, 93–98.Google Scholar
Virk, P. S. 1975a Drag reduction by collapsed and extended polyelectrolytes. Nature 253, 109–110.10.1038/253109a0Google Scholar
Virk, P. S. 1975b Drag reduction fundamentals. AIChE J. 21, 625–656.10.1002/aic.690210402Google Scholar
Virk, P. S., Mickley, H. S. & Smith, K. A. 1967 The Toms phenomenom: turbulent pipe flow of dilute polymer solutions. J. Fluid Mech. 22, 22–30.Google Scholar
Virk, P. S., Mickley, H. S. & Smith, K. A. 1970 The ultimate asymptote and mean flow structure in Toms’ phenomenon. Trans. ASME J. Appl. Mech. 37, 488–493.10.1115/1.3408532Google Scholar
Waleffe, F. 2001 Exact coherent structures in channel flow. J. Fluid Mech. 435, 93–102.10.1017/S0022112001004189Google Scholar
Warholic, M. D., Massah, H. & Hanratty, T. J. 1999 Influence of drag-reducing polymers on turbulence: effects of Reynolds number, concentration and mixing. Exp. Fluids 27, 461–472.10.1007/s003480050371Google Scholar
Watanabe, T. & Gotoh, T. 2013 Hybrid Eulerian-Lagrangian simulations for polymer–turbulence interactions. J. Fluid Mech. 717, 535–574.10.1017/jfm.2012.595Google Scholar
Whalley, R. D., Park, J. S., Kushwaha, A., Dennis, D. J. C., Graham, M. D. & Poole, R. J. 2017 Low-drag events in transitional wall-bounded turbulence. Phys. Rev. Fluids 2 (034602), 1–9.10.1103/PhysRevFluids.2.034602Google Scholar
White, C. M., Dubief, Y. & Klewicki, J. 2012 Re-examining the logarithmic dependence of the mean velocity distribution in polymer drag reduced wall-bounded flow. Phys. Fluids 24, 021701.10.1063/1.3681862Google Scholar
White, C. M. & Mungal, M. G. 2008 Mechanics and prediction of turbulent drag reduction whit polymer additives. Annu. Rev. Fluid Mech. 40, 235–256.10.1146/annurev.fluid.40.111406.102156Google Scholar
Xi, L. & Graham, M. D. 2010 Active and hibernating turbulence in minimal channel flow of Newtonian and polymerc fluids. Phys. Rev. Lett. 104, 218301.10.1103/PhysRevLett.104.218301Google Scholar
Xi, L. & Graham, M. D. 2012 Dynamics on the laminar–turbulent boundary and the origin of the maximum drag reduction asymptote. Phys. Rev. Lett. 108, 028301.10.1103/PhysRevLett.108.028301Google Scholar
Xiong, X., Tao, J., Chen, S. & Brandt, L. 2015 Turbulent bands in plane-poiseuille flow at moderate Reynolds numbers. Phys. Fluids 27 (041702), 1–7.10.1063/1.4917173Google Scholar