×

zbMATH — the first resource for mathematics

Common features between the Newtonian laminar-turbulent transition and the viscoelastic drag-reducing turbulence. (English) Zbl 1430.76223
Summary: The transition from laminar to turbulent flows has challenged the scientific community since the seminal work of O. Reynolds [Philos. Trans. R. Soc. Lond. 174, 935-982 (1883; JFM 16.0845.02)]. 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.

MSC:
76F06 Transition to turbulence
76A10 Viscoelastic fluids
76F70 Control of turbulent flows
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Alizard, F.; Biau, D., Restricted nonlinear model for high and low drag events in a plane channel flow, J. Fluid Mech., 864, 221-243, (2019) · Zbl 1415.76320
[2] Armfield, S. W.; Street, R. L., Fractional step methods for the Navier-Stokes equations on non-staggered grids, ANZIAM J., 42(E), C134-C156, (2000) · Zbl 1008.76058
[3] Barkley, D., Theoretical perspective on the route to turbulence in a pipe, J. Fluid Mech., 803, 1-80, (2016) · Zbl 1454.76047
[4] Barkley, D.; Song, B.; Mukund, V.; Lemoult, G.; Avila, M.; Hof, B., The rise of fully turbulent flow, Nature, 526, 550-564, (2015)
[5] Bird, R.; Curtiss, C. F.; Armstrong, R.; Hassager, O., Dynamics of Polymeric Liquids. Volume 2: Kinetic Theory, (1987), Wiley-Interscience
[6] Choueiri, G. H.; Lopez, J. M.; Hof, B., Exceeding the asymptotic limit of polymer drag reduction, Phys. Rev. Lett., 120, 124501, 1-5, (2018)
[7] Dubief, Y.; Terrapon, V. E.; Soria, J., On the mechanism of elasto-inertial turbulence, Phys. Fluids, 25, (2013)
[8] Dubief, Y.; Terrapon, V. E.; White, C. M.; Shaqfeh, E. S. G.; Moin, P.; Lele, S. K., New answers on the interaction between polymers and vortices in turbulent flows, Flow Turbul. Combust., 74, 311-329, (2005) · Zbl 1200.76106
[9] Dubief, Y., White, C. M., Shaqfeh, E. S. G. & Terrapon, V. E.2011 Polymer maximum drag reduction: a unique transitional state. arXiv:1106.4482v1.
[10] Dubief, Y.; White, C. M.; Terrapon, V. E.; Shaqfeh, E. S. G.; Moin, P.; Lele, S. K., On the coherent drag-reducing and turbulence-enhancing behaviour of polymers in wall flows, J. Fluid Mech., 514, 271-280, (2004) · Zbl 1067.76052
[11] Eckert, M., The troublesome birth of hydrodynamic stability theory: Sommerfeld and the turbulence problem, Eur. Phys. J. H, 35, 29-51, (2010)
[12] Elbing, B. R.; Perlin, M.; Dowling, D. R.; Ceccio, S. L., 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, (2013)
[13] Fu, Z.; Iwaki, Y.; Motozawa, M.; Tsukara, T.; Kawaguchi, Y., 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, (2015)
[14] Graham, M. D., Drag reduction and the dynamics of turbulence in simple and complex fluids, Phys. Fluids, 26, 101301, 1-24, (2014)
[15] Graham, M. D., Turbulence spreads like wildfire, Nature, 526, 508-509, (2015)
[16] Grundestam, O.; Wallin, S.; Johansson, A. V., Direct numerical simulations of rotating turbulent channel flow, J. Fluid Mech., 598, 177-199, (2008) · Zbl 1151.76517
[17] Hansen, R. J.; Little, R. C., Early turbulence and drag reduction phenomena in larger pipes, Nature, 252, 690-690, (1974)
[18] Henningson, D. S.; Lundbladh, A.; Johansson, A. V., A mechanism for bypass transition from localized disturbances in wall-bounded shear flows, J. Fluid Mech., 250, 169-207, (1993) · Zbl 0773.76030
[19] Housiadas, K. D.; Beris, A. N., On the skin friction coefficient in viscoelastic wall-bounded flows, Intl J. Heat Fluid Flow, 42, 49-67, (2013)
[20] 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.
[21] Johansson, A. V.; Alfredsson, P. H.; Kim, J., Evolution and dynamics of shear-layer structures in near-wall turbulence, J. Fluid Mech., 224, 579-599, (1991) · Zbl 0717.76057
[22] Kim, K.; Li, C.-F.; Sureshkumar, R.; Balachandar, L.; Adrian, R. J., Effects of polymer stresses on eddy structures in drag-reduced turbulent channel flow, J. Fluid Mech., 584, 281-299, (2007) · Zbl 1175.76069
[23] Komminaho, J.; Lundbladh, A.; Johansson, A. V., Very large structures in plane turbulent Couette flow, J. Fluid Mech., 320, 259-285, (1996) · Zbl 0875.76160
[24] Lundbladh, A.; Johansson, A. V., Direct simulation of turbulent spots in plane Couette flow, J. Fluid Mech., 229, 499-516, (1991) · Zbl 0850.76256
[25] Min, T.; Yoo, J. Y.; Choi, H., Maximum drag reduction in a turbulent channel flow by polymer additives, J. Fluid Mech., 492, 91-100, (2003) · Zbl 1063.76579
[26] Min, T.; Yoo, J. Y.; Choi, H.; Joseph, D. D., Drag reduction by polymer additives in a turbulent channel flow, J. Fluid Mech., 486, 213-238, (2003) · Zbl 1054.76041
[27] Park, J. S.; Shekar, A.; Graham, M., Bursting and critical layer frequencies in minimal turbulent dynamics and connections to exact coherent states, Phys. Rev. Fluids, 3, 14611, 1-18, (2018)
[28] Pereira, A. S.2016 Transient aspects of the polymer induced drag reduction phenomenon. PhD thesis, pp. 1-211.
[29] Pereira, A. S.; Mompean, G.; Soares, E. J., Modeling and numerical simulations of polymer degradation in a drag reducing plane Couette flow, J. Non-Newtonian Fluid Mech., 256, 1-7, (2018)
[30] Pereira, A. S.; Mompean, G.; Thais, L.; Soares, E. J., Transient aspects of drag reducing plane Couette flows, J. Non-Newtonian Fluid Mech., 241, 60-69, (2017)
[31] Pereira, A. S.; Mompean, G.; Thais, L.; Soares, E. J.; Thompson, R. L., Active and hibernating turbulence in drag-reducing plane Couette flows, Phys. Rev. Fluids, 2, 84605, 1-14, (2017)
[32] Pereira, A. S.; Mompean, G.; Thais, L.; Thompson, R. L., Statistics and tensor analysis of polymer coil-stretch mechanism in turbulent drag reducing channel flow, J. Fluid Mech., 824, 135-173, (2017)
[33] Pereira, A. S.; Mompean, G.; Thompson, R. L.; Soares, E. J., Elliptical, parabolic, and hyperbolic exchanges of energy in drag reducing plane Couette flows, Phys. Fluids, 29, (2017)
[34] Pomeau, Y., Front motion, metastability and subcritical bifurcations in hydrodynamics, Physica D, 23, 3-11, (1986)
[35] Pomeau, Y., The transition to turbulence in parallel flows: a personal view, C. R. Méc., 343, 210-218, (2015)
[36] Reynolds, O., 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, (1883) · JFM 16.0845.02
[37] Sano, M.; Tamai, K., A universal transition to turbulence in channel flow, Nat. Phys., 12, 249-253, (2016)
[38] Shekar, A.; McMullen, R. M.; Wang, S.-N.; McKeon, B. J.; Graham, M. D., Critical-layer structures and mechanisms in elastoinertial turbulence, Phys. Rev. Lett., 122, (2019)
[39] Sid, S.; Terrapon, V. E.; Dubief, Y., Two-dimensional dynamics of elasto-inertial turbulence and its role in polymer drag reduction, Phys. Rev. Fluids, 3, 11301, 1-9, (2018)
[40] Sureshkumar, R.; Beris, A. N.; Handler, R. A., Direct numerical simulation of the turbulent channel flow of a polymer solution, Phys. Fluids, 9, 743-755, (1997)
[41] Thais, L.; Gatski, T. B.; Mompean, G., Some dynamical features of the turbulent flow of a viscoelastic fluid for reduced drag, J. Turbul., 13, 1-26, (2012) · Zbl 1273.76045
[42] Thais, L.; Gatski, T. B.; Mompean, G., Analysis of polymer drag reduction mechanisms from energy budgets, Intl J. Heat Fluid Flow, 43, 52-61, (2013)
[43] Thais, L.; Gatski, T. B.; Mompean, G., Spectral analysis of turbulent viscoelastic and newtonian channel flows, J. Non-Newtonian Fluid Mech., 200, 165-176, (2013)
[44] Thais, L.; Tejada-Martinez, A.; Gatski, T. B.; Mompean, G., A massively parallel hybrid scheme for direct numerical simulation of turbulent viscoelastic channel flow, Comput. Fluids, 43, 134-142, (2011) · Zbl 1452.76075
[45] Toms, B. A.1948Some 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.
[46] Tuckerman, L. S.; Kreilos, T.; Schrobsdorff, H.; Scneider, T. M.; Gibson, J. F., Turbulent-laminar patterns in plane poiseuille flow, Phys. Fluids, 26, 114103, 1-14, (2014)
[47] Vinogradov, G. V.; Mannin, V. N., An experimental study of elastic turbulence, Colloid Polym. Sci., 201, 93-98, (1965)
[48] Virk, P. S., Drag reduction by collapsed and extended polyelectrolytes, Nature, 253, 109-110, (1975)
[49] Virk, P. S., Drag reduction fundamentals, AIChE J., 21, 625-656, (1975)
[50] Virk, P. S.; Mickley, H. S.; Smith, K. A., The Toms phenomenom: turbulent pipe flow of dilute polymer solutions, J. Fluid Mech., 22, 22-30, (1967)
[51] Virk, P. S.; Mickley, H. S.; Smith, K. A., The ultimate asymptote and mean flow structure in Toms’ phenomenon, Trans. ASME J. Appl. Mech., 37, 488-493, (1970)
[52] Waleffe, F., Exact coherent structures in channel flow, J. Fluid Mech., 435, 93-102, (2001) · Zbl 0987.76034
[53] Warholic, M. D.; Massah, H.; Hanratty, T. J., Influence of drag-reducing polymers on turbulence: effects of Reynolds number, concentration and mixing, Exp. Fluids, 27, 461-472, (1999)
[54] Watanabe, T.; Gotoh, T., Hybrid Eulerian-Lagrangian simulations for polymer – turbulence interactions, J. Fluid Mech., 717, 535-574, (2013) · Zbl 1284.76043
[55] Whalley, R. D.; Park, J. S.; Kushwaha, A.; Dennis, D. J. C.; Graham, M. D.; Poole, R. J., Low-drag events in transitional wall-bounded turbulence, Phys. Rev. Fluids, 2, 34602, 1-9, (2017)
[56] White, C. M.; Dubief, Y.; Klewicki, J., Re-examining the logarithmic dependence of the mean velocity distribution in polymer drag reduced wall-bounded flow, Phys. Fluids, 24, (2012)
[57] White, C. M.; Mungal, M. G., Mechanics and prediction of turbulent drag reduction whit polymer additives, Annu. Rev. Fluid Mech., 40, 235-256, (2008) · Zbl 1229.76043
[58] Xi, L.; Graham, M. D., Active and hibernating turbulence in minimal channel flow of Newtonian and polymerc fluids, Phys. Rev. Lett., 104, (2010)
[59] Xi, L.; Graham, M. D., Dynamics on the laminar – turbulent boundary and the origin of the maximum drag reduction asymptote, Phys. Rev. Lett., 108, (2012)
[60] Xiong, X.; Tao, J.; Chen, S.; Brandt, L., Turbulent bands in plane-poiseuille flow at moderate Reynolds numbers, Phys. Fluids, 27, 41702, 1-7, (2015)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.