zbMATH — the first resource for mathematics

Dynamics of viscoelastic pipe flow at low Reynolds numbers in the maximum drag reduction limit. (English) Zbl 1419.76040
Summary: Polymer additives can substantially reduce the drag of turbulent flows and the upper limit, the so-called state of ‘maximum drag reduction’ (MDR), is to a good approximation independent of the type of polymer and solvent used. Until recently, the consensus was that, in this limit, flows are in a marginal state where only a minimal level of turbulence activity persists. Observations in direct numerical simulations at low Reynolds numbers \((Re)\) using minimal sized channels appeared to support this view and reported long ‘hibernation’ periods where turbulence is marginalized. In simulations of pipe flow at \(Re\) near transition we find that, indeed, with increasing Weissenberg number \((Wi)\), turbulence expresses long periods of hibernation if the domain size is small. However, with increasing pipe length, the temporal hibernation continuously alters to spatio-temporal intermittency and here the flow consists of turbulent puffs surrounded by laminar flow. Moreover, upon an increase in \(Wi\), the flow fully relaminarizes, in agreement with recent experiments. At even larger \(Wi\), a different instability is encountered causing a drag increase towards MDR. Our findings hence link earlier minimal flow unit simulations with recent experiments and confirm that the addition of polymers initially suppresses Newtonian turbulence and leads to a reverse transition. The MDR state on the other hand results at these low\(Re\) from a separate instability and the underlying dynamics corresponds to the recently proposed state of elasto-inertial turbulence.

76A10 Viscoelastic fluids
76F06 Transition to turbulence
76F70 Control of turbulent flows
Full Text: DOI
[1] Barkley, D.; Song, B.; Mukund, V.; Lemoult, G.; Avila, M.; Hof, B., The rise of fully turbulent flow, Nature, 526, 7574, 550-553, (2015)
[2] Benzi, R.; De Angelis, E.; L’Vov, V. S.; Procaccia, I.; Tiberkevich, V., Maximum drag reduction asymptotes and the cross-over to the newtonian plug, J. Fluid Mech., 551, 185-195, (2006) · Zbl 1085.76004
[3] Beris, A. N.; Dimitropoulos, C. D., Pseudospectral simulation of turbulent viscoelastic channel flow, Comput. Meth. Appl. Mech. Engng, 180, 3, 365-392, (1999) · Zbl 0966.76064
[4] Bird, R.; Dotson, P.; Johnson, N., Polymer solution rheology based on a finitely extensible beadspring chain model, J. Non-Newtonian Fluid Mech., 7, 2, 213-235, (1980) · Zbl 0432.76012
[5] Choueiri, G. H.; Lopez, J. M.; Hof, B., Exceeding the asymptotic limit of polymer drag reduction, Phys. Rev. Lett., 120, (2018)
[6] Dubief, Y.; Terrapon, V. E.; Soria, J., On the mechanism of elasto-inertial turbulence, Phys. Fluids, 25, 11, (2013)
[7] 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, 8, (2013)
[8] Giudice, F. D.; Haward, S. J.; Shen, A. Q., Relaxation time of dilute polymer solutions: a microfluidic approach, J. Rheol., 61, 2, 327-337, (2017)
[9] Hof, B.; De Lozar, A.; Avila, M.; Tu, X.; Schneider, T. M., Eliminating turbulence in spatially intermittent flows, Science, 327, 5972, 1491-1494, (2010)
[10] Li, C.-F., Sureshkumar, R. & Khomami, B.2006Influence of rheological parameters on polymer induced turbulent drag reduction. J. Non-Newtonian Fluid Mech.140 (1), 23-40; special issue on the XIVth International Workshop on Numerical Methods for Non-Newtonian Flows, Santa Fe, 2005. · Zbl 1143.76337
[11] Little, R. C.; Wiegard, M., Drag reduction and structural turbulence in flowing polyox solutions, J. Appl. Polym. Sci., 14, 2, 409-419, (1970)
[12] L’Vov, V. S.; Pomyalov, A.; Procaccia, I.; Tiberkevich, V., Drag reduction by polymers in wall bounded turbulence, Phys. Rev. Lett., 92, (2004)
[13] Orszag, S. A.; Patera, A. T., Secondary instability of wall-bounded shear flows, J. Fluid Mech., 128, 347-385, (1983) · Zbl 0556.76039
[14] Ptasinsky, P. K.; Boersma, B. J.; Nieuwstadt, F. T. M.; Hulsen, M. A.; Van Den Brule, B. H. A. A.; Hunt, J. C. R., Turbulent channel flow near maximum drag reduction: simulations, experiments and mechanisms, J. Fluid Mech., 490, 251-291, (2003) · Zbl 1063.76580
[15] Ram, A.; Tamir, A., Structural turbulence in polymer solutions, J. Appl. Polym. Sci., 8, 6, 2751-2762, (1964)
[16] Samanta, D.; Dubief, Y.; Holzner, M.; Schäfer, C.; Morozov, A. N.; Wagner, C.; Hof, B., Elasto-inertial turbulence, Proc. Natl Acad. Sci., 110, 26, 10557-10562, (2013)
[17] 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)
[18] Shi, L.; Rampp, M.; Hof, B.; Avila, M., A hybrid mpi-openmp parallel implementation for pseudospectral simulations with application to taylorcouette flow, Comput. Fluids, 106, 1-11, (2015) · Zbl 1390.76623
[19] 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, (2018)
[20] Sreenivasan, K. R.; White, C. M., The onset of drag reduction by dilute polymer additives, and the maximum drag reduction asymptote, J. Fluid Mech., 409, 149-164, (2000) · Zbl 0959.76005
[21] Sureshkumar, R.; Beris, A. N.; Handler, R. A., Direct numerical simulation of the turbulent channel flow of a polymer solution, Phys. Fluids, 9, 3, 743-755, (1997)
[22] Toms, B. A.1948Some observation on the flow of linear polymer solutions through straight tubes at large Reynolds numbers. In Proceedings of the 1st Intl. Congr. on Rheology, vol. II, pp. 135-141. North Holland Publishing Company.
[23] Virk, P.; Mickley, H.; Smith, K., The ultimate asymptote and mean flow structure in Toms’ phenomenon, J. Appl. Mech., 37, 2, 488-493, (1970)
[24] Wang, S.-N.; Shekar, A.; Graham, M. D., Spatiotemporal dynamics of viscoelastic turbulence in transitional channel flow, J. Non-Newtonian Fluid Mech., 244, 104-122, (2017)
[25] Warholic, M.; Massah, H.; Hanratty, T., Influence of drag-reducing polymers on turbulence: effects of Reynolds number, concentration and mixing, Exp. Fluids, 27, 5, 461-472, (1999)
[26] 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, 2, (2012)
[27] White, C. M.; Dubief, Y.; Klewicki, J., Properties of the mean momentum balance in polymer drag-reduced channel flow, J. Fluid Mech., 834, 409-433, (2018) · Zbl 1419.76332
[28] White, C. M.; Mungal, M. G., Mechanics and prediction of turbulent drag reduction with polymer additives, Annu. Rev. Fluid Mech., 40, 1, 235-256, (2008) · Zbl 1229.76043
[29] Willis, A. P., The openpipeflow Navier-Stokes solver, SoftwareX, 6, 124-127, (2017)
[30] Wygnanski, I. J.; Champagne, F. H., On transition in a pipe. Part 1. The origin of puffs and slugs and the flow in a turbulent slug, J. Fluid Mech., 59, 2, 281-335, (1973)
[31] Xi, L.; Graham, M. D., Active and hibernating turbulence in minimal channel flow of Newtonian and polymeric fluids, Phys. Rev. Lett., 104, (2010)
[32] Xi, L.; Graham, M. D., Turbulent drag reduction and multistage transitions in viscoelastic minimal flow units, J. Fluid Mech., 647, 421-452, (2010) · Zbl 1189.76326
[33] 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)
[34] Xi, L.; Graham, M. D., Intermittent dynamics of turbulence hibernation in Newtonian and viscoelastic minimal channel flows, J. Fluid Mech., 693, 433-472, (2012) · Zbl 1250.76127
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.