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Turbulent drag reduction in plane Couette flow with polymer additives: a direct numerical simulation study

Published online by Cambridge University Press:  08 May 2018

Hao Teng ,
Nansheng Liu Open the ORCID record for Nansheng Liu [Opens in a new window] ,
Xiyun Lu Open the ORCID record for Xiyun Lu [Opens in a new window]  and
Bamin Khomami
Hao Teng
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
Nansheng Liu*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
Xiyun Lu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
Bamin Khomami*
Affiliation:
Department of Chemical and Biomolecular Engineering, University of Tennessee, Knoxville, TN 37996, USA
*
†Email addresses for correspondence: lns@ustc.edu.cn, bkhomami@utk.edu
†Email addresses for correspondence: lns@ustc.edu.cn, bkhomami@utk.edu
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Abstract

Drag reduction (DR) in plane Couette flow (PCF) induced by the addition of flexible polymers has been studied via direct numerical simulation (DNS). The similarities and differences in the drag reduction features of PCF and plane Poiseuille flow (PPF) have been examined in detail, particularly in regard to the polymer-induced modification of large-scale structures (LSSs) in the near-wall turbulence. Specifically, it has been demonstrated that in the near-wall region, drag-reduced PCF has features similar to those of drag-reduced PPF; however, in the core region, intriguing differences are found between these two drag-reduced shear flows. Chief among these differences is the significant polymer stretch that arises from the enhanced exchanges between elastic potential energy and turbulent kinetic energy and the commensurate observation of peak values of the conformation tensor components $\unicode[STIX]{x1D60A}_{yy}$ and $\unicode[STIX]{x1D60A}_{zz}$ in this region. This finding is in stark contrast to that of drag-reduced PPF where the polymer stretch and the exchanges between elastic potential energy and turbulent kinetic energy in the core region are insignificant; to this end, in drag-reduced PPF, peak values of the conformation tensor components appear in the near-wall region. Therefore, this study paves the way for understanding the underlying flow physics in drag-reduced PCF, particularly in the context of elastic theory. Moreover, the longitudinal large-scale streaks at the channel centre of drag-reduced PCF are greatly strengthened due to the increased production/dissipation ratio; the LSS imprint effects on the near-wall flow of drag-reduced PCF monotonically increase as the Weissenberg number is enhanced.

JFM classification

Flow Control: Drag reduction Non-Newtonian Flows: Polymers Turbulent Flows: Turbulent Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 846 , 10 July 2018 , pp. 482 - 507
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Copyright
© 2018 Cambridge University Press 

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References

Avsarkisov, V., Hoyas, S., Oberlack, M. & García-Galache, J. P. 2014 Turbulent plane Couette flow at moderately high Reynolds number. J. Fluid Mech. 751, R1.Google Scholar
Balakumar, B. J. & Adrian, R. J. 2007 Large- and very-large-scale motions in channel and boundary-layer flows. Phil. Trans. R. Soc. Lond. A 365, 665–681.Google ScholarPubMed
Bech, K. H., Tillmark, N., Alfredsson, P. H. & Andersson, H. I. 1995 An investigation of turbulent plane Couette flow at low Reynolds numbers. J. Fluid Mech. 286, 291–325.Google Scholar
Benzi, R., Ching, E. S. C., Horesh, N. & Procaccia, I. 2004 Theory of concentration dependence in drag reduction by polymers and of the maximum drag reduction asymptote. Phys. Rev. Lett. 92, 078302.Google Scholar
Benzi, R., De Angelis, E., Lvov, V. S. & Procaccia, I. 2005 Identification and calculation of the universal asymptote for drag reduction by polymers in wall bounded turbulence. Phys. Rev. Lett. 95, 194502.CrossRefGoogle ScholarPubMed
Benzi, R., De Angelis, E., L’vov, V. S., Procaccia, I. & Tiberkevich, V. 2006 Maximum drag reduction asymptotes and the cross-over to the Newtonian plug. J. Fluid Mech. 551, 185–195.Google Scholar
Bernardini, M., Pirozzoli, S. & Orlandi, P. 2013 The effect of large-scale turbulent structures on particle dispersion in wall-bounded flows. Intl J. Multiphase Flow 51, 55–64.CrossRefGoogle Scholar
Biancofiore, L., Brandt, L. & Zaki, T. A. 2017 Streak instability in viscoelastic Couette flow. Phys. Rev. Fluids 2, 043304.CrossRefGoogle Scholar
Dallas, V., Vassilicos, J. C. & Hewitt, G. F. 2010 Strong polymer-turbulence interactions in viscoelastic turbulent channel flow. Phys. Rev. E 82, 066303.Google ScholarPubMed
Debusschere, B. & Rutland, C. J. 2004 Turbulent scalar transport mechanisms in plane channel and Couette flows. Intl J. Heat Mass Transfer 47, 1171–1781.CrossRefGoogle Scholar
Dimitropoulos, C. D., Sureshkumar, R., Beris, A. N. & Handler, R. A. 2001 Budgets of Reynolds stress, kinetic energy and streamwise enstrophy in viscoelastic turbulent channel flow. Phys. Fluids 13, 1016–1027.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.Google Scholar
Graham, M. D. 2014 Drag reduction and the dynamics of turbulence in simple and complex fluids. Phys. Fluids 26, 101301.Google Scholar
Guala, M., Hommema, S. E. & Adrian, R. J. 2006 Large-scale and very-large-scale motions in turbulent pipe flow. J. Fluid Mech. 554, 521–542.Google Scholar
Hamilton, J. M., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 314–348.CrossRefGoogle Scholar
Hellström, L. H. O., Marusic, I. & Smits, A. J. 2016 Self-similarity of the large-scale motions in turbulent pipe flow. J. Fluid Mech. 792, R1.CrossRefGoogle Scholar
Hosseiniebalam, F., Hassanzadeh, S. & Ghaffarpasand, O. 2014 Dispersion and deposition mechanisms of particles suspended in a turbulent plane Couette flow. Appl. Math. Model. 37, 2417–2429.Google Scholar
Hu, Z., Morfey, C. L. & Sandham, N. D. 2003 Sound radiation in turbulent channel flows. J. Fluid Mech. 475, 269–302.Google Scholar
Hwang, J., Lee, J., Sung, H. J. & Zaki, T. A. 2016 Inner-outer interactions of large-scale structures in turbulent channel flow. J. Fluid Mech. 790, 128–157.CrossRefGoogle Scholar
Hwang, Y. & Cossu, C. 2010 Self-sustained process at large scales in turbulent channel flow. Phys. Rev. Lett. 105, 044505.Google Scholar
Jiménez, J. & Hoyas, S. 2008 Turbulent fluctuations above the buffer layer of wall-bounded flows. J. Fluid Mech. 611, 215–236.Google Scholar
Jiménez, J. & Moin, P. 1991 The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213–240.Google Scholar
Jovanović, M. R. & Kumar, S. 2010 Transient growth without inertia. Phys. Fluids 22, 023101.CrossRefGoogle Scholar
Kawata, T. & Alfredsson, P. H. 2016 Experiments in rotating plane Couette flow – momentum transport by coherent roll-cell structure and zero-absolute-vorticity state. J. Fluid Mech. 791, 191–213.CrossRefGoogle Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.CrossRefGoogle Scholar
Kim, K. C. & Adrian, R. J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11, 417–422.Google Scholar
Kitoh, O., Nakabyashi, K. & Nishimura, F. 2005 Experimental study on mean velocity and turbulence characteristics of plane Couette flow: low-Reynolds-number effects and large longitudinal vortical structure. J. Fluid Mech. 539, 199–227.Google Scholar
Kitoh, O. & Umeki, M. 2008 Experimental study on large-scale streak structure in the core region of turbulent plane Couette flow. Phys. Fluids 20, 025107.Google Scholar
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741–773.CrossRefGoogle Scholar
Komminaho, J., Lundbladh, A. & Johansson, A. V. 1996 Very large structures in plane turbulent Couette flow. J. Fluid Mech. 320, 259–285.CrossRefGoogle Scholar
Lam, K. & Banerjee, S. 1992 On the condition of streak formation in a bounded turbulent flow. Phys. Fluids A 4, 306.CrossRefGoogle Scholar
Li, C.-F., Sureshkumar, R. & Khomami, B. 2015 Simple framework for understanding the universality of the maximum drag reduction asymptote in turbulent flow of polymer solutions. Phys. Rev. E 92, 043014.Google Scholar
Li, C.-F., Sureshkumar, R. & Khomami, B. 2006 Influence of rheological parameters on polymer induced turbulent drag reduction. J. Non-Newtonian Fluid Mech. 140, 23–40.Google Scholar
Liu, C.-H. 2003 Turbulent plane Couette flow and scalar transport at low Reynolds number. Trans. ASME J. Heat Transfer 125, 988–998.Google Scholar
Liu, N. & Khomami, B. 2013a Elastically induced turbulence in Taylor–Couette flow: direct numerical simulation and mechanistic insight. J. Fluid Mech. 737, R4.Google Scholar
Liu, N. & Khomami, B. 2013b Polymer-induced drag enhancement in turbulent Taylor–Couette flows: direct numerical simulations and mechanistic insight. Phys. Rev. Lett. 111, 114501.Google Scholar
Lumley, J. L. 1969 Drag reduction by additives. Annu. Rev. Fluid Mech. 1, 367–384.CrossRefGoogle Scholar
L’vov, V. S., Pomyalov, A., Procaccia, I. & Tiberkevich, V. 2004 Drag reduction by polymers in wall bounded turbulence. Phys. Rev. Lett. 92, 244503.Google Scholar
Marusic, I., Mathis, R. & Hutchins, N. 2010 Predictive model for wall-bounded turbulent flow. Science 329, 193–196.Google Scholar
Mathis, R., Hutchins, N. & Marusic, I. 2009 Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J. Fluid Mech. 628, 311–337.Google Scholar
Mathis, R., Marusic, I., Hutchins, N. & Sreenivasan, K. R. 2011 The relationship between the velocity skewness and the amplitude modulation of the small scale by the large scale in turbulent boundary layers. Phys. Fluids 23, 121702.Google Scholar
Min, T., Choi, H. & Yoo, J. Y. 2003a Maximum drag reduction in a turbulent channel flow by polymer additives. J. Fluid Mech. 492, 91–100.Google 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.Google Scholar
Monty, J. P., Hutchins, N., Ng, H. C. H., Marusic, I. & Chong, M. S. 2009 A comparison of turbulent pipe, channel and boundary layer flows. J. Fluid Mech. 632, 431–442.Google Scholar
Nguyen, M. Q., Delache, A., Simoens, S., Bos, W. J. T. & Hajem, M. E. 2016 Small scale dynamics of isotropic viscoelastic turbulence. Phys. Rev. Fluids 1, 083301.Google Scholar
Niebling, M. J., Tallakstad, K. T., Toussaint, R. & Måløy, K. J. 2014 Direct velocity measurement of a turbulent shear flow in a planar Couette cell. Phys. Rev. E 89, 013026.Google Scholar
Orlandi, P., Bernardini, M. & Pirozzoli, S. 2015 Poiseuille and Couette flows in the transitional and fully turbulent regime. J. Fluid Mech. 770, 424–441.Google Scholar
Page, J. & Zaki, T. A. 2014 Streak evolution in viscoelastic couette flow. J. Fluid Mech. 742, 520–551.Google Scholar
Page, J. & Zaki, T. A. 2015 The dynamics of spanwise vorticity perturbations in homogeneous viscoelastic shear flow. J. Fluid Mech. 777, 327–363.Google Scholar
Pasinato, H. D. 2011 Velocity and temperature dissimilarity in fully developed turbulent channel and plane Couette flows. Intl J. Heat Fluid Flow 32, 11–25.Google 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.Google 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.Google Scholar
Pereira, A. S., Mompean, G., Thompson, R. L. & Soares, E. J. 2017c Elliptical, parabolic, and hyperbolic exchanges of energy in drag reducing plane Couette flows. Phys. Fluids 29, 115106.CrossRefGoogle Scholar
Pizorroli, S., Bernardini, M. & Orlandi, P. 2011 Large-scale motions and inner/outer layer interactions in turbulent Couette-Poiseuille flows. J. Fluid Mech. 680, 534–563.Google Scholar
Pirozzoli, S., Bernardini, M. & Orlandi, P. 2014 Turbulence statistics in Couette flow at high Reynolds number. J. Fluid Mech. 758, 327–343.Google Scholar
Procaccia, I., L’vov, V. S. & Benzi, R. 2008 Colloquium: theory of drag reduction by polymers in wall-bounded turbulence. Rev. Mod. Phys. 80, 225–247.Google Scholar
Ptasinski, P. K., Boersma, B. J., Nieuwstadt, F. T. M., Hulsen, M. A., van den Brule, B. H. A. A. & Hunt, J. C. R. 2003 Turbulent channel flow near maximum drag reduction: simulations, experiments and mechanisms. J. Fluid Mech. 490, 251–291.Google Scholar
Rawat, S., Cossu, C., Hwang, Y. & Rincon, F. 2015 On the self-sustained nature of large-scale motions in turbulent Couette flow. J. Fluid Mech. 782, 515–540.CrossRefGoogle Scholar
Samanta, G., Housiadas, K. D., Handler, R. A. & Beris, A. N. 2009 Effects of viscoelasticity on the probability density functions in turbulent channel flow. Phys. Fluids 21, 115106.Google Scholar
Smits, A. J. 2015 Canonical wall-bounded flows: how do they differ? J. Fluid Mech. 774, 1–4.Google Scholar
Stone, P. A., Roy, A., Larson, R. G., Waleffe, F. & Graham, M. D. 2004 Polymer drag reduction in exact coherent structures of plane shear flow. Phys. Fluids 16, 3470–3482.CrossRefGoogle Scholar
Stone, P. A., Waleffe, F. & Graham, M. D. 2002 Toward a structural understanding of turbulent drag reduction: nonlinear coherent states in viscoelastic shear flows. Phys. Rev. Lett. 89, 208301.Google 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.Google Scholar
Tabor, M. & de Gennes, P. G. 1986 A cascade theory of drag reduction. Europhys. Lett. 2, 519–522.Google Scholar
Teng, H., Liu, N., Lu, X. & Khomami, B. 2015 Direct numerical simulation of Taylor–Couette flow subjected to a radial temperature gradient. Phys. Fluids 27, 125101.Google Scholar
Thais, L., Gatskid, T. B. & Mompeana, 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., Gatskid, T. B. & Mompeana, G. 2013 Analysis of polymer drag reduction mechanisms from energy budgets. Intl J. Heat Fluid Flow 43, 52–61.CrossRefGoogle Scholar
Tiederman, W. G. 1990 The effect of dilute polymer solutions on viscous drag and turbulence structure. In Structure of Turbulence and Drag Reduction, pp. 187–200. Springer.Google Scholar
Toms, B. A. 1949 Some observations on the flow of linear polymer solutions through straight tubes at large Reynolds numbers. In Proceedings of the 1st International Congress of Rheology, Vol. 2 (ed. Burgers, J. M.), vol. 2, pp. 135–141. North Holland.Google Scholar
Tsukahara, T., Ishigamia, T., Yub, B. & Kawaguchia, Y. 2011 DNS study on viscoelastic effect in drag-reduced turbulent channel flow. J. Turbul. 12, 1–25.Google Scholar
Tsukahara, T., Kawamura, H. & Shingai, K. 2006 DNS of turbulent Couette flow with emphasis on the large-scale structure in the core region. J. Turbul. 7, 19.Google Scholar
Virk, P. S. 1975 Drag reduction fundamentals. AIChE J. 21, 625–656.Google Scholar
Waleffe, F. 1997 On a self-sustaining process in shear flows. Phys. Fluids 9, 883–900.Google Scholar
White, C. M. & Mungal, M. G. 2008 Mechanics and prediction of turbulent drag reduction with polymer additives. Annu. Rev. Fluid Mech. 40, 235–256.Google Scholar
Wu, X., Baltzer, J. R. & Adrian, R. J. 2012 Direct numerical simulation of a 30R long turbulent pipe flow at R + = 685: large- and very large-scale motions. J. Fluid Mech. 698, 235–281.Google Scholar
Xi, L. & Graham, M. D. 2012 Intermittent dynamics of turbulence hibernation in Newtonian and viscoelastic minimal channel flows. J. Fluid Mech. 693, 433–472.Google Scholar