Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2025-01-05T15:05:09.608Z Has data issue: false hasContentIssue false
  • English
  • Français

Effects of polymer stresses on eddy structures in drag-reduced turbulent channel flow

Published online by Cambridge University Press:  25 July 2007

KYOUNGYOUN KIM ,
CHANG-F. LI ,
R. SURESHKUMAR ,
S. BALACHANDAR  and
RONALD J. ADRIAN
KYOUNGYOUN KIM
Affiliation:
Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287, USA
CHANG-F. LI
Affiliation:
Department of Energy, Environmental and Chemical Engineering, Washington University, Saint Louis, MO 63130, USA
R. SURESHKUMAR
Affiliation:
Department of Energy, Environmental and Chemical Engineering, Washington University, Saint Louis, MO 63130, USA
S. BALACHANDAR
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA
RONALD J. ADRIAN
Affiliation:
Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The effects of polymer stresses on near-wall turbulent structures are examined by using direct numerical simulation of fully developed turbulent channel flows with and without polymer stress. The Reynolds number based on friction velocity and half-channel height is 395, and the stresses created by adding polymer are modelled by a finite extensible nonlinear elastic, dumbbell model. Both low- (18%) and high-drag reduction (61%) cases are investigated. Linear stochastic estimation is employed to compute the conditional averages of the near-wall eddies. The conditionally averaged flow fields for Reynolds-stress-maximizing Q2 events show that the near-wall vortical structures are weakened and elongated in the streamwise direction by polymer stresses in a manner similar to that found by Stone et al. (2004) for low-Reynolds-number quasi-streamwise vortices (‘exact coherent states: ECS’). The conditionally averaged fields for the events with large contribution to the polymer work are also examined. The vortical structures in drag-reduced turbulence are very similar to those for the Q2 events, i.e. counter-rotating streamwise vortices near the wall and hairpin vortices above the buffer layer. The three-dimensional distributions of conditionally averaged polymer force around these vortical structures show that the polymer force components oppose the vortical motion. More fundamentally, the torques due to polymer stress are shown to oppose the rotation of the vortices, thereby accounting for their weakening. The observations also extend concepts of the vortex retardation by viscoelastic counter-torques to the heads of hairpins above the buffer layer, and offer an explanation of the mechanism of drag reduction in the outer region of wall turbulence, as well as in the buffer layer.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 584 , 10 August 2007 , pp. 281 - 299
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Adrian, R. J. 1996 Stochastic estimation of the structure of turbulent flows. In Eddy Structure Identification (ed. Bonnet, J. P.), pp. 145–196. Springer.CrossRefGoogle Scholar
Adrian, R. J., Jones, B. G., Chung, M. K., Hassan, Y., Nithianandan, C. K. & Tung, A. T.-C. 1989 Approximation of turbulent conditional averages by stochastic estimation. Phys. Fluids A 1, 992–998.CrossRefGoogle Scholar
Adrian, R. J., Meinhart, C. D. & Tomkins, C. D. 2000 Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 1–54.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Brooke, J. W. & Hanratty, T. J. 1993 Origin of turbulence-producing eddies in a channel flow. Phys. Fluids 5, 1011–1022.CrossRefGoogle Scholar
Chakraborty, P., Balachandar, S. & Adrian, R. J. 2005 On the relationships between local vortex identification schemes. J. Fluid Mech. 535, 189–214.CrossRefGoogle Scholar
Choi, H., Moin, P. & Kim, J. 1993 Direct numerical simulation of turbulent flow over riblets. J. Fluid Mech. 255, 503–539.CrossRefGoogle Scholar
Choi, H., Moin, P. & Kim, J. 1994 Active turbulence control for drag reduction in wall-bounded flows. J. Fluid Mech. 262, 75–110.CrossRefGoogle Scholar
DeAngelis, E. Angelis, E., Casciola, C. M., L'vov, V. S., Piva, R. & Procaccia, I. 2003 Drag reduction by polymers in turbulent channel flows: Energy redistribution between invariant empirical modes. Phys. Rev. E 67, 056312.Google Scholar
DeAngelis, E. Angelis, E., Casciola, C. M. & Piva, R. 2002 DNS of wall turbulence: Dilute polymers and self-sustaining mechanisms. Comput. Fluids 31, 495–507.Google Scholar
Dimitropoulos, C. D., Sureshkumar, R. & Beris, A. N. 1998 Direct numerical simulation of viscoelastic turbulent channel flow exhibiting drag reduction: Effect of the variation of rheological parameters. J. Non-Newtonian Fluid Mech. 79, 433–468.CrossRefGoogle Scholar
Dimitropoulos, C. D., Sureshkumar, R., Beris, A. N. & Handler, R. A. 2001 Budget of Reynolds stress, kinetic energy and streamwise enstrophy in viscoelastic turbulent channel flow. Phys. Fluids 13, 1016–1027.CrossRefGoogle 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, Turbulence and Combustion 74, 311–329.CrossRefGoogle 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 behavior of polymers in wall flows. J. Fluid Mech. 514, 271–280.CrossRefGoogle Scholar
Ganapathisubramani, B., Longmire, E. K. & Marusic, I. 2003 Characteristics of vortex packets in turbulent boundary layers. J. Fluid Mech. 478, 35–46.CrossRefGoogle Scholar
Gupta, V. K., Sureshkumar, R. & Khomami, B. 2005 Passive scalar transport in polymer drag-reduced turbulent channel flow. AIChE J. 51, 1938–1950.CrossRefGoogle Scholar
Housiadas, K. D., Beris, A. N. & Handler, R. A. 2005 Viscoelastic effects on higher order statistics and on coherent structures in turbulent channel flow. Phys. Fluids 17, 035106.CrossRefGoogle Scholar
Kendall, T. M. 1992 Dynamics of conditional vortices in turbulent channel flow: A direct numerical simulation. Master's thesis, University of Illinois, Urbana, Illinois.Google Scholar
Li, C.-F., Sureshkumar, R. & Khomami, B. 2006 a Influence of rheological parameters on polymer induced turbulent drag reduction. J. Non-Newtonian Fluid Mech. 140, 23–40.CrossRefGoogle Scholar
Li, W., Xi, L. & Graham, M. D. 2006 b Nonlinear travelling waves as a framework for understanding turbulent drag reduction. J. Fluid Mech. 565, 353–362.CrossRefGoogle Scholar
Lim, J., Choi, H. & Kim, J. 1998 Control of streamwise vortices with uniform magnetic fluxes. Phys. Fluids 10, 1997–2005.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.CrossRefGoogle ScholarPubMed
Min, T., Yoo, J. Y. & Choi, H. 2003 a Maximum drag reduction in a turbulent channel flow by polymer additives. J. Fluid Mech. 492, 91–100.CrossRefGoogle Scholar
Min, T., Yoo, J. Y., Choi, H. & Joseph, D. D. 2003 b Drag reduction by polymer additives in a turbulent channel flow. J. Fluid Mech. 486, 213–238.CrossRefGoogle Scholar
Moehlis, J., Faisst, H. & Eckhardt, B. 2004 A low-dimensional model for turbulent shear flows. New J. Phys. 6, 56.CrossRefGoogle Scholar
Moin, P., Adrian, R. J. & Kim, J. 1987 Stochastic estimation of organized structures in turbulent channel flow. In Proc. 6th Turbulent Shear Flow Symp., pp. 16.9.1–16.9.8.Google Scholar
Oldaker, D. K. & Tiederman, W. G. 1977 Spatial structure of the viscous sublayer in drag-reducing channel flows. Phys. Fluids 20, 133–144.CrossRefGoogle Scholar
Peterlin, A. 1961 Streaming birefringence of soft linear macromolecules with finite chain length. Polymer 2, 257–291.CrossRefGoogle Scholar
Ptasinski, P. K., Boersma, B. J., Nieuwstadt, F. T. M., Hulsen, M. A., Vanden Brule, B. H. A. A. 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.CrossRefGoogle Scholar
Ptasinski, P. K., Nieuwstadt, F. T. M., Van den Brule, B. H. A. A. & Hulsen, M. A. 2001 Experiments in turbulent pipe flow with polymer additives at maximum drag reduction. Flow, Turbulence and Combustion 66, 159–182.CrossRefGoogle Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601–639.CrossRefGoogle Scholar
Roy, A., Morozov, A., vanSaarloos, W. Saarloos, W. & Larson, R. G. 2006 Mechanism of polymer drag reduction using a low-dimensional model Phys. Rev. Lett. 97, 234501.CrossRefGoogle ScholarPubMed
Sreenivasan, K. R. & White, C. M. 2000 The onset of drag reduction by dilute polymer additives, and the maximum drag reduction asymptote. J. Fluid Mech. 409, 149–164.CrossRefGoogle 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: Non-linear coherent states in viscoelastic shear flows. Phys. Rev. Lett. 89, 208301.CrossRefGoogle 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.CrossRefGoogle Scholar
Terrapon, V. E., Dubief, Y., Moin, P., Shaqfeh, E. S. G. & Lele, S. K. 2004 Simulated polymer stretch in a turbulent flow using Brownian dynamics. J. Fluid Mech. 504, 61–71.CrossRefGoogle Scholar
Virk, P. S. 1971 An elastic sublayer model for drag reduction by dilute solutions of linear macromolecules. J. Fluid Mech. 45, 417–440.CrossRefGoogle Scholar
Virk, P. S., Merrill, E. W., Mickley, H. S., Smith, K. A. & Mollo-Christensen, E. L. 1967 The Toms phenomenon: Turbulent pipe flow of dilute polymer solutions. J. Fluid Mech. 30, 305–328.CrossRefGoogle Scholar
Waleffe, F. 1997 On a self-sustaining process in shear flows. Phys. Fluids 9, 883–900.CrossRefGoogle Scholar
Warholic, M. D., Heist, D. K., , M. K. & Hanratty, T. J. 2001 A study with particle-image velocimetry of the influence of drag-reducing polymers on the structure of turbulence. Exps Fluids 31, 474–483.CrossRefGoogle Scholar
Warholic, M. D., Massah, H. & Hanratty, T. J. 1999 Influence of drag-reducing polymers on turbulence: Effects of Reynolds number, concentration and mixing. Exps Fluids 27, 461–472.CrossRefGoogle Scholar
Wei, T. & Willmarth, W. W. 1992 Modifying turbulent structure with drag-reducing polymer additives in turbulent channel flows. J. Fluid Mech. 245, 619–641.CrossRefGoogle Scholar
White, C. M., Somandepalli, V. S. R. & Mungal, M. G. 2004 The turbulence structure of drag reduced boundary layer flow. Exps Fluids 36, 62–69.CrossRefGoogle Scholar
Willmarth, W. W., Wel, T. & Lee, C. O. 1987 Laser anemometer measurements of Reynolds stress in a turbulent channel flow with drag reducing polymer additives. Phys. Fluids 30, 933–935.CrossRefGoogle Scholar
Zhou, J., Adrian, R. J., Balachandar, S. & Kendall, T. M. 1999 Mechanisms for generating coherent packets of hairpin vortices. J. Fluid Mech. 387, 353–396.CrossRefGoogle Scholar