Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-23T13:33:00.476Z Has data issue: false hasContentIssue false
  • English
  • Français

DNS study of decaying homogeneous isotropic turbulence with polymer additives

Published online by Cambridge University Press:  19 October 2010

W.-H. CAI ,
F.-C. LI  and
H.-N. ZHANG
W.-H. CAI
Affiliation:
School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, China
F.-C. LI*
Affiliation:
School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, China
H.-N. ZHANG
Affiliation:
School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, China
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In order to investigate the turbulent drag reduction phenomenon and understand its mechanism, direct numerical simulation (DNS) was carried out on decaying homogeneous isotropic turbulence (DHIT) with and without polymer additives. We explored the polymer effect on DHIT from the energetic viewpoint, i.e. the decay of the total turbulent kinetic energy and energy distribution at each scale in Fourier space and from the phenomenological viewpoint, i.e. the alterations of vortex structures, the enstrophy and the strain. It was obtained that in DHIT with polymer additives the decay of the turbulent kinetic energy is faster than that in the Newtonian fluid case and a modification of the turbulent kinetic energy transfer process for the Newtonian fluid flow is observed due to the release of the polymer elastic energy into flow structures at certain small scales. Besides, we deduced the transport equations of the enstrophy and the strain, respectively, for DHIT with polymer additives. Based on the analyses of these transport equations, it was found that polymer additives depress both the enstrophy and the strain in DHIT as compared to the Newtonian fluid case, indicating the inhibition effect on small-scale vortex structures and turbulence intensity by polymers.

JFM classification

Flow Control: Drag reduction Turbulent Flows: Isotropic turbulence Non-Newtonian Flows: Viscoelasticity
Type
Papers
Information
Journal of Fluid Mechanics , Volume 665 , 25 December 2010 , pp. 334 - 356
Copyright
Copyright © Cambridge University Press 2010

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

Barnard, B. J. S. & Sellin, R. H. J. 1969 Grid turbulence in dilute polymer solutions. Nature Lond. 222, 1160–1162.CrossRefGoogle Scholar
Beris, A. N. & Dimitropoulos, C. D. 1999 Pesudospectral simulation of turbulent viscoelastic channel flow. Comput. Meth. Appl. Mech. Engng 180, 365–392.Google Scholar
Berti, S., Bistagnino, A., Boffetta, G., Celani, A. & Musacchio, S. 2006 Small-scale statistics of viscoelastic turbulence. Europhys. Lett. 76, 63–69.CrossRefGoogle Scholar
Bonn, D., Amarouchéne, Y., Wagner, C., Douady, S. & Cadot, O. 2005 Turbulent drag reduction by polymers. J. Phys.: Condens. Matter 17, S1195–S1202.Google Scholar
Cadot, O., Bonn, D. & Douady, S. 1998 Turbulent drag reduction in a closed flow system: boundary layer versus bulk effects. Phys. Fluids 10, 426–436.Google Scholar
Cai, W.-H., Li, F.-C., Zhang, H.-N., Li, X.-B., Yu, B., Wei, J.-J., Kawaguchi, Y. & Hishida, K. 2009 Study on the characteristics of turbulent drag-reducing channel flow by particle image velocimetry combining with proper orthogonal decomposition analysis. Phys. Fluids 21, 115103.CrossRefGoogle Scholar
Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, T. A. 1988 Spectral Methods in Fluid Dynamics. Springer.Google Scholar
Crawford, A., Mordant, N., Xu, H.-T. & Bodenschatz, E. 2008 Fluid acceleration in the bulk of turbulent dilute polymer solutions. New J. Phys. 10, 123015.Google Scholar
De Angelis, E., Casciola, C. M., Benzi, R. & Piva, R. 2002 b Homogeneous isotropic turbulence in dilute polymers: scale by scale budget. Chao. Dyn. (nlin-CD) 0208016.Google Scholar
De Angelis, E., Casciola, C. M., Benzi, R. & Piva, R. 2005 Homogeneous isotropic turbulence in dilute polymers. J. Fluid Mech. 531, 1–10.CrossRefGoogle Scholar
De Angelis, E., Casciola, C. M. & Piva, R. 2002 a DNS of wall turbulence: dilute polymers and self-sustaining mechanisms. Comput. Fluids 31, 495–507.CrossRefGoogle Scholar
Den Toonder, J. M. J., Hulsen, M. A., Kuiken, G. D. C. & Nieuwstadt, F. T. M. 1997 Drag reduction by polymer additives in a turbulent pipe flow: numerical and laboratory experiments. J. Fluid Mech. 337, 193–231.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.Google Scholar
van Doorn, E., White, C. M. & Sreenivasan, K. R. 1999 The decay of grid turbulence in polymer and surfactant solutions. Phys. Fluids 8, 2387–2393.CrossRefGoogle Scholar
Douady, S., Couder, Y. & Brachet, C. M. 1991 Direct observation of the intermittency of intense vorticity filaments in turbulence. Phys. Rev. Lett. 67, 983–986.Google Scholar
Drappier, J., Divoux, T., Amarouchéne, Y., Bertrand, F., Rodts, S., Cadot, O., Meunier, J. & Bonn, D. 2006 Turbulent drag reduction by surfactants. Europhys. Lett. 74, 362–368.Google Scholar
Dupret, F. & Marchal, J. M. 1986 Loss of evolution in the flow of viscoelastic fluids. J. Non-Newtonian Fluid Mech. 20, 143–171.Google Scholar
Fabula, A. G. 1966 An experimental study of grid turbulence in dilute high-polymer solutions. PhD thesis, The Pennsylvania State University.Google Scholar
Friehe, C. A. & Schwarz, W. H. 1970 Grid-generated turbulence in dilute polymer solutions. J. Fluid Mech. 44, 173–193.Google Scholar
De Gennes, P. G. 1986 Towards a cascade theory of drag reduction. Physica A 140, 9–25.CrossRefGoogle Scholar
Jeong, J. & Hussain, F. 1995 On the definition of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
Jiménez, J. & Wray, A. A. 1998 On the characteristics of vortex filaments in isotropic turbulence. J. Fluid Mech. 373, 255–285.Google Scholar
Jin, S. 2007 Numerical simulations of a dilute polymer solution in isotropic turbulence. PhD thesis, Cornell University.Google Scholar
Kalelkar, C., Govindarajan, R. & Pandit, R. 2005 Drag reduction by polymer additives in decaying turbulence. Phys. Rev. E 72, 017301.CrossRefGoogle ScholarPubMed
Kolmogorov, A. N. 1991 The local structure of turbulence in incompressible viscous fluid for very large Reynolds number. Dokl. Akad. Nauk SSSR 1941, 30, 9–13 (reprinted in Proc. R. Soc. Lond. A 434, 9–13).Google Scholar
Kraichnan, R. H. 1964 Decay of isotropic turbulence in the direct-interaction approximation. Phys. Fluids 7, 1030–1048.CrossRefGoogle Scholar
Li, F.-C., Kawaguchi, Y. & Hishida, K. 2004 Investigation on the characteristics of turbulence transport for momentum and heat in a drag-reducing surfactant solution flow. Phys. Fluids 16, 3281–3295.CrossRefGoogle Scholar
Li, F.-C., Kawaguchi, Y., Hishida, K. & Oshima, M. 2006 Investigation of turbulence structures in a drag-reduced turbulent channel flow with surfactant additive using stereoscopic particle image velocimetry. Exp. Fluids 40, 218–230.CrossRefGoogle Scholar
Li, F.-C., Kawaguchi, Y., Segawa, T. & Hishida, K. 2005 Reynolds-number dependence of turbulence structures in a drag-reducing surfactant solution channel flow investigated by PIV. Phys. Fluids 17, 075104.CrossRefGoogle Scholar
Liberatore, M. W., Baik, S., McHugh, A. J. & Hanratty, T. J. 2004 Turbulent drag reduction of polyacrylamide solutions: effect of degradation on molecular weight distribution. J. Non-Newtonian Fluid Mech. 123, 175–183.Google Scholar
Liberzon, A., Guala, M., Kinzelbach, W. & Tsinober, A. 2006 On turbulent kinetic energy production and dissipation in dilute polymer solutions. Phys. Fluids 18, 125101.Google Scholar
Liberzon, A., Guala, M., Lüthi, B., Kinzelbach, W. & Tsinober, A. 2005 Turbulence in dilute polymer solutions. Phys. Fluids 17, 031707.Google Scholar
Lumley, J. L. 1973 Drag reduction in turbulent flow by polymer additives. J. Polym. Sci. Macromol. Rev. 7, 263–290.Google Scholar
Mansour, N. N. & Wray, A. A. 1994 Decay of isotropic turbulence at low Reynolds number. Phys. Fluids 6, 808–813.CrossRefGoogle Scholar
McComb, W. D., Allan, J. & Greated, C. A. 1977 Effect of polymer additives on the small-scale structure of grid-generated turbulence. Phys. Fluids 20, 873–879.CrossRefGoogle Scholar
Meng, Q.-G. 2004 On the evolution of decaying isotropic turbulence. Acta Mechanica Sin. 20, 113–116.Google Scholar
Min, T., Yoo, J. Y. & Choi, H. 2001 Effect of spatial discretization schemes on numerical solution schemes on numerical solutions of viscoelastic fluid flow. J. Non-Newtonian Fluid Mech. 100, 24–47.Google Scholar
Ouellette, N. T., Xu, H.-T. & Bodenschatz, E. 2009 Bulk turbulence in dilute polymer solutions. J. Fluid Mech. 629, 375–385.Google Scholar
Perlekar, P., Mitra, D. & Pandit, R. 2006 Manifestations of drag reduction by polymer additives in decaying, homogenous, isotropic turbulence. Phys. Rev. Lett. 97 (264501), 1–4.Google Scholar
Perry, A. E. & Chong, M. S. 1987 A description of eddying motions and flow patterns using critical-point concepts. Annu. Rev. Fluid Mech. 19, 125–155.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
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 Turbul. Combust. 66, 159–182.CrossRefGoogle Scholar
Rogallo, R. S. 1981 Numerical experiments in homogeneous isotropic turbulence. Tech Rep. 81315. NASA.Google Scholar
Siggia, E. D. 1986 Numerical study of small-scale intermittency in three-dimensional turbulence. J. Fluid Mech. 107, 375–406.CrossRefGoogle Scholar
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
Sureshkumar, R. & Beris, A. N. 1995 Effect of artificial stress diffusivity on the stability of numerical calculations and the flow dynamics of time-dependent viscoelastic flows. J. Non-Newtonian Fluid Mech. 60, 53–80.Google Scholar
Sureshkumar, R., Beris, A. N. & Handler, A. H. 1997 Direct numerical simulation of turbulent channel flow of a polymer solution. Phys. Fluids 9, 743–755.CrossRefGoogle Scholar
Tabor, M. & De Gennes, P. G. 1986 A cascade theory of drag reduction. Europhys. Lett. 2, 519–522.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.Google Scholar
Toms, B. A. 1949 Some observation on the flow of linear polymer solutions through straight tubes at large Reynolds number. In Proceedings of First International Congress on Rheology, vol. 2, pp. 135–141. North-Holland.Google Scholar
Tsinober, A. 2000 Vortex stretching versus production of strain/dissipation. In Turbulence Structure and Vortex Dynamics (ed. Hunt, J. C. R. & Vassilicos, J. C.), pp. 164–191. Cambridge University Press.Google Scholar
Vaithianathan, T. & Collins, L. R. 2003 Numerical approach to simulating turbulent flow of a viscoelastic polymer solution. J. Comput. Phys. 187, 1–23.Google Scholar
Vaithianathan, T., Robert, A., Brasseur, J. G. & Collins, L. R. 2006 An improved algorithm for simulating three-dimensional, viscoelastic turbulence. J. Non-Newtonian Fluid Mech. 140, 3–22.Google Scholar
Walker, D. T. & Tiederman, W. G. 1990 Turbulent structure in a channel flow with polymer injection at the wall. J. Fluid Mech. 218, 377–403.CrossRefGoogle Scholar
Warholic, M. D., Heist, D. K., Katcher, M. & Hanratty, T. J. 2001 A study with particle image velocimetry of the influence of drag-reducing polymers on the structure of turbulence. Exp. Fluids 31, 474–483.Google Scholar
Yu, B. & Kawaguchi, Y. 2004 Direct numerical simulation of viscoelastic drag-reducing flow: a faithful finite difference method. J. Non-Newtonian Fluid Mech. 116, 431–466.Google Scholar
Zhong, J., Huang, T. S. & Adrian, R. J. 1998 Extracting 3D vortices in turbulent fluid flow. IEEE Trans. Pattern Anal. Mach. Intell. 20, 193–199.Google Scholar
Zhou, J., Adrian, R. J., Balachandar, S. & Kendall, T. M. 1999 Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353–396.Google Scholar