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Poiseuille and Couette flows in the transitional and fully turbulent regime

Published online by Cambridge University Press:  10 April 2015

Paolo Orlandi ,
Matteo Bernardini  and
Sergio Pirozzoli
Paolo Orlandi*
Affiliation:
Dipartimento di Ingegneria Meccanica e Aerospaziale, Università di Roma La Sapienza, Via Eudossiana 16, I-00184, Roma, Italy
Matteo Bernardini
Affiliation:
Dipartimento di Ingegneria Meccanica e Aerospaziale, Università di Roma La Sapienza, Via Eudossiana 16, I-00184, Roma, Italy
Sergio Pirozzoli
Affiliation:
Dipartimento di Ingegneria Meccanica e Aerospaziale, Università di Roma La Sapienza, Via Eudossiana 16, I-00184, Roma, Italy
*
†Email address for correspondence: orlandi@kolmogorov.ing.uniroma1.it
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Abstract

We present an extensive compilation of direct numerical simulation (DNS) data for Poiseuille and Couette flows, from the laminar into the fully turbulent regime, with the goal of highlighting similarities and differences. The data suggest that, for a given bulk velocity, Couette flow yields less resistance than Poiseuille flow and greater turbulence kinetic energy, which may be beneficial for more efficient diffusion, thus suggesting the effectiveness of fluid transport devices based on moving belts as opposed to classical ducts. Both flows exhibit similar trends for the wall-parallel velocity variances, which increase logarithmically with the Reynolds number. The shear stress and the wall-normal stress tend to saturate faster in Couette flow, which can thus be regarded as a limit to which Poiseuille flow tends, in the limit of high Reynolds number. Excess production over dissipation is found in the outer part of Poiseuille and Couette flow, which is responsible for non-local transfer of energy. However, the structure of the core flow seems to attain an asymptotic state which consists of a parabolic and linear mean velocity profile, respectively, and it seems unlikely that substantial changes to this scenario will occur at Reynolds numbers reachable by DNS in the foreseeable future.

JFM classification

Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulent Flows
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Papers
Information
Journal of Fluid Mechanics , Volume 770 , 10 May 2015 , pp. 424 - 441
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Copyright
© 2015 Cambridge University Press 

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References

Aydin, E. M. & Leutheusser, H. J. 1991 Plane-Couette flow between smooth and rough walls. Exp. Fluids 11, 302–312.CrossRefGoogle Scholar
Bernardini, M., Pirozzoli, S. & Orlandi, P. 2014 Velocity statistics in turbulent channel flow up to $Re_{{\it\tau}}=4000$ . J. Fluid Mech. 742, 171–191.CrossRefGoogle Scholar
Bernardini, M., Pirozzoli, S., Quadrio, M. & Orlandi, P. 2013 Turbulent channel flow simulations in convecting reference frames. J. Comput. Phys. 232, 1–6.Google Scholar
Boussinesq, J. 1877 Essai sur la théorie des eaux courantes. In Mémoires présentés par divers Savants à l’Acad. des Sci. (ed. Institut de France), vol. XXIII, pp. 1–680. Imprimerie Nationale.Google Scholar
El Telbany, M. M. M. & Reynolds, A. J. 1982 Velocity distributions in plane turbulent channel flows. Trans. ASME: J. Fluids Engng 104, 367–372.Google Scholar
Hamilton, J. M., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulent structures. J. Fluid Mech. 287, 317348.CrossRefGoogle Scholar
Hoyas, S. & Jiménez, J. 2006 Scaling of velocity fluctuations in turbulent channels up to $Re_{{\it\tau}}=2003$ . Phys. Fluids 18, 011702.Google Scholar
Hultmark, M., Vallikivi, M., Bailey, S. C. C. & Smits, A. J. 2012 Turbulent pipe flow at extreme Reynolds numbers. Phys. Rev. Lett. 108, 094501.CrossRefGoogle ScholarPubMed
Jiménez, J. 2013 Near-wall turbulence. Phys. Fluids 25, 101302.CrossRefGoogle Scholar
Jiménez, J. & Moin, P. 1991 The minimal flow unit in near wall turbulence. J. Fluid Mech. 225, 213–241.CrossRefGoogle Scholar
Kim, J., Moin, P. & Moser, R. D. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.CrossRefGoogle Scholar
Lee, M. & Moser, R. D.2014 Direct simulation of turbulent channel flow layer up to $Re_{{\it\tau}}=5200$ . arXiv:1410.7809v1 [physics.flu-dyn] 28 Oct 2014.Google Scholar
Lee, M. L., Kim, J. & Moin, P. 1990 Structure of turbulence at high shear rate. J. Fluid Mech. 216, 561–583.Google Scholar
Lozano-Duran, A. & Jiménez, J. 2014 Effect of the computational domain on direct simulations of turbulent channels up to $Re=4200$ . Phys. Fluids 26, 011702.Google Scholar
Marusic, I., Mathis, R. & Hutchins, N. 2010 High Reynolds number effects in wall turbulence. Intl J. Heat Fluid Flow 31, 418–428.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
McKeon, B. J., Swanson, C. J., Zagarola, M. V., Donnelly, R. J. & Smits, A. J. 2004 Friction factors for smooth pipe flow. J. Fluid Mech. 511, 41–44.Google Scholar
Orlandi, P. 2000 Fluid Flow Phenomena: A Numerical Toolkit. Kluwer.Google Scholar
Orlandi, P. 2011 DNS of transitional rough channels. J. Turbul. 12, 1–20.Google Scholar
Orlandi, P. 2013 The importance of wall-normal Reynolds stress in turbulent rough channel flows. Phys. Fluids 25 (11), 110813.Google Scholar
Orszag, S. A. & Patera, A. T. 1980 Subcritical transition to turbulence in plane channel flows. Phys. Rev. Lett. 45, 989–993.CrossRefGoogle Scholar
Pirozzoli, S. 2014 Revisiting the mixing-length hypothesis in the outer part of turbulent wall layers: mean flow and wall friction. J. Fluid Mech. 745, 378–397.CrossRefGoogle Scholar
Pirozzoli, S., Bernardini, M. & Orlandi, P. 2011 Large-scale organization and inner-outer layer interactions in turbulent Couette–Poiseuille flows. J. Fluid Mech. 680, 534–563.CrossRefGoogle 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
Reichardt, H. 1956 Über die Geschwindigkeitsverteilung in einer geradlinigen turbulenten Couetteströmung. Z. Angew. Math. Mech. 36, 26–29.Google Scholar
Robertson, J. M. 1959 On turbulent plane Couette flow. In Proceedings of the Sixth Midwestern Conference on Fluid Mechanics, pp. 169–182. University of Texas.Google Scholar
Schultz, M. P. & Flack, K. A. 2013 Reynolds-number scaling of turbulent channel flow. Phys. Fluids 25, 025104.Google Scholar
Smits, A. J. & Marusic, I. 2013 Wall-bounded turbulence. Phys. Today 66 (9), 25–30.Google Scholar
Spalart, P. R. & Allmaras, S. R. 1994 A one-equation turbulence model for aerodynamic flows. La Rech. Aerospatiale 1, 5–21.Google Scholar
Tillmark, N. & Alfredsson, P. H. 1992 Experiments on transition in plane Couette flow. J. Fluid Mech. 235, 89–102.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.Google Scholar
Wu, X. & Moin, P. 2008 A direct numerical simulation study on the mean velocity characteristics in turbulent pipe flow. J. Fluid Mech. 608, 81–112.Google Scholar