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Passive scalars in turbulent channel flow at high Reynolds number

Published online by Cambridge University Press:  12 January 2016

Sergio Pirozzoli ,
Matteo Bernardini  and
Paolo Orlandi
Sergio Pirozzoli*
Affiliation:
Dipartimento di Ingegneria Meccanica e Aerospaziale, Università di Roma ‘La Sapienza’, Via Eudossiana 18, 00184 Roma, Italy
Matteo Bernardini
Affiliation:
Dipartimento di Ingegneria Meccanica e Aerospaziale, Università di Roma ‘La Sapienza’, Via Eudossiana 18, 00184 Roma, Italy
Paolo Orlandi
Affiliation:
Dipartimento di Ingegneria Meccanica e Aerospaziale, Università di Roma ‘La Sapienza’, Via Eudossiana 18, 00184 Roma, Italy
*
†Email address for correspondence: [email protected]
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Abstract

We study passive scalars in turbulent plane channels at computationally high Reynolds number, thus allowing us to observe previously unnoticed effects. The mean scalar profiles are found to obey a generalized logarithmic law which includes a linear correction term in the whole lower half-channel, and they follow a universal parabolic defect profile in the core region. This is consistent with recent findings regarding the mean velocity profiles in channel flow. The scalar variances also exhibit a near universal parabolic distribution in the core flow and hints of a sizeable log layer, unlike the velocity variances. The energy spectra highlight the formation of large scalar-bearing eddies with size proportional to the channel height which are caused by a local production excess over dissipation, and which are clearly visible in the flow visualizations. Close correspondence of the momentum and scalar eddies is observed, with the main difference being that the latter tend to form sharper gradients, which translates into higher scalar dissipation. Another notable Reynolds number effect is the decreased correlation of the passive scalar field with the vertical velocity field, which is traced to the reduced effectiveness of ejection events.

JFM classification

Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulent convection
Type
Papers
Information
Journal of Fluid Mechanics , Volume 788 , 10 February 2016 , pp. 614 - 639
Copyright
© 2016 Cambridge University Press 

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References

Abe, H. & Antonia, R. A. 2009 Near-wall similarity between velocity and scalar fluctuations in a turbulent channel flow. Phys. Fluids 21, 025109.Google Scholar
Abe, H., Kawamura, H. & Choi, H. 2004a Very large-scale structures and their effects on the wall shear-stress fluctuations in a turbulent channel flow up to $Re_{{\it\tau}}=640$ . J. Fluids Engng 126, 835–843.CrossRefGoogle Scholar
Abe, H., Kawamura, H. & Matsuo, Y. 2004b Surface heat-flux fluctuations in a turbulent channel flow up to $Re_{{\it\tau}}=1020$ with $Pr=0.025$ and 0.71. Intl J. Heat Fluid Flow 25, 404–419.CrossRefGoogle Scholar
Afzal, N. & Yajnik, K. 1973 Analysis of turbulent pipe and channel flows at moderately large Reynolds number. J. Fluid Mech. 61, 23–31.CrossRefGoogle Scholar
del Álamo, J. C. & Jiménez, J. 2003 Spectra of the very large anisotropic scales in turbulent channels. Phys. Fluids 15, L41–L44.Google Scholar
del Álamo, J. C., Jiménez, J., Zandonade, P. & Moser, R. D. 2004 Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135–144.Google Scholar
Antonia, R. A., Abe, H. & Kawamura, H. 2009 Analogy between velocity and scalar fields in a turbulent channel flow. J. Fluid Mech. 628, 241–268.CrossRefGoogle Scholar
Batchelor, G. K. 1959 Small-scale variation of convected quantities like temperature in turbulent fluid. Part 1. General discussion and the case of small conductivity. J. Fluid Mech. 5, 113–133.Google 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.Google 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
Cebeci, T. 1973 A model for eddy conductivity and turbulent Prandtl number. J. Heat Transfer 95, 227–234.CrossRefGoogle Scholar
Cebeci, T. & Bradshaw, P. 1984 Physical and Computational Aspects of Convective Heat Transfer. Springer.Google Scholar
DeGraaff, D. B. & Eaton, J. K. 2000 Reynolds-number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422, 319–346.Google Scholar
Durbin, P. A. 1991 Near-wall turbulence closure modeling without damping functions. Theoret. Comput. Fluid Dyn. 3, 1–13.CrossRefGoogle Scholar
Gnielinski, V. 1976 New equations for heat and mass transfer in turbulent pipe and channel flow. Intl Chem. Eng. 16, 359–367.Google Scholar
Gowen, R. A. & Smith, J. W. 1967 The effect of the Prandtl number on temperature profiles for heat transfer in turbulent pipe flow. Chem. Eng. Sci. 22, 1701–1711.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28.CrossRefGoogle Scholar
Hutchins, N., Nickels, T. B., Marusic, I. & Chong, M. S. 2009 Hot-wire spatial resolution issues in wall-bounded turbulence. J. Fluid Mech. 635, 103–136.Google Scholar
Jiménez, J. & Pinelli, A. 1999 The autonomous cycle of near-wall turbulence. J. Fluid Mech. 389, 335–359.Google Scholar
Kader, B. A. 1981 Temperature and concentration profiles in fully turbulent boundary layers. Intl J. Heat Mass Transfer 24, 1541–1544.CrossRefGoogle Scholar
Kawamura, H., Abe, H. & Matsuo, Y. 1999 DNS of turbulent heat transfer in channel flow with respect to Reynolds and Prandtl number effects. Intl J. Heat Fluid Flow 20, 196–207.Google Scholar
Kawamura, H., Abe, H. & Matsuo, Y. 2004 Very large-scale structures observed in DNS of turbulent channel flow with passive scalar transport. In Proc. 15th Australasian Fluid Mechanics Conference, pp. 15–32.Google Scholar
Kawamura, H., Abe, H. & Shingai, K. 2000 DNS of turbulence and heat transport in a channel flow with different Reynolds and Prandtl numbers and boundary conditions. In Proc. 3rd Int. Symp. on Turbulence, Heat and Mass Transfer (ed. Nagano, Y.), pp. 15–32. Engineering Foundation.Google Scholar
Kawamura, H., Ohsaka, K., Abe, H. & Yamamoto, K. 1998 DNS of turbulent heat transfer in channel flow with low to medium–high Prandtl number. Intl J. Heat Fluid Flow 19, 482–491.CrossRefGoogle Scholar
Kays, W. M., Crawford, M. E. & Weigand, B. 1980 Convective Heat and Mass Transfer. McGraw-Hill.Google Scholar
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59, 308–323.CrossRefGoogle Scholar
Kim, J. & Moin, P. 1989 Transport of passive scalars in a turbulent channel flow. In Turbulent Shear Flows 6, pp. 85–96. Springer.Google 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.Google Scholar
Kleiser, L. & Zang, T. A. 1991 Numerical simulation of transition in wall-bounded shear flows. Annu. Rev. Fluid Mech. 23, 495–537.Google Scholar
Lee, M. & Moser, R. D. 2015 Direct simulation of turbulent channel flow layer up to $Re_{{\it\tau}}=5200$ . J. Fluid Mech. 774, 395–415.CrossRefGoogle Scholar
Lyons, S. L., Hanratty, T. J. & McLaughlin, J. B. 1991 Direct numerical simulation of passive heat transfer in a turbulent channel flow. Intl J. Heat Mass Transfer 34, 1149–1161.CrossRefGoogle Scholar
Monin, A. S. & Yaglom, A. M. 1971 Statistical Fluid Mechanics: Mechanics of Turbulence, vol. 1. MIT Press.Google Scholar
Moser, R. D., Kim, J. & Mansour, N. N. 1999 Direct numerical simulation of turbulent channel flow up to $Re_{{\it\tau}}=590$ . Phys. Fluids 11, 943–945.Google Scholar
Nagano, Y. & Tagawa, M. 1988 Statistical characteristics of wall turbulence with a passive scalar. J. Fluid Mech. 196, 157–185.Google Scholar
Orlandi, P. 2000 Fluid Flow Phenomena: A Numerical Toolkit. Kluwer.CrossRefGoogle Scholar
Orlandi, P., Bernardini, M. & Pirozzoli, S. 2015 Poiseuille and Couette flows in the transitional and fully turbulent regime. J. Fluid Mech. 424–441.Google Scholar
Perry, A. E. & Marusic, I. 1995 A wall-wake model for the turbulence structure of boundary layers. Part 1. Extension of the attached eddy hypothesis. J. Fluid Mech. 298, 361–388.Google 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.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
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.Google Scholar
Priyadarshana, P. J. A. & Klewicki, J. C. 2004 Study of the motions contributing to the Reynolds stress in high and low Reynolds number turbulent boundary layers. Phys. Fluids 16, 4586–4600.Google Scholar
Schwertfirm, F. & Manhart, M. 2007 DNS of passive scalar transport in turbulent channel flow at high Schmidt numbers. Intl J. Heat Fluid Flow 28, 1204–1214.CrossRefGoogle Scholar
Sleicher, C. A. & Rouse, M. W. 1975 A convenient correlation for heat transfer to constant and variable property fluids in turbulent pipe flow. Intl J. Heat Mass Transfer 18, 677–683.CrossRefGoogle Scholar
Subramanian, C. S. & Antonia, R. A. 1981 Effect of Reynolds number on a slightly heated turbulent boundary layer. Intl J. Heat Mass Transfer 24, 1833–1846.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.Google Scholar
Wikström, P. M. & Johansson, A. V. 1998 DNS and scalar-flux transport modelling in a turbulent channel flow. In Proc. 2nd EF Conference in Turbulent Heat Transfer, pp. 6.46–6.51. Engineering Foundation.Google Scholar