zbMATH — the first resource for mathematics

Passive scalars in turbulent channel flow at high Reynolds number. (English) Zbl 1381.76109
Summary: 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.

76F40 Turbulent boundary layers
76F35 Convective turbulence
Full Text: DOI
[1] Abe, H.; Antonia, R. A., Near-wall similarity between velocity and scalar fluctuations in a turbulent channel flow, Phys. Fluids, 21, (2009) · Zbl 1183.76062
[2] Abe, H.; Kawamura, H.; Choi, H., Very large-scale structures and their effects on the wall shear-stress fluctuations in a turbulent channel flow up to \(Re_{{\textit\tau}}=640\), J. Fluids Engng, 126, 835-843, (2004)
[3] Abe, H.; Kawamura, H.; Matsuo, Y., Surface heat-flux fluctuations in a turbulent channel flow up to \(Re_{{\textit\tau}}=1020\) with \(Pr=0.025\) and 0.71, Intl J. Heat Fluid Flow, 25, 404-419, (2004)
[4] Afzal, N.; Yajnik, K., Analysis of turbulent pipe and channel flows at moderately large Reynolds number, J. Fluid Mech., 61, 23-31, (1973)
[5] Del Álamo, J. C.; Jiménez, J., Spectra of the very large anisotropic scales in turbulent channels, Phys. Fluids, 15, L41-L44, (2003) · Zbl 1186.76136
[6] Del Álamo, J. C.; Jiménez, J.; Zandonade, P.; Moser, R. D., Scaling of the energy spectra of turbulent channels, J. Fluid Mech., 500, 135-144, (2004) · Zbl 1059.76031
[7] Antonia, R. A.; Abe, H.; Kawamura, H., Analogy between velocity and scalar fields in a turbulent channel flow, J. Fluid Mech., 628, 241-268, (2009) · Zbl 1181.76078
[8] Batchelor, G. K., 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, (1959) · Zbl 0085.39701
[9] Bernardini, M.; Pirozzoli, S.; Orlandi, P., Velocity statistics in turbulent channel flow up to \(Re_{{\textit\tau}}=4000\), J. Fluid Mech., 742, 171-191, (2014)
[10] Bernardini, M.; Pirozzoli, S.; Quadrio, M.; Orlandi, P., Turbulent channel flow simulations in convecting reference frames, J. Comput. Phys., 232, 1-6, (2013)
[11] Cebeci, T., A model for eddy conductivity and turbulent Prandtl number, J. Heat Transfer, 95, 227-234, (1973)
[12] Cebeci, T.; Bradshaw, P., Physical and Computational Aspects of Convective Heat Transfer, (1984), Springer · Zbl 0545.76090
[13] Degraaff, D. B.; Eaton, J. K., Reynolds-number scaling of the flat-plate turbulent boundary layer, J. Fluid Mech., 422, 319-346, (2000) · Zbl 0958.76509
[14] Durbin, P. A., Near-wall turbulence closure modeling without damping functions, Theoret. Comput. Fluid Dyn., 3, 1-13, (1991) · Zbl 0728.76053
[15] Gnielinski, V., New equations for heat and mass transfer in turbulent pipe and channel flow, Intl Chem. Eng., 16, 359-367, (1976)
[16] Gowen, R. A.; Smith, J. W., The effect of the Prandtl number on temperature profiles for heat transfer in turbulent pipe flow, Chem. Eng. Sci., 22, 1701-1711, (1967)
[17] Hutchins, N.; Marusic, I., Evidence of very long meandering features in the logarithmic region of turbulent boundary layers, J. Fluid Mech., 579, 1-28, (2007) · Zbl 1113.76004
[18] Hutchins, N.; Nickels, T. B.; Marusic, I.; Chong, M. S., Hot-wire spatial resolution issues in wall-bounded turbulence, J. Fluid Mech., 635, 103-136, (2009) · Zbl 1183.76025
[19] Jiménez, J.; Pinelli, A., The autonomous cycle of near-wall turbulence, J. Fluid Mech., 389, 335-359, (1999) · Zbl 0948.76025
[20] Kader, B. A., Temperature and concentration profiles in fully turbulent boundary layers, Intl J. Heat Mass Transfer, 24, 1541-1544, (1981)
[21] Kawamura, H.; Abe, H.; Matsuo, Y., DNS of turbulent heat transfer in channel flow with respect to Reynolds and Prandtl number effects, Intl J. Heat Fluid Flow, 20, 196-207, (1999)
[22] Kawamura, H., Abe, H. & Matsuo, Y.2004Very large-scale structures observed in DNS of turbulent channel flow with passive scalar transport. In Proc. 15th Australasian Fluid Mechanics Conference, pp. 15-32.
[23] Kawamura, H., Abe, H. & Shingai, K.2000DNS 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.
[24] Kawamura, H.; Ohsaka, K.; Abe, H.; Yamamoto, K., DNS of turbulent heat transfer in channel flow with low to medium – high Prandtl number, Intl J. Heat Fluid Flow, 19, 482-491, (1998)
[25] Kays, W. M.; Crawford, M. E.; Weigand, B., Convective Heat and Mass Transfer, (1980), McGraw-Hill
[26] Kim, J.; Moin, P., Application of a fractional-step method to incompressible Navier-Stokes equations, J. Comput. Phys., 59, 308-323, (1985) · Zbl 0582.76038
[27] Kim, J. & Moin, P.1989Transport of passive scalars in a turbulent channel flow. In Turbulent Shear Flows 6, pp. 85-96. Springer. doi:10.1007/978-3-642-73948-4_9
[28] Kim, J.; Moin, P.; Moser, R. D., Turbulence statistics in fully developed channel flow at low Reynolds number, J. Fluid Mech., 177, 133-166, (1987) · Zbl 0616.76071
[29] Kleiser, L.; Zang, T. A., Numerical simulation of transition in wall-bounded shear flows, Annu. Rev. Fluid Mech., 23, 495-537, (1991)
[30] Lee, M.; Moser, R. D., Direct simulation of turbulent channel flow layer up to \(Re_{{\textit\tau}}=5200\), J. Fluid Mech., 774, 395-415, (2015)
[31] Lyons, S. L.; Hanratty, T. J.; Mclaughlin, J. B., Direct numerical simulation of passive heat transfer in a turbulent channel flow, Intl J. Heat Mass Transfer, 34, 1149-1161, (1991)
[32] Monin, A. S. & Yaglom, A. M.1971Statistical Fluid Mechanics: Mechanics of Turbulence, vol. 1. MIT Press. · Zbl 1140.76003
[33] Moser, R. D.; Kim, J.; Mansour, N. N., Direct numerical simulation of turbulent channel flow up to \(Re_{{\textit\tau}}=590\), Phys. Fluids, 11, 943-945, (1999) · Zbl 1147.76463
[34] Nagano, Y.; Tagawa, M., Statistical characteristics of wall turbulence with a passive scalar, J. Fluid Mech., 196, 157-185, (1988) · Zbl 0657.76050
[35] Orlandi, P., Fluid Flow Phenomena: A Numerical Toolkit, (2000), Kluwer
[36] Orlandi, P.; Bernardini, M.; Pirozzoli, S., Poiseuille and Couette flows in the transitional and fully turbulent regime, J. Fluid Mech., 424-441, (2015)
[37] Perry, A. E.; Marusic, I., 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, (1995) · Zbl 0849.76030
[38] Pirozzoli, S., Revisiting the mixing-length hypothesis in the outer part of turbulent wall layers: mean flow and wall friction, J. Fluid Mech., 745, 378-397, (2014)
[39] Pirozzoli, S.; Bernardini, M.; Orlandi, P., Turbulence statistics in Couette flow at high Reynolds number, J. Fluid Mech., 758, 327-343, (2014)
[40] Pope, S. B., Turbulent Flows, (2000), Cambridge University Press · Zbl 0966.76002
[41] Priyadarshana, P. J. A.; Klewicki, J. C., Study of the motions contributing to the Reynolds stress in high and low Reynolds number turbulent boundary layers, Phys. Fluids, 16, 4586-4600, (2004) · Zbl 1187.76428
[42] Schwertfirm, F.; Manhart, M., DNS of passive scalar transport in turbulent channel flow at high Schmidt numbers, Intl J. Heat Fluid Flow, 28, 1204-1214, (2007)
[43] Sleicher, C. A.; Rouse, M. W., A convenient correlation for heat transfer to constant and variable property fluids in turbulent pipe flow, Intl J. Heat Mass Transfer, 18, 677-683, (1975)
[44] Subramanian, C. S.; Antonia, R. A., Effect of Reynolds number on a slightly heated turbulent boundary layer, Intl J. Heat Mass Transfer, 24, 1833-1846, (1981)
[45] Tennekes, H.; Lumley, J. L., A First Course in Turbulence, (1972), MIT · Zbl 0285.76018
[46] Townsend, A. A., The Structure of Turbulent Shear Flow, (1976), Cambridge University Press · Zbl 0325.76063
[47] Wikström, P. M. & Johansson, A. V.1998DNS 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.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.