The heat and fluid flow in a fully developed turbulent channel flow have been investigated. The closure model of Reynolds shear stress and Reynolds heat flux as a function of a series of logarithmic functions in the mesolayer variable have been adopted. The interaction between inner and outer layers in the mesolayer (intermediate layer) arising from the balance of viscous effect, pressure gradient and Reynolds shear stress (containing the maxima of Reynolds shear stress) was first proposed by Afzal (1982, “Fully Developed Turbulent Flow in a Pipe: An Intermediate Layer,” Arch. Appl. Mech., 53, 355–377). The unknown constants in the closure models for Reynolds shear stress and Reynolds heat flux have been estimated from the prescribed boundary conditions near the axis and surface of channel. The predictions are compared with the DNS data Iwamoto et al. and Abe et al. for Reynolds shear stress and velocity profile and Abe et al. data of Reynolds heat flux and temperature profile. The limitations of the closure models are presented.
Issue Section:
Technical Briefs
1.
Sreenivasan
, K. R.
, and Bershadskii
, A.
, 2006, “The Mean Velocity Distribution Near the Peak of the Reynolds Shear Stress, Extending Also to the Buffer Region
,” IUTAM Symposium on One Hundred Years of Boundary Layer Research
, G. E. A.
Meier
and K. R.
Sreenivasan
, eds., Springer
, Dordrecht, The Netherlands
.2.
Sreenivasan
, K. R.
, and Bershadskii
, A.
, 2006, “Finite-Reynolds-Number Effects in Turbulence Using Logarithmic Expansions
,” J. Fluid Mech.
0022-1120, 554
, pp. 477
–498
.3.
Panton
, R. L.
, 1997, “A Reynolds Stress Function for Wall Layers
,” ASME J. Fluids Eng.
0098-2202, 119
, pp. 325
–330
.4.
Panton
, R. L.
, 2005, “Review of Wall Turbulence as Described by Composite Expansions
,” Appl. Mech. Rev.
0003-6900, 58
, pp. 1
–40
.5.
Panton
, R. L.
, 2007, “Composite Asymptotic Expansions and Scaling Wall Turbulence
,” Philos. Trans. R. Soc. London, Ser. A
0962-8428, 365
, pp. 733
–754
.6.
Afzal
, N.
, 1982, “Fully Developed Turbulent Flow in a Pipe: An Intermediate Layer
,” Arch. Appl. Mech.
0939-1533, 53
, pp. 355
–377
.7.
Afzal
, N.
, 1984, “The Mesolayer Theory of Turbulent Flows
,” AIAA J.
0001-1452, 22
, pp. 437
–439
.8.
Afzal
, N.
, 1982, “A Sub-Boundary Layer With a Two Dimensional Turbulent Boundary Layer
,” Journal de Mecanique Theorique et Appliquee
, 1
, pp. 963
–973
.9.
Afzal
, N.
, 1984, “Period Between Bursting in Turbulent Shear Flow: Intermediate Scaling
,” Curr. Sci.
0011-3891, 53
(12
), pp. 640
–642
.10.
Sahay
, A.
, 1997, “The Mean Velocity and the Reynolds Shear Stress in Turbulent Pipe and Channel Flows
,” Ph.D. thesis, Yale University.11.
Long
, R. R.
, and Chen
, T. C.
, 1981, “Experimental Evidence of the Existence of the Mesolayer in Turbulent Systems
,” J. Fluid Mech.
0022-1120, 105
, pp. 19
–59
.12.
Afzal
, N.
, 1983, “Three Layer Theory of Turbulent Boundary Layer on a Flat Plate
,” Proceedings of the Second Asian Congress of Fluid Mechanics
, Science, Beijing
, pp. 316
–321
.13.
Sreenivasan
, K. R.
, 1983, “Characteristics of Fine Scale of Turbulence in Boundary Layers
,” Proceedings of the Second Asian Congress of Fluid Mechanics
, Science, Beijing
, pp. 84
–90
.14.
Sreenivasan
, K. R.
, and Sahay
, A.
, 1997, “The Persistence of Viscous Effects in the Overlap Region, and the Mean Velocity in Turbulent Pipe and Channel Fows
,” Self Sustaining Mechanisms of Wall Turbulence
, R.
Panton
, ed. WIT
, Bath, UK
.15.
Sahay
, A.
, and Sreenivasan
, K. R.
, 1999, “The Wall-Normal Position in Pipe and Channel Flows at Which Viscous and Turbulent Shear Stresses Are Equal
,” Phys. Fluids
1070-6631, 11
(10
), pp. 3186
–3188
.16.
McKeon
, B. J.
, and Sreenivasan
, K. R.
, 2007, “Introduction: Scaling and Structure in High Reynolds Number Wall-Bounded Flows
,” Philos. Trans. R. Soc. London, Ser. A
0962-8428, 365
, pp. 635
–646
.17.
Sreenivasan
, K. R.
, 1987, “A Unified View of the Origin and Morphology of the Turbulent Boundary Layer Structure
,” Turbulence Management and Relaminarisation
, H. W.
Liepmann
and R.
Narasimha
, eds., Springer-Verlag
, New York
, p. 37
–61
.18.
Sreenivasan
, K. R.
, 1989, “The Turbulent Boundary Layer
,” Frontiers in Experimental Fluid Mechanics
, M.
Gad-el-Hak
, ed., Springer-Verlag
, Berlin
, pp. 159
–209
.19.
Johansson
, A. V.
, and Alferdsson
, P. H.
, 1982, “On the Structure of Turbulent Channel Flow
,” J. Fluid Mech.
0022-1120, 121
, pp. 295
–314
.20.
Antonia
, R. A.
, Teitel
, M.
, Kim
, J.
, and Browne
, L. W. B.
, 1992, “Low Reynolds-Number Effects in a Fully Developed Turbulent Channel Flow
,” J. Fluid Mech.
0022-1120, 236
, p. 579
–605
.21.
Tsuji
, Y.
, 1999, “Peak Position of Dissipation Spectrum in Turbulent Boundary Layers
,” Phys. Rev. E
1063-651X, 59
, pp. 7235
–7238
.22.
Guala
, M.
, Hommema
, S. E.
, and Adrian
, R. J.
, 2006, “Large-Scale and Very Large Scale Motions in Turbulent Pipe Flow
,” J. Fluid Mech.
0022-1120, 554
, pp. 521
–542
.23.
Balakumar
, B. J.
, and Adrian
, R. J.
, 2007, “Large- and Very-Large Scale Motions in Channel and Boundary Layer Flows
,” Philos. Trans. R. Soc. London, Ser. A
0962-8428, 365
, pp. 665
–681
.24.
Zanoun
, E. S.
, 2003, “Answer to Some Open Questions in Wall-Bounded Laminar and Turbulent Flows
,” Doctor-Ingeniur, University of Erlangen-Nurnberg.25.
Wei
, T.
, McMurtry
, P.
, Klewicki
, J.
, and Fife
, P.
, 2005, “Mesoscaling of the Reynolds Shear Stress in Turbulent Channel and Pipe Flows
,” AIAA J.
0001-1452, 43
(11
), pp. 2350
–2353
.26.
Klewicki
, J. C.
, Fife
, P.
, Wei
, T.
, and McMurtry
, P. A.
, 2006, “Overview of a Methodology for Scaling the Indeterminate Equations of Wall Turbulence
,” AIAA J.
0001-1452, 44
(11
), pp. 2475
–2481
, see also AIAA Paper No. 2005-4671.
27.
Klewicki
, J.
, Fife
, P.
, and Wei
, T.
, 2007, “A Physical Model of the Turbulent Boundary Layer Consonant with Mean Momentum Balance Structure
,” Philos. Trans. R. Soc. London, Ser. A
0962-8428, 365
, 823
–839
.28.
Fife
, P.
, Klewicki
, J.
, McMurtry
, P.
, and Wei
, T.
, 2005, “Multiscaling in the Presence of Indeterminacy: Wall-Induced Turbulence
,” Multiscale Model. Simul.
1540-3459, 4
(3
), pp. 936
–959
.29.
Wei
, T.
, Fife
, P.
, Klewicki
, J.
, and McMurtry
, P.
, 2005, “Scaling Heat Transfer in Fully Developed Turbulent Channel Flows
,” Int. J. Heat Mass Transfer
0017-9310, 48
, pp. 5284
–5296
.30.
Phuong
, M. L.
, and Papavassiliou
, D. V.
2008, “On the Scaling of Heat Transfer Using Thermal Flux Gradients for Fully Developed Turbulent Channel and Couette Flows
,” Int. Commun. Heat Mass Transfer
0735-1933, 35
, pp. 404
–412
.31.
Morrison
, J. F.
, McKeon
, B. J.
, Jiang
, W.
, and Smith
, A. J.
, 2004, “Scaling of the Streamwise Velocity Component in Turbulent Pipe Flow
,” J. Fluid Mech.
0022-1120, 508
, pp. 88
–131
.32.
Morrison
, J. F.
, 2007, “The Interaction Between Inner and Outer Regions of Turbulent Wall-Bounded Flow
,” Philos. Trans. R. Soc. London, Ser. A
0962-8428, 365
, pp. 683
–698
.33.
Wosnik
, M.
, Castillo
, L.
, and George
, W. K.
, 2000, “A Theory for Turbulent Pipe and Channel Flows
,” J. Fluid Mech.
0022-1120, 421
, pp. 115
–145
.34.
Alferdsson
, P. H.
, and Johansson
, A. V.
, 1984, “Time Scales in Turbulent Channel Flow
,” Phys. Fluids
0031-9171, 27
, pp. 1974
–1981
.35.
Shah
, D. A.
, and Antonia
, R. A.
, 1989, “Scaling of Bursting Period in Turbulent Boundary Layer and Duct Flows
,” Phys. Fluids A
0899-8213, 1
(2
), pp. 318
–325
.36.
Osterlund
, J. M.
, Lindgren
, B.
, and Johansson
, A. V.
, 2003, “Flow Structure in Zero Pressure Gradient Turbulent Boundary Layer at High Reynolds Numbers
,” Eur. J. Mech. B/Fluids
0997-7546, 22
, pp. 379
–370
.37.
Nagano
, Y.
, and Houra
, T.
, 2004, “Scaling of Near Wall Structures in Turbulent Boundary Layers Subjected to Adverse Pressure Gradient
,” Reynolds Number Scaling in Turbulent Flow, IUTAM Symposium
, Kluwer Academic
, Dordrecht
, pp. 291
–296
.38.
Iwamoto
, K.
, Suzuki
, Y.
, and Kasagi
, N.
, 2002, “Reynolds Number Effect on Wall Turbulence: Toward Effective Feedback Control
,” Int. J. Heat Fluid Flow
0142-727X, 23
, pp. 678
–689
.39.
McKeon
, B. J.
, 2003, “High Reynolds Number Turbulent Pipe Flow
,” Ph.D. thesis, Princeton University.40.
Seena
, A.
, and Afzal
, N.
, 2008, “Intermediate Scaling of Turbulent Momentum and Heat Transfer in a Transitional Rough Channel
,” ASME J. Heat Transfer
0022-1481, 130
, p. 031701
.41.
Abe
, H.
, Kawamura
, H.
, and Matsuo
, Y.
, 2004, “Surface Heat-Flux Fluctuations in a Turbulent Channel up to Rτ=1020 With Pr=0.025 and 0.71
,” Int. J. Heat Fluid Flow
0142-727X, 25
, pp. 404
–419
.42.
Abe
, H.
, Kawamura
, H.
, and Matsuo
, Y.
, 2001, “Direct Numerical Simulation of a Fully Developed Turbulent Channel Flow With Respect to the Reynolds Number Dependence
,” ASME J. Fluids Eng.
0098-2202, 123
, pp. 382
–393
.43.
Lundgren
, T. S.
, 2007, “Asymptotic Analysis of the Constant Pressure Turbulent Boundary Layer
,” Phys. Fluids
1070-6631, 19
, p. 055105
.44.
Afzal
, N.
, and Bush
, W. B.
, 1985, “A Three Layer Asymptotic Analysis of Turbulent Channel Flows
,” Proc. Indian Acad. Sci., Sect. A
0370-0089, 94
, pp. 135
–148
.45.
Afzal
, N.
, 1983, “Analysis of a Turbulent Boundary Layer Subjected to a Strong Adverse Pressure Gradient
,” Int. J. Eng. Sci.
0020-7225, 21
, pp. 563
–576
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