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Research Papers: Forced Convection

Intermediate Scaling of Turbulent Momentum and Heat Transfer in a Transitional Rough Channel

[+] Author and Article Information
Abu Seena

Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, 305-701 Koreaabuseena@kaist.ac.kr

Noor Afzal

Department of Mechanical Engineering, Aligarh University, Aligarh 202 002, Indianoor.afzal@yahoo.com

J. Heat Transfer 130(3), 031701 (Mar 06, 2008) (10 pages) doi:10.1115/1.2804945 History: Received September 17, 2006; Revised September 12, 2007; Published March 06, 2008

The properties of the mean momentum and thermal balance in fully developed turbulent channel flow on transitional rough surface have been explored by method of matched asymptotic expansions. Available high quality data support a dynamically relevant three-layer description that is a departure from two-layer traditional description of turbulent wall flows. The scaling properties of the intermediate layer are determined. The analysis shows the existence of an intermediate layer, with its own characteristic of mesolayer scaling, between the traditional inner and outer layers. Our predictions of the peak values of the Reynolds shear stress and Reynolds heat flux and their locations in the intermediate layer are well supported by the experimental and direct numerical simulation (DNS) data. The inflectional surface roughness data in a turbulent channel flow provide strong support to our proposed universal log law in the intermediate layer, that is, explicitly independent transitional surface roughness. There is no universality of scalings in traditional variables and different expressions are needed for various types of roughness, as suggested, for example, with inflectional type roughness, Colebrook–Moody monotonic roughness, etc. In traditional variables, the roughness scale for inflectional roughness is supported very well by experimental and DNS data. The higher order effects are also presented, which show the implications of the low Reynolds-number flows, where the intermediate layer provides the uniformly valid solutions in terms of generalized logarithmic laws for the velocity and the temperature distributions.

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Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

The comparison of fully smooth channel DNS data of Iwamoto (21) with the intermediate layer theory. (a) Half-defect (Um=Uc∕2) velocity profile data and our prediction Eq. 30. (b) Reynolds shear stress data and our prediction 31.

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Figure 2

The comparison of fully smooth channel DNS data of Abe (22) with the intermediate layer theory. (a) Half-defect (Um=Uc∕2) velocity profile data and our prediction Eq. 30. (b) Reynolds shear steers data and our prediction 31.

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Figure 3

The comparison of fully smooth channel DNS data of Hoyas and Jimenez (24) with the intermediate layer theory. (a) Half-defect (Um=Uc∕2) velocity profile data and our prediction Eq. 30. (b) Reynolds shear steers data and our prediction 31.

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Figure 4

Comparison of the maxima of the Reynolds shear stress (a) Location y+max (b) Maximum value τmax∕τw with fully smooth (ϕ=1) pipe and channel data of Zanoun (26), channel DNS data of Iwamoto (21), Abe (22-23), Hoyas and Jiemenz (24), and Moser (27).

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Figure 5

Half-defect (Um=Uc∕2) velocity profile data in the intermediate layer for transitional rough surface from Shockling (28) for machined honed pipe roughness. (a) Nonuniversal behavior in traditional mesolayer variables (u−Um)∕2 versus ξ. (b) Our universal intermediate layer half-defect law (u−Um)∕2 versus η. Predictions based on roughness scale 47 with j=11.

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Figure 6

The comparison of the fully smooth channel (ϕ=1,η=ξ) DNS data of Abe (22-23) with the intermediate layer thermal convection theory. (a) Half-defect [Tm=(Tw+Tc)∕2] temperature profile data and our prediction Eq. 36. (b) Reynolds heat flux profile data and our prediction 37.

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Figure 7

Comparison of our predictions with the peak of the Reynolds heat flux with DNS data of Abe (22-23) fully smooth channel. (a) Location y+tm; (b) Maximum value τtm∕qw.

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Figure 8

Comparison of the intermediate layer velocity UmR and intermediate layer temperature TmR at the points of maximum Reynolds shear stress and Reynolds heat flux with fully smooth channel DNS data by Iwamoto (21), Abe (22-23), and Hoyas and Jiemenez (24). Present proposal: —— 2/3 asymptote for large Reynolds numbers.

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Figure 9

Velocity distribution (u−Um1)∕uτ in the intermediate layer from smooth channel DNS data of Iwamoto (21), where the velocity Um1 is estimated at maxima of Reynolds shear stress. (a) Intermediate layer variable ξ. (b) Alternate intermediate layer variable ξ−ξm from maxima in Reynolds shear stress. (—) Intermediate layer log region for velocity distribution.

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Figure 10

Velocity distribution (u−UmR)∕uτ data in the intermediate layer from smooth channel DNS data of Abe (22) and Hoyas and Jimenez (24), where the velocity UmR is estimated at maxima of Reynolds shear stress. (a) Intermediate layer variable ξ. (b) Alternate intermediate layer variable ξ−ξm from maxima in Reynolds shear stress. (—) Intermediate layer log region for velocity distribution.

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Figure 11

Temperature distribution (T−TmR)∕Tτ in the intermediate layer from smooth channel DNS data of Abe (22), where the temperature TmR is estimated at maxima of Reynolds heat flux. (a) Intermediate layer variable ξ. (b) Alternate intermediate layer variable ξ−ξtm from maxima in Reynolds shear stress. (—) Intermediate layer log region for temperature distribution.

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