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Research Papers: Flows in Complex Systems

An Integral Solution for Skin Friction in Turbulent Flow Over Aerodynamically Rough Surfaces With an Arbitrary Pressure Gradient

[+] Author and Article Information
James Sucec

Department of Mechanical Engineering,
University of Maine,
Orono, ME 04469-5711

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received June 4, 2013; final manuscript received March 5, 2014; published online June 2, 2014. Assoc. Editor: Feng Liu.

J. Fluids Eng 136(8), 081103 (Jun 02, 2014) (8 pages) Paper No: FE-13-1357; doi: 10.1115/1.4027140 History: Received June 04, 2013; Revised March 05, 2014

The combined law of the wall and wake, with the inclusion of the “roughness depression function” for the inner law in the “Log” region, is used as the inner coordinates' velocity profile in the integral form of the x momentum equation to solve for the local skin friction coefficient. The “equivalent sand grain roughness” concept is employed in the roughness depression function in the solution. Calculations are started at the beginning of roughness on a surface, as opposed to starting them using the measured experimental values at the first data point, when making comparisons of predictions with data sets. The dependence of the velocity wake strength on both pressure gradient and momentum thickness Reynolds number are taken into account. Comparisons of the prediction with experimental skin friction data, from the literature, have been made for some adverse, zero, and favorable (accelerating flows) pressure gradients. Predictions of the shape factor, roughness Reynolds number, and momentum thickness Reynolds number and comparisons with data are also made for some cases. In addition, some comparisons with the predictions of earlier investigators have also been made.

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Figures

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Fig. 1

Comparison of present predictions and those of Taylor et al. [3], with data for the strong equilibrium acceleration of Coleman [16], L = 2.286 m (7.5 ft)

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Fig. 2

Comparison of present predictions and those of Taylor et al. [3], with data for the mild equilibrium acceleration of Coleman [16], L = 2.286 m

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Fig. 3

Comparison of present predictions with data from the nonequilibrium acceleration case of Coleman [16], L = 2.286 m

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Fig. 4

Comparison of present predictions with data for the zero pressure gradient case of Coleman [16], L = 2.286 m

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Fig. 5

Comparison of present predictions with data for H, Rem, and Rek for Coleman's [16] strong equilibrium acceleration, L = 2.286 m, data points, (▪) Rek/10, • Rem/1000, and H

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Fig. 6

Comparison of present predictions and data for H, Rem, and Rek for the mild acceleration case of Coleman [16], L = 2.286 m, data points, (▪) Rem /1000; • Rek /10, and H

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Fig. 7

Comparison of present predictions with data for H, Rem and Rek for the nonequilibrium acceleration of Coleman [16], K¯ = 0.28 × 10−6, L = 2.286 m. Data points, • Rek/10, top set; Rem/1000, middle set; and H, lowest set.

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Fig. 8

Comparison of present predictions with data for H, Rem and Rek for the zero pressure gradient case of Coleman [16]. L = 2.286 m, data points: • Rem/1000, top set; Rek/10, middle set; and H, lowest set.

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Fig. 9

Comparison of present predictions with data for Healzer's constant Us = 58 m/s, from Moffat et al. [31], L = 2.286 m

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Fig. 10

Comparison of present predictions with data for Pimenta's constant Us = 27 m/s, from Moffat et al. [31], L = 2.286 m

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Fig. 11

Comparison of present predictions with data for constant Us = 58 m/s, 41.7 m/s, 9.8 m/s, and smooth surface 9.8 m/s from Moffat et al. [31]. L = 2.286 m, data points: (▪) 72.6 m/s; (▲) 58 m/s; (♦) 41.7 m/s; and (•) 9.8 m/s.

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Fig. 12

Comparison of present predictions with data for the zero pressure gradient, λ = 12, in the case of Liu et al. [32], L = 3.66 m (12 ft)

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Fig. 13

Comparison of present predictions and those of Dvorak [2], with experimental data of profile II of Perry and Joubert [30], L = 6.1 m (20 ft)

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Fig. 14

Comparison of present predictions and predictions of Dvorak [2], also Cebeci and Chang [5], with data of profile III of Perry and Joubert [30]. L = 6.1 m (20 ft).

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Fig. 15

Comparison of present predictions of the velocity wake strength parameter to data, for profile II, of Perry and Joubert [30], L = 6.1 m

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Fig. 16

Comparison of present predictions of the velocity wake strength parameter to data, for profile III of Perry and Joubert [30], L = 6.1 m

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