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Research Papers: Fundamental Issues and Canonical Flows

A Relatively Simple Integral Method for Turbulent Flow Over Rough Surfaces

[+] 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 August 4, 2016; final manuscript received July 26, 2017; published online September 20, 2017. Assoc. Editor: Samuel Paolucci.

J. Fluids Eng 139(12), 121204 (Sep 20, 2017) (12 pages) Paper No: FE-16-1495; doi: 10.1115/1.4037523 History: Received August 04, 2016; Revised July 26, 2017

The integral form of the equation for x momentum is solved for the skin friction coefficient, in external thin boundary layer flow, on surfaces whose technical roughness elements' size is given. This is done by using a “roughness depression function” in the law of the wall and wake which serves as the needed velocity profile. The method uses the equivalent sand grain size concept in its calculations. Predictions are made of the friction coefficient, Cf, as a function of momentum thickness Reynolds number and also, of Cf's dependence on the ratio of momentum thickness to the size of the technical (actual) roughness elements. In addition, boundary layer thicknesses and velocity profiles on rough surfaces are calculated and, when available, comparisons are made with the experimental data from a number of sources in the literature. Also, comparisons are made with the results of another major predictive scheme which does not use the equivalent sand grain concept.

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References

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Figures

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Fig. 1

Comparison of present predictions and those of Hosni et al. [1] with data for L/d = 2, us = 58 m/s of Hosni et al.

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Fig. 2

Comparison of present predictions and those of Hosni et al. [1] with data for L/d = 2, us = 12 m/s of Hosni et al.

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Fig. 3

Comparison of present predictions and those of Hosni et al. [1] with data for L/d = 4, us = 12 m/s of Hosni et al.

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Fig. 4

Comparison of present predictions and those of Hosni et al. [1] with data for L/d = 4, us = 58 m/s of Hosni et al.

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Fig. 5

Comparison of present predictions and those of Hosni et al. [1] with data for L/d = 10, us = 12 m/s of Hosni et al.

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Fig. 6

Comparison of present predictions and those of Hosni et al. [1] with data for L/d = 10, us = 6 m/s of Hosni et al.

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Fig. 7

Comparison of present predictions with data for u+ versus y+ of Hosni et al. [1]; (•) L/d = 2; (▲) L/d = 4; and (▪) L/d = 10

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Fig. 8

Comparison of present predictions with data for u/us versus y/θ of Hosni et al. [1]

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Fig. 9

Comparison of present predictions with data for more cases of u/us versus y/θ of Hosni et al. [1]; (▪) L/d = 2; (•) L/d = 4; (▲) L/d = 10; and (♦) smooth

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Fig. 10

Comparison of present predictions with data for δ versus us of Hosni et al. [1]; (▪) L/d = 2; (•) L/d = 4; (▲) L/d = 10; and (♦) smooth

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Fig. 11

Prediction of δ for various degrees of roughness

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Fig. 12

Comparison of present predictions with data for Cf/2 versus θ/k of Hosni et al. [1] for L/d = 2; (•) 12 m/s; and (▪) 58 m/s

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Fig. 13

Comparison of present predictions with data for Cf/2 versus θ/k of Hosni et al. [1] for L/d = 10; (•) 6 m/s; and (∎) 12 m/s

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Fig. 14

Comparison of present predictions with data for u/us and y/θ data, L/d = 2, L/d = 4, L/d 10, Hosni et al. [1]; (▪) L/d = 2; (•) L/d = 4; (▲) L/d = 10; and (♦) smooth

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Fig. 15

Comparison of present predictions with data for the case of Pimenta et al. [21] us = 40 m/s

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Fig. 16

Present predictions of the velocity defect function (us − u)/u* versus y/δ for a smooth surface and two rough surfaces

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Fig. 17

Comparison of present predictions with data for rough surface 2 of McClain et al. [11] for the data point at Rex = 923,000

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Fig. 18

Comparison of present predictions with data for the rough 2 (upper curve) and rough 1 (lower curve) test surfaces of Belnap et al. [4]

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