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Research Papers: Fundamental Issues and Canonical Flows

Pressure Gradient Effects on Smooth and Rough Surface Turbulent Boundary Layers—Part I: Favorable Pressure Gradient

[+] Author and Article Information
Ju Hyun Shin

Mechanical and Aerospace Engineering,
Seoul National University,
Seoul 151-744, Korea
e-mail: asuna1@snu.ac.kr

Seung Jin Song

Mechanical and Aerospace Engineering,
Seoul National University,
Seoul 151-744, Korea

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received December 16, 2013; final manuscript received April 18, 2014; published online September 10, 2014. Assoc. Editor: Mark F. Tachie.

J. Fluids Eng 137(1), 011203 (Sep 10, 2014) (9 pages) Paper No: FE-13-1733; doi: 10.1115/1.4027474 History: Received December 16, 2013; Revised April 18, 2014

The effects of the pressure gradient and surface roughness on turbulent boundary layers have been experimentally investigated. In Part I, smooth- and rough-surface turbulent boundary layers with and without favorable pressure gradients (FPG) are presented. All of the tests have been conducted at the same Reynolds number (based on the length of the flat plate) of 900,000. Streamwise time-mean and fluctuating velocities have been measured using a single-sensor hot-wire probe. For smooth surfaces, the FPG decreases the mean velocity defect and increases the wall shear stress; however, the friction coefficient hardly changes due to the increased freestream velocity. The FPG effect on the streamwise normal Reynolds stress has been examined. The FPG increases the streamwise normal Reynolds stress for y less than 0.6 times the boundary layer thickness. With the zero pressure gradient (ZPG), the roughness increases the mean velocity defect throughout the boundary layer and increases the normal Reynolds stress for y greater than twice the average roughness height. The roughness effect on the mean velocity defect is stronger under the FPG than under the ZPG for y less than 30 times the average roughness height. For y less than 25 times the average roughness height, the roughness effect of increasing normal Reynolds stress is also stronger under the FPG than under the ZPG. Consequently, for a rough surface, the FPG increases the integrated streamwise turbulent kinetic energy, friction coefficient, roughness Reynolds number, and roughness shift. Furthermore, the FPG increases the roughness effects on the integral boundary layer parameters—the boundary layer thickness, momentum thickness, ratio of the displacement thickness to the boundary layer thickness, and shape factor. Thus, the FPG augments the roughness effects on turbulent boundary layers.

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Figures

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Fig. 1

A schematic of the wind tunnel

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Fig. 2

A schematic of the test section

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Fig. 3

Mean velocity distributions

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Fig. 4

Mean velocity profiles in the smooth surface ZPG boundary layers: (a) velocity defects and (b) velocity profile in the inner coordinate. Case 1: K×106 = 0.01, Rex = 729,000, Reθ = 2070 and Castillo and Johansson [29]: Reθ = 1497.

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Fig. 5

Turbulence intensity profiles in the smooth surface ZPG boundary layers. Here, K, Rex, and Reθ for case 1 as in Fig. 3.

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Fig. 6

Mean velocity profiles in the smooth surface boundary layers: (a) velocity defects and (b) velocity profiles in the inner coordinate. Case 1: K×106 = 0.01, Rex = 729,000, Reθ = 2070. Case 2: K×106 = 0.28, Rex = 903,000, Reθ = 1420.

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Fig. 7

Streamwise normal Reynolds stress distributions in the smooth surface boundary layers. Here, K, Rex, and Reθ for cases 1 and 2 as in Fig. 6.

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Fig. 8

Friction coefficients in the smooth surface boundary layers. Case 1: K×106 = − 0.02–0.01, Rex = 203,000–816,000. Case 2: K×106 = 0.38–0.28, Rex = 207,000–1,046,000.

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Fig. 9

Mean velocity profiles in the smooth and rough surface ZPG boundary layers: (a) velocity defect and (b) velocity profile in the inner coordinate. Case 1: K×106 = 0.01, Rex = 729,000, Reθ = 2070. Case 3: K×106 = − 0.01, Rex = 724,000, Reθ = 2770.

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Fig. 10

Normal Reynolds stress profiles in the smooth and rough surface ZPG boundary layers. Here, K, Rex, and Reθ for cases 1 and 3 as in Fig. 9.

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Fig. 11

Mean velocity defect profiles in the smooth and rough surface boundary layers. Case 1: K×106 = 0.01, Rex = 729,000, Reθ = 2070. Case 2: K×106 = 0.28, Rex = 903,000, Reθ = 1420, Case 3: K×106 = − 0.01, Rex = 724,000, Reθ = 2770. Case 4: K×106 = 0.27, Rex = 919,000, Reθ = 2420.

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Fig. 12

Streamwise normal Reynolds stress profiles in the smooth and rough surface boundary layers. Here, K, Rex, and Reθ for each test case as in Fig. 11.

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Fig. 13

Friction coefficients in the smooth and rough surface boundary layers. Case 1: K×106 = − 0.02–0.01, Rex = 203,000–816,000. Case 2: K×106 = 0.38– 0.28, Rex = 207,000–1,046,000. Case 3: K×106 = −0.03–0.04, Rex = 201,000– 809,000. Case 4: K×106 = 0.35–0.27, Rex = 213,000–1,058,000.

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Fig. 14

Mean velocity profiles in the rough surface boundary layers. Here, K, Rex, and Reθ for cases 3 and 4 as in Fig. 11.

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Fig. 15

Boundary layer thickness and momentum thickness in the smooth and rough surface boundary layers: (a) boundary layer thickness and (b) momentum thickness. Case 1: K×106 = −0.02–0.01, Reθ = 880 ∼ 2220. Case 2: K×106 = 0.38– 0.27, Reθ = 540–1510. Case 3: K×106 = −0.03–0.04, Reθ = 950–2970. Case 4: K×106 = 0.35–0.27, Reθ = 620–2640.

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Fig. 16

Distributions of δ*/δ in the smooth and rough surface boundary layers. Here, K and Rex for Cases 1, 2, 3, and 4 as in Fig. 13.

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Fig. 17

Distributions of H in the smooth and rough surface boundary layers. Here, K and Rex for Cases 1, 2, 3, and 4 as in Fig. 13.

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