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Research Papers: Fundamental Issues and Canonical Flows

Pressure Gradient Effects on Smooth- and Rough-Surface Turbulent Boundary Layers—Part II: Adverse 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), 011204 (Sep 10, 2014) (7 pages) Paper No: FE-13-1734; doi: 10.1115/1.4027475 History: Received December 16, 2013; Revised April 18, 2014

An experimental investigation has been conducted to identify the effects of pressure gradient and surface roughness on turbulent boundary layers. In Part II, smooth- and rough-surface turbulent boundary layers with and without adverse pressure gradient (APG) are presented at a fixed Reynolds number (based on the length of flat plate) of 900,000. Flat-plate boundary layer measurements have been conducted using a single-sensor, hot-wire probe. For smooth surfaces, compared to the zero pressure gradient (ZPG) boundary layer, the APG boundary layer has a higher mean velocity defect throughout the boundary layer and lower friction coefficient. APG decreases the streamwise normal Reynolds stress for y less than 0.4 times the boundary layer thickness and increases it slightly in the outer region. For rough surfaces, APG reduces the roughness effects of increasing the mean velocity defect and normal Reynolds stress for y less than 23 and 28 times the average roughness height, respectively. Consistently, for the same roughness, APG decreases the integrated streamwise turbulent kinetic energy. APG also decreases the roughness effect on the friction coefficient, roughness Reynolds number, and roughness shift. Compared to the ZPG boundary layers, the roughness effects on integral boundary layer parameters—boundary layer thickness and momentum thickness—are weaker under APG. Thus, contrary to the favorable pressure gradient (FPG) in part I, APG reduces the roughness effects on turbulent boundary layers.

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Figures

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Fig. 1

A schematic of test section

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Fig. 4

Streamwise normal Reynolds stress distributions in the smooth-surface boundary layers. K, Rex, and Reθ for Cases 1 and 2 are as in Fig. 3.

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Fig. 5

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 = −0.22 ∼ −0.14, Rex = 196,000 ∼ 711,000, and Tay et al. [12]: K×106 = −0.45.

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Fig. 2

Mean velocity distributions

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Fig. 3

Mean velocity profiles in the smooth-surface boundary layers: (a) velocity defects and (b) velocity profile in inner coordinate. Case 1: K×106 = 0.01, Rex = 729,000, Reθ = 2070 and Case 2: K×106 = −0.14, Rex = 644,000, Reθ = 2660.

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Fig. 6

Mean velocity defect profiles in the smooth- and rough-surface boundary layers. Case 1: K×106 = 0.01, Rex = 720,000, Reθ = 2070, Case 2: K×106 = −0.14, Rex = 644,000, Reθ = 2660, Case 3: K×106 = −0.01, Rex = 724,000, Reθ = 2770, and Case 4: K×106 = −0.14, Rex = 645,000, Reθ = 3350.

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Fig. 7

Streamwise normal Reynolds stress profiles in the smooth- and rough-surface boundary layers. K, Rex, and Reθ for each test case are as in Fig. 6.

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Fig. 8

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 = −0.22 ∼ −0.14, Rex = 196,000 ∼ 711,000, Case 3: K×106 = −0.03 ∼ 0.04, Rex = 201,000 ∼ 809,000, and Case 4: K×106 = −0.21 ∼ −0.14, Rex = 196,000 ∼ 716,000.

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Fig. 9

Mean velocity profiles in the rough-surface boundary layers. K, Rex, and Reθ for Cases 3 and 4 are as in Fig. 6.

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Fig. 10

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 = −0.22 ∼ −0.14, Reθ = 1160 ∼ 2810, Case 3: K×106 = −0.03 ∼ 0.04, Reθ = 950 ∼ 2970, and Case 4: K×106 = −0.21 ∼ −0.14, Reθ = 1210 ∼ 3630.

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Fig. 11

Distributions of δ*/δ in the smooth- and rough-surface boundary layers. K and Rex for Cases 1–4 are as in Fig. 8.

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Fig. 12

Distributions of H in the smooth- and rough-surface boundary layers. K and Rex for Cases 1–4 are as in Fig. 8.

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Fig. 13

APG and FPG effects on the streamwise normal Reynolds stress in the rough-surface boundary layers. K, Rex, and Reθ for Cases 3 and 4 are as in Fig. 6. Rough/FPG: K×106 = 0.27, Rex = 919,000, Reθ = 2420.

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Fig. 14

APG and FPG effects on the friction coefficient in the rough-surface boundary layers. K and Rex for Cases 3 and 4 are as in Fig. 8. Rough/FPG: K×106 = 0.35 ∼ 0.27, Rex = 213,000 ∼ 1,058,000.

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