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Research Papers: Fundamental Issues and Canonical Flows

# Particle Image Velocimetry Study of Rough-Wall Turbulent Flows in Favorable Pressure Gradient

[+] Author and Article Information
G. F. K. Tay, M. F. Tachie

Department of Mechanical and Manufacturing Engineering, University of Manitoba, Winnipeg, MB, R3T 5V6, Canada

D. C. S. Kuhn1

Department of Mechanical and Manufacturing Engineering, University of Manitoba, Winnipeg, MB, R3T 5V6, Canadadkuhn@cc.umanitoba.ca

1

Corresponding author.

J. Fluids Eng 131(6), 061205 (May 15, 2009) (12 pages) doi:10.1115/1.3112389 History: Received September 04, 2008; Revised February 08, 2009; Published May 15, 2009

## Abstract

This paper reports an experimental investigation of the effects of wall roughness and favorable pressure gradient on low Reynolds number turbulent flow in a two-dimensional asymmetric converging channel. Flow convergence was produced by means of ramps (of angles 2 deg and 3 deg) installed on the bottom wall of a plane channel. The experiments were conducted over a smooth surface and over transitionally rough and fully rough surfaces produced from sand grains and gravel of nominal mean diameters 1.55 mm and 4.22 mm, respectively. The dimensionless acceleration parameter was varied from $0.38×10−6$ to $3.93×10−6$ while the Reynolds number based on the boundary layer momentum thickness was varied from 290 to 2250. The velocity measurements were made using a particle image velocimetry technique. From these measurements, the distributions of the mean velocity and Reynolds stresses were obtained to document the salient features of transitionally and fully rough low Reynolds number turbulent boundary layers subjected to favorable pressure gradient.

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## Figures

Figure 10

Effects of surface roughness on the mean velocity defect, turbulent intensities, and the Reynolds shear stress. The vertical lines in (b), (d), (f), and (h) correspond to the edge of the roughness sublayer.

Figure 11

Effects of surface roughness on the stress ratios. (a) ρuv=−uv/(u2v2)0.5, (b) v2/u2, (c) −uv/u2, and (d) −uv/v2. The symbols are as in Fig. 1.

Figure 12

Effects of combined FPT and surface roughness on the mean velocity, turbulent intensities, and the Reynolds shear stress

Figure 13

Effects of combined FPG and surface roughness on the stress ratios. The symbols are as in Fig. 1.

Figure 1

Schematic of the test section: (a) test channel showing the converging section and the three measurement planes where data were acquired; (b) a three-dimensional view of the ramp used to produce the converging section; W=179 mm is the internal width of the test channel, and α=2 deg or 3 deg Is the angle of the ramp. In (a), P denotes measurement plane and L defines the exact x-location where profiles were extracted in a given plane.

Figure 9

Effects of FPG on the turbulent intensities and Reynolds shear stress normalized by (Uτ,h∗), and correlation coefficient over the smooth surface ((a), (c), (e), and (g)) and sand grain roughness ((b), (d), (f), and (h))

Figure 2

Profiles of boundary layer parameters. Symbols: ○, SMα2U0.25; ●, SMα2U0.50; ◑, SMα3U0.25; ⊕, SMα3U0.50; ◻, SGα2U0.25; ◼, SGα2U0.50; ◨, SGα3U0.25, ⊞, SGα3U0.50; △, GVα2U0.25; ▲, GVα2U0.50; ◮, GVα3U0.25; and △+, GVα3U0.50. Lines are for visual aid only.

Figure 3

Mean velocity profiles over the smooth- and rough-walls in the inner coordinates

Figure 4

Distributions of the mean velocity and mean velocity defect over the smooth-wall and the sand grain roughness. The numbers in parentheses correspond to the value of Reθ for the particular test conditions.

Figure 5

Turbulent intensities and Reynolds shear stress over the smooth-wall and sand grain

Figure 6

Distributions of the Reynolds stresses and stress ratios over the smooth surface compared with DNS from Ref. 31

Figure 7

Effects of FPG on the distributions of the mean velocity and the mean velocity defect over the smooth surface ((a), (c), and (e)) and sand grain roughness ((b), (d), and (f)) in the outer coordinates

Figure 8

Effects of FPG on the distributions of the turbulent intensities and Reynolds shear stress over the smooth surface ((a), (c), and (e)) and sand grain roughness ((b), (d), and (f)) in the outer coordinates

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