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TECHNICAL PAPERS

PIV Study of Shallow Open Channel Flow Over d- and k-Type Transverse Ribs

[+] Author and Article Information
M. F. Tachie

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

K. K. Adane

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

J. Fluids Eng 129(8), 1058-1072 (Mar 13, 2007) (15 pages) doi:10.1115/1.2746910 History: Received November 16, 2006; Revised March 13, 2007

A particle image velocimetry was used to study shallow open channel turbulent flow over d-type and k-type transverse ribs of square, circular, and semi-circular cross sections. The ratio of boundary layer thickness to depth of flow varied from 50% to 90%. The mean velocities and turbulent quantities were evaluated at the top plane of the ribs to characterize interaction between the cavities and overlying boundary layer. It was found that the overlying boundary layer interacts more strongly with k-type cavities than observed for d-type cavities. The profiles of the mean velocities and turbulent statistics were then spatially averaged over a pitch, and these profiles were used to study the effects of rib type and cross section on the flow field. The mean velocity gradients were found to be non-negligible across the boundary layer, and the implications of this observation for momentum transport, eddy viscosity, and mixing length distributions are discussed. The results show that the skin friction coefficient, Reynolds stresses and mixing length distributions are independent of rib cross section for d-type. For the k-type ribs, significant variations in skin friction coefficient values, mean flow, and turbulence fields are observed between square ribs and circular/semi-circular ribs.

Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) A schematic of experimental setup and coordinate system; (b) side view of test section and semi-circular ribs, do denotes the virtual origin; (c) circular ribs; (d) square ribs. All dimensions are in mm; k(=6mm) is rib height and λ is the pitch.

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Figure 2

(a) and (b) are, respectively, mean velocity profiles in outer and inner coordinates; (c) and (d) are turbulent intensities and Reynolds shear stress normalized by freestream velocity and friction velocity. Error bars in this and subsequent figures represent measurement uncertainty at 95% confidence level. In (b) dashed line: U+=y+; solid line: U+=2.44y++5.0. Symbols in (c) and (d) are 엯: u; ◻: v; and ▵: −uv¯. Open symbols represent present data and solid symbols represent previous LDA data from (12).

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Figure 3

Mean and turbulent quantities obtained over d-type square ribs using different interrogation area sides in pixels: 32×32: 엯; 32×16 ★. Note that the horizontal axes are staggered.

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Figure 4

Streamlines inside cavities and immediately above ribs. (a) d-type circular; (b) k-type circular; (c) d-type square; (d) k-type square. In (b) and (d), s and r, respectively, denote separation point and reattachment point.

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Figure 5

Variation of mean velocities (a, c), turbulent intensities (b, d) and momentum fluxes (e, f) at the top plane of ribs (y∕k=0). d-type: semi-circular (SC): ▴; circular (RD): ●; square (SQ): ∎; Kameda : ☆. k-type: SC: ▵; RD: 엯; SQ: ◻; Kameda : ★. Note that the horizontal axes are staggered.

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Figure 6

Mean velocity profiles at rib centers, various x-locations in the cavity and spatial averaged profiles (SAvg). (a) comparison among d-type; (b) among k-type; (c) between d-type and k-type. For d-type profiles, SC: ▴; RD: ●; SQ: ∎ and SA, SB and SC, respectively, correspond to x′∕λ=0, 0.50 and 0.75. For k-type profiles, SC: ▵; RD: 엯; SQ: ◻ and SA, SB, SC and SD, respectively, correspond to x′∕λ=0, 0.25, 0.50 and 0.75. Symbols in (c) are: d-type SC (averaged: ▴, rib center: half-closed triangle); k-type SC (averaged: ▵, rib center: right-filled triangle); d-type RD (averaged: ●, rib center: ◓); k-type RD (averaged: 엯, rib center: ◑); d-type SQ (averaged: ∎, rib center: half-closed square); k-type SQ (averaged: ◻, rib center: ◨). Note that the horizontal axes are staggered.

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Figure 7

Wall-normal mean velocity profiles at rib centers, various x-locations in the cavity and averaged profiles (SAvg). (a) comparison among d-type; (b) among k-type; (c) between d-type and k-type. Symbols and notations are as in Fig. 6. Note that the horizontal axes are staggered.

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Figure 8

Averaged velocity gradients across the boundary layer. (a) ∂V∕∂y [SC: ▴; RD: ●; SQ: ∎] and ∂U∕∂x [SC: ▵; RD: 엯; SQ: ◻] across d-type; (b) ∂V∕∂y and ∂U∕∂x across k-type, symbols are as in (a); (c) ∂U∕∂y [SC: ▴; RD: ●; SQ: ∎] and ∂V∕∂x [SC: ▵; RD: 엯; SQ: ◻] across d-type; (d) ∂U∕∂y and ∂V∕∂x across k-type, symbols are as in (c).

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Figure 9

Mean velocity profiles at rib centers and spatial averaged profiles in inner coordinates. Symbols are as in Fig. 6. Solid lines are power law fits (Eq. 2); dashed lines are log law for a smooth surface (U+=2.44lny++5), dotted lines are U+=2.44lny++5−ΔU+, where ΔU+ is the roughness shift.

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Figure 10

Profiles of streamwise turbulent intensity at rib centers, various x-locations in the cavity and spatial averaged profiles (SAvg). (a) comparison among d-type; (b) among k-type; (c) between d-type and k-type. Symbols and notations are as in Fig. 6. Note that the horizontal axes are staggered.

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Figure 11

Profiles of (a) wall-normal turbulent intensity and (b) Reynolds shear stress at rib centers and averaged profiles. Symbols and notations are as in Fig. 6. Note that the horizontal axes are staggered.

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Figure 12

(a) Profiles of turbulent intensities: (a), (b); and Reynolds shear stress (c) in inner coordinates. Distribution of stress ratios: (d), (e), (f). Symbols as in Fig. 6, ★ denotes previous LDA data from (12).

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Figure 13

Various terms in the x-momentum equations. (a) d-type circular ribs; (b) k-type circular ribs; (c) d-type square ribs; (d) k-type square ribs. Symbols are as follows: Convective: ∎; Reynolds stress: 엯; Viscous: barred diamond; Pressure: ▵.

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Figure 14

Various terms in the y-momentum equations. (a) d-type circular ribs; (b) k-type circular ribs; (c) d-type square ribs; (d) k-type square ribs. Symbols are as follows: Convective: ∎; Reynolds stress: 엯; Viscous: barred diamond; Pressure: ▵.

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Figure 15

Distribution of eddy viscosity (a, b) and mixing length (c, d) across the boundary layer. Symbols and notations are as in Fig. 6. ★ in (c) represents previous boundary layer data over wire mesh; solid and dash lines in (b) and (c) represent, respectively, previous open channel data over wire mesh and sand grains.

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