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Research Papers: Fundamental Issues and Canonical Flows

# PIV Study of Turbulent Flow in Asymmetric Converging and Diverging Channels

[+] Author and Article Information
M. K. Shah

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

M. F. Tachie

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

J. Fluids Eng 130(1), 011204 (Jan 18, 2008) (15 pages) doi:10.1115/1.2829590 History: Received September 11, 2006; Revised September 20, 2007; Published January 18, 2008

## Abstract

An experimental investigation of turbulent flow subjected to variable adverse and favorable pressure gradients in two-dimensional asymmetric channels is reported. The floors of the diverging and converging channels were flat while the roofs of the channels were curved. Adverse pressure gradient flows at $Reh=27,050$ and 12,450 and favorable pressure gradient flow at $Reh=19,280$ were studied. A particle image velocimetry was used to conduct detailed measurements at several planes upstream, within the variable section and within the downstream sections. The boundary layer parameters were obtained in the upper and lower boundary layers to study the effects of pressure gradients on the development of the mean flow on the floor and roof of the channels. The profiles of the mean velocities, turbulence intensities, Reynolds shear stress, mixing length, eddy viscosity, and turbulence production were also obtained to document the salient features of pressure gradient turbulent flows in asymmetric converging and diverging channels.

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## Figures

Figure 1

Experimental setup: (a) converging channel, (b) diverging channel, and (c) P1 to P5 denoted x-y planes in which PIV measurements were made. L1 to L5 correspond to locations where detailed data analysis was performed.

Figure 2

Profiles of the mean velocity and turbulent quantities obtained using the two IAs at the L2 of Test D2: (a) U, (b) u, (c) v, and (d) −uv. Error bars in this and subsequent figures denote measurement uncertainty at 95% confidence level.

Figure 3

Various mean flow parameters: (a) local freestream velocity, (b) displacement thickness, (c) momentum thickness, (d) shape factor, (e) velocity gradient, and (f) acceleration parameter.

Figure 4

Mean quantities in outer coordinates: (a) mean velocity, (b) mean momentum flux, and (c) mean vorticity.

Figure 5

Mean velocity profiles in inner coordinates: (a) L1, (b) L2, (c) L3, (d) L4, (e) L5, and (f) Wake parameter.

Figure 6

Skin friction distribution: (a) Test D1, lower; (b) Test D1, upper; (c) Test D2, lower; (d) Test D2, upper; (e) Test C, lower; (f) Test C, upper. Trend lines are for visual aid only.

Figure 7

Mean velocity defect profiles normalized by friction velocity. Note that in (a) and (b) y by δ; in (c) and (d) y by Δ.

Figure 8

Mean velocity defect profiles normalized by mixed scaling proposed by Zagarola and Smits (1998). Note that in (a) and (b) y by δ; in (c) and (d) y by Δ.

Figure 9

Profiles of turbulence intensities and Reynolds shear stress in outer coordinates: (a) streamwise turbulent intensity, (b) transverse turbulent intensity, and (c) Reynolds shear stress.

Figure 10

Stress ratio profiles: (a) v2∕u2, (b) −uv∕u2, and (c) uv∕v2.

Figure 11

Profiles of turbulence intensities and Reynolds shear stress normalized by friction velocity: (a) streamwise turbulence intensity, lower; (b) streamwise turbulence intensity, upper; (c) trasnverse turbulence intensity, lower; (d) transverse turbulence intensity, upper; (e) Reynolds shear stress, lower; (f) Reynolds shear stress, upper.

Figure 12

Profiles of mixing length and eddy viscosity in outer coordinates (a) mixing length, lower; (b) mixing length, upper; (c) eddy viscosity, lower; (d) eddy viscosity, upper.

Figure 13

Profiles of turbulence production: (a) −uvdU∕dy and (b) −v2dU∕dy

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