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TECHNICAL PAPERS

# Scaling of the Wall Pressure Field Around Surface-Mounted Pyramids and Other Bluff Bodies

[+] Author and Article Information
Robert Martinuzzi

Department of Mechanical and Manufacturing Engineering, University of Calgary, Calgary, AB, T2N 1N4, Canada

Mazen AbuOmar

Stantec Consulting Ltd., 3260 Devon Drive, Windsor, ON, N8X 4L4, Canada

Eric Savory

Department of Mechanical and Materials Engineering, University of Western Ontario, London, ON, N6A 5B9, Canada

J. Fluids Eng 129(9), 1147-1156 (Mar 20, 2007) (10 pages) doi:10.1115/1.2754325 History: Received September 06, 2006; Revised March 20, 2007

## Abstract

The turbulent flow around square-based, surface-mounted pyramids, of height $h$, in thin and thick boundary layers was experimentally investigated. The influence of apex angle $ζ$ and angle of attack $α$ was ascertained from mean surface flow patterns and ground plane pressure measurements taken at a Reynolds number of $3.3×104$ based on $h$. For both boundary layer flows, it was found that the normalized ground plane pressure distributions in the wakes of all the pyramids for all angles of attack may be scaled using an attachment length $(Xa′)$ measured from the upstream origin of the separated shear layer to the near-wake attachment point on the ground plane. It was also shown that this scaling is applicable to data reported in the literature for other bluff body shapes, namely, cubes, cones, and hemispheres. The ground plane pressure coefficient distributions in the upstream separated flow region, for all the shapes and angles of attack examined, were found to collapse onto two curves by scaling their streamwise location using a length scale $(Xu)$, which is a function of the frontal projected width of the body $(w′)$ and the height of the body. These two curves were for cases where $δ∕h<1$ (“thin” boundary layer) or $δ∕h≥1$ (“thick” boundary layer), where $δ$ is the oncoming boundary layer thickness. Further work is required to provide a more detailed statement on the influence of boundary layer thickness (or state) on the upstream pressure field scaling.

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Copyright © 2007 by American Society of Mechanical Engineers
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## Figures

Figure 1

Experimental setup and geometry

Figure 2

Mean velocity, U∕U∞, and turbulence intensity, u′∕U∞, profiles of approach flow in a thick boundary layer at X=17h and X=18h as well as X=21h (downstream of obstacle) as measured prior to placement of obstacle with apex at X=20h. Power-law fit is provided for X=18h(U∞=10m∕s)

Figure 3

Oil-film flow patterns around pyramid ζ=60deg for α=0deg in thin boundary layer (Re=3.3×104)

Figure 4

(a)Cp and Cprms contours around pyramid ζ=60deg at α=0deg and Re=3.3×104 in thin boundary layer and (b) profiles along different sections labeled in (a). Letters correspond to flow structures in Fig. 3.

Figure 5

Oil-film flow patterns around pyramid ζ=60deg and α=0deg in thick boundary layer

Figure 6

(a)Cp and Cprms contours around pyramid ζ=60deg at α=0deg and Re=3.3×104 in thick boundary layer and (b) profiles along different sections labelled in (a). Letters correspond to flow structures in Fig. 5.

Figure 7

Oil-film picture for pyramid ζ=90deg for α=0deg in (a) thin boundary layer and (b) thick boundary layer (Re=3.3×104)

Figure 8

Oil-film flow pattern for pyramid ζ=60deg in thin boundary layer at (a)α=22.5deg and (b)α=45deg

Figure 9

Schematic representation of the more pertinent length scales in relation to the main topological features and geometric parameters

Figure 10

Cp distribution along z∕h=0, with position scaled using length of separated flow region Xs, for the bluff bodies in (a) thin boundary layer and (b) thick boundary layer (T is used to indicate thick boundary layer data)

Figure 11

Upstream Cp distribution along z∕h=0 with position scaled using Xu for bluff bodies in (a) thin boundary layer and (b) thick boundary layer

Figure 12

Ground plane pressure distribution downstream of the bluff bodies, C¯p=[(Cp−Cpmin)∕(Cpmax−Cpmin)], with location scaled by Xa in (a) thin boundary layer and (b) thick boundary layer

Figure 13

Ground plane pressure distribution downstream of the bluff bodies, C¯p=[(Cp−Cpmin)∕(Cpmax−Cpmin)], with location scaled by Xa′ in (a) thin boundary layer and (b) thick boundary layer

Figure 14

Ground plane pressure distribution, C¯p=[(Cp−Cpmin)∕(Cpmax−Cpmin)], downstream of all the bodies in all the boundary layers, with location scaled by (a)Xa and (b)Xa′

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