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Research Papers: Fundamental Issues and Canonical Flows

An Experimental Investigation of Aspect Ratio and Incidence Angle Effects for the Flow Around Surface-Mounted Finite-Height Square Prisms

[+] Author and Article Information
J. F. McClean

Department of Mechanical Engineering,
University of Saskatchewan,
57 Campus Drive,
Saskatoon, Saskatchewan, CanadaS7N 5A9

D. Sumner

Department of Mechanical Engineering,
University of Saskatchewan,
57 Campus Drive,
Saskatoon, Saskatchewan, CanadaS7N 5A9
e-mail: david.sumner@usask.ca

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received October 25, 2012; final manuscript received February 28, 2014; published online June 2, 2014. Editor: Malcolm J. Andrews.

J. Fluids Eng 136(8), 081206 (Jun 02, 2014) (10 pages) Paper No: FE-12-1540; doi: 10.1115/1.4027138 History: Received October 25, 2012; Revised February 28, 2014

The flow around a surface-mounted finite-height square prism was investigated using a low-speed wind tunnel. The experiments were conducted at a Reynolds number of Re = 7.3 × 104 for prism aspect ratios of AR = 3, 5, 7, 9, and 11 and incidence angles from α = 0 deg to 45 deg. The thickness of the boundary layer on the ground plane relative to the side length was δ/D = 1.5. Measurements of the vortex shedding frequency were made with a single-component hot-wire probe, and measurements of the mean drag and lift forces were obtained with a force balance. For all aspect ratios and incidence angles, the mean drag coefficient and Strouhal number were lower than those of an infinite prism, while the mean lift coefficient was of nearly similar magnitude. As the aspect ratio was increased from AR = 3 to 11, the force coefficients and Strouhal number slowly approached the infinite-square-prism data. The mean drag coefficient and Strouhal number for the finite prism were less sensitive to changes in incidence angle compared to the infinite square prism. The critical incidence angle, corresponding to minimum mean drag coefficient, minimum (most negative) mean lift coefficient, and maximum Strouhal number, shifted to a higher incidence angle compared to the infinite square prism, with values ranging from αcritical = 15 deg to 18 deg; this shift was greatest for the prisms of higher aspect ratio. The behavior of the force coefficients and Strouhal number for the prism of AR = 3 was distinct from the other prisms (with lower values of mean drag coefficient and mean lift coefficient magnitude, and a different Strouhal number trend), suggesting the critical aspect ratio was between AR = 5 and AR = 3 in these experiments. In the wall-normal direction, the power spectra for AR = 11 and 9 tended to have weaker and/or more broad-banded vortex shedding peaks near the ground plane and near the free end at α = 0 deg and 15 deg. For AR = 7 to 3, well-defined vortex shedding peaks were detected along the entire height of the prisms. For AR = 11 and 9, at α = 30 deg and 45 deg, vortex shedding peaks were absent in the power spectra in the upper part of the wake.

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Figures

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Fig. 2

Schematics of the main flow patterns for an infinite square prism at Re ≈ 104 using the classification systems in the literature: (a) example of the “perfect separation type (symmetric)” flow pattern [5], “subcritical” flow regime [18], or “leading edge separation” mode [10]; (b) example of the “perfect separation type (asymmetric)” flow pattern [5] or “separation bubble” mode [10,11], showing what occurs at the critical incidence angle; (c) example of the “reattachment flow type” flow pattern [5], “supercritical” flow regime [18], “attached flow” mode [10], or “separation” flow pattern [11]; and (d) example of the “wedge type” flow pattern [5], “wedge” flow regime [18], “attached flow” mode [10], or “boundary-layer attached” flow pattern [11]

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Fig. 1

Schematic of the flow around a surface-mounted finite-height square prism partially immersed in a flat-plate boundary layer: (a) top view, (b) side view, and (c) main flow features for a prism at zero incidence angle with an aspect ratio greater than the critical aspect ratio

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Fig. 3

Boundary layer mean streamwise velocity profile on the ground plane at the location of the finite square prism (measured with the prism removed)

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Fig. 6

Power spectra of the wake velocity fluctuations obtained at mid-height (z/H = 0.5) as a function of incidence angle: (a) AR = 11, (b) AR = 9, (c) AR = 7, (d) AR = 5, and (e) AR = 3. Each spectrum is the average of 100 individual spectra. The vertical scale is arbitrary but the same scale is used for each spectrum.

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Fig. 9

Power spectra along the height (varying wall-normal position, z/D) of the finite square prism, for AR = 3, obtained at x/D = 5, y/D = −2.5: (a) α = 0 deg; (b) α = 15 deg; (c) α = 30 deg; and (d) α = 45 deg. Each spectrum is the average of 100 individual spectra. The vertical scale is arbitrary but the same scale is used for each spectrum.

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Fig. 7

Power spectra along the height (varying wall-normal position, z/D) of the finite square prism, for AR = 11, obtained at x/D = 5, y/D = − 2.5: (a) α = 0 deg; (b) α = 15 deg; (c) α = 30 deg; and (d) α = 45 deg. Each spectrum is the average of 100 individual spectra. The vertical scale is arbitrary but the same scale is used for each spectrum.

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Fig. 8

Power spectra along the height (varying wall-normal position, z/D) of the finite square prism, for AR = 7, obtained at x/D = 5, y/D = −2.5: (a) α = 0 deg; (b) α = 15 deg; (c) α = 30 deg; and (d) α = 45 deg. Each spectrum is the average of 100 individual spectra. The vertical scale is arbitrary but the same scale is used for each spectrum.

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Fig. 4

Data (based on side length, D) for a surface-mounted finite-height square prism as a function of incidence angle, Re = 7.2 × 104: (a) mean drag coefficient; (b) mean lift coefficient; and (c) Strouhal number at mid-height. Present study: ▪, AR = 3; •, AR = 5; ▲, AR = 7; ▼, AR = 9; ♦, AR = 11. Infinite square prism data: □, Re = 3.7 × 104 [5]; ○, Re = 5.6 × 104 [5]; △, Re = 2.2 × 104 to 4.4 × 104 [6]; ▽ or ·····, Re = 1.3 × 104 [7]; ◇, Re = 4.74 × 104 [4]; ◁, Re = 3.6 × 104 [10]. Finite square prism data: + , AR = 5, Re = 3.3 × 104 to 1.7 × 105, δ/H = 0.7 [25].

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Fig. 5

Data (based on projected width, D′) for a surface-mounted finite square prism as a function of incidence angle, Re = 7.2 × 104: (a) mean drag coefficient; (b) mean lift coefficient; and (c) Strouhal number at mid-height. Symbols as in Fig. 3.

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Fig. 10

Mean velocity vector and in-plane vorticity fields (from PIV experiments) in the vertical symmetry plane above the free end of a surface-mounted finite-height square prism of AR = 9, Re = 4.2 × 104, δ/D = 1.7: (a) α = 0 deg and (b) α = 45 deg. The mean velocity field is based on an ensemble of 1000 instantaneous velocity fields. Experimental setup and flow conditions similar to Ref. [33]. Every third vector is omitted in the x-direction, and every second vector is omitted in the z-direction, for clarity. Dimensionless in-plane mean vorticity levels are shown in gray scale.

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