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Research Papers: Fundamental Issues and Canonical Flows

On the Relationships Among Strouhal Number, Pressure Drag, and Separation Pressure for Blocked Bluff-Body Flow

[+] Author and Article Information
W. W. H. Yeung

Yeung's Consultancy, #04-352 Blk 281, Choa Chua Kang Avenue 3, Singapore 680281, Singaporewwhyeung@yahoo.com.sg

J. Fluids Eng 132(2), 021201 (Feb 03, 2010) (10 pages) doi:10.1115/1.4000575 History: Received November 24, 2008; Revised October 13, 2009; Published February 03, 2010; Online February 03, 2010

Abstract

Strouhal number, pressure drag, and separation pressure are some of the intrinsic parameters for investigating the flow around a bluff-body. An attempt is made to formulate a relationship involving these quantities for flow around a two-dimensional bluff section of various shapes in a confined environment such as a wind tunnel. It includes (a) establishing a relation between the Strouhal number and a modified Strouhal number by a theoretical wake width and (b) incorporating this wake width into a momentum equation to determine the pressure drag. Comparisons have been made with the experimental data, a theoretical prediction (for unconfined flow), and an empirical proposal in literature to indicate that the present methodology is appropriate. Together with its extension to axisymmetric bodies, the current method is able to provide proper limits to the experimental data for a rectangular flat-plate of various width-to-span ratios. In addition, if the separation pressure is given, then the Strouhal number is inversely proportional to the drag coefficient, being comparable to a proposal based on statistical results. Finally, through an example, it is also demonstrated how one of these three parameters may be reasonably estimated from the measured values of the other two.

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Figures

Figure 1

Relationships of Scd, k, and z. (a) z=0: — —: Eq. 1; ⋯: Eq. 2; −•−: Eq. 3; —— : Eq. 8. (b) S∗∗=0.15: — —: Eq. 7 with z=25% and α=90 deg; and ——: Eq. 8.

Figure 2

Definition sketch for (a) an inclined flat-plate and (b) rectangular section in a wind tunnel.

Figure 3

Variations in (a) Strouhal numbers with angle of incidence and (b) Scd with k for flat-plate in unconfined flow. (a) ●: S from Fage and Johansen (19); +: S∗∗ from Eq. 4 with z=0. (b) ●: from Fage and Johansen (19), ◇: from Roshko (3); ◻: from Bearman and Trueman (9); — —: Eq. 1; ⋯: Eq. 2; and ——: Eq. 8.

Figure 4

Variations in Strouhal numbers for a rectangular section with blockage ratio in (a) and (b) and with d/h in (c). (a) S from Awbi (21). (b) and (c) S∗∗ from Eq. 5 with α=90 deg; ○: d/h=0.2, +: 0.5, △: 1.0, ◻: 1.5; and ◇: d/h=0.03 from Fage and Johansen (19).

Figure 5

Variation in Scd with k for a rectangular prism in confined flow from Awbi (21). (a) d/h=0.2, (b) 0.5, and (c) 1.0; ●: z=5%, ◇: z=25%; — —: Eq. 1; ⋯: Eq. 2; −•− : Eq. 7; and ——: Eq. 8.

Figure 6

Flow around a symmetrical wedge in a wind tunnel. (a) Definition sketch. (b) Variations in Strouhal numbers with apex angle. ○: S from Okamoto (22), +: S∗∗ from Eq. 10; ×: S from Simmons (7), and ◻: S∗∗ from Eq. 10. (c) Variation in Scd with k. ● (22): with 15 deg≤δ≤180 deg; △ (7): with δ=60 deg; ◇: Roshko (3) with δ=90 deg; — —:Eq. 1; ⋯: Eq. 2; and ——: Eq. 8.

Figure 7

Variations in (a) Strouhal numbers with blockage ratio, (b)Scd with k for a 60 deg wedge in confined flow from Ramamurthy and Ng (23). (a) ○: S, +: S∗∗ from Eq. 12 with β=60 deg. (b) ●: z=14%; ◇: z=28%; — —: Eq. 1; ⋯: Eq. 2; ——: Eq. 13 with z=14%; and −•− : Eq. 13 with z=28%.

Figure 8

Flow past a circular cylinder in confinement. (a) Definition sketch. (b) Pressure distributions from Parkinson and Hameury (25). ○: z=8.3%, △: 13.8%, +: 25%, and ×: 33.3%.

Figure 9

Variations in (a) Strouhal numbers with blockage ratio, (b) and (c) Scd with k for a circular cylinder. — —: Eq. 1; ⋯: Eq. 2. (a) ○: S from Kong (26), +: S∗∗ from Eq. 15 with βs=80 deg. (b) ◇: Roshko (3), ●: Roshko (28), +: Norberg (27), ▽: Bearman (6), and ——: Eq. 8. (c) ●: z=8.3%, ◻: z=33.3% from Parkinson and Hameury (25) and Kong (26), ——: Eq. 16 with βs=80 deg and z=8.3%, and −•−: Eq. 16 with βs=80 deg and z=33.3%.

Figure 10

Flow past a normal disk in confinement. (a) Definition sketch. (b) Variations in Strouhal numbers with blockage ratio z. ○: S from Miau and Liu (29), +: S∗∗ from Eq. 19.

Figure 11

Unconfined flow past an axisymmetric bluff-body. (a) Definition sketch of the flow past a sphere. (b) Variations in product of Scd with k. Disk: × from Fail (30), ◻ from Calvert (14) and Hoerner (17), ⋯: Eq. 20 with z=10%; ——: Eq. 21; sphere: △ from Kim and Durbin (33), ● from Achenbach (31-32), −•−: Eq. 24; and — —: Eq. 1.

Figure 12

Scd versus k for unconfined flow past a rectangular flat-plate of various aspect ratios. ×: aspect ratio=1, +: 2, ◇: 5, △: 10, ◻: 20, from Fail (30), ○: two-dimensional from Fage and Johansen (19), ——: Eq. 8, and — —: Eq. 21.

Figure 13

Variation in Strouhal number with drag coefficient of different two-dimensional bluff-bodies. ×: supercritical blunt bodies, △ : structural shapes, ◻, ○: circular cylinder and plate, ●: stalled RAE airfoil from Hoerner (17), ▽: circular cylinder at Re=2.13×105 from Bearman (6), ——: Eq. 25, — —: Eq. 26, −•−: Eq. 27.

Figure 14

Prediction of Strouhal number from pressure drag and separation pressure for a circular disk at various blockage ratios. (a) ×: cd, ◻: −cps from Melbourne (35) and (b) ○: S from Miau and Liu (29); +: from Eq. 20.

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