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On pressure invariance, wake width and drag prediction of a bluff body in confined flow

Published online by Cambridge University Press:  10 March 2009

W. W. H. YEUNG
W. W. H. YEUNG*
Affiliation:
School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore
*
†Email address for correspondence: mwhyeung@ntu.edu.sg
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Abstract

In the present investigation, the form drag on a bluff body in confined flow is studied. From the observation of invariance in pressure distribution between a disk and a flat plate normal to free upstream in unconfined flow, a linear relation linking the drag to the base pressure is derived when the potential-flow model by Parkinson & Jandali (J. Fluid Mech., vol. 40, 1970, p. 577) is incorporated. A theoretical wake width deduced from well-documented experimental data for a disk is proposed such that the wake Strouhal number is independent of inclination. This width, when combined with the momentum equation and solved simultaneously with the aforementioned linear equation, leads to realistic predictions of the drag and the base pressure. The method is consistent when applied to a cone of arbitrary vertex angle, a circular cylinder at subcritical Reynolds numbers and a sphere at subcritical as well as supercritical Reynolds numbers. The case of the inclined disk is also discussed. As the pressure distribution is invariant under wall constraint, analytical expressions for the effect of confinement on the loading of bluff bodies are derived and found to provide the correct trend of experimental data.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 622 , 10 March 2009 , pp. 321 - 344
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Achenbach, E. 1968 Distribution of local pressure and skin friction around a circular cylinder in cross-flow up to Re = 5 × 106. J. Fluid Mech. 34, 625–639.Google Scholar
Achenbach, E. 1972 Experiments on the flow past spheres at very high Reynolds numbers. J. Fluid Mech. 54, 565–575.CrossRefGoogle Scholar
Achenbach, E. 1974 The effects of surface roughness and tunnel blockage on the flow past spheres. J. Fluid Mech. 65, 113–125.CrossRefGoogle Scholar
Apelt, C. J. & West, G. S. 1975 The effects of wake splitter plates on bluff-body flow in the range 104 < R < 5 × 104. Part 2. J. Fluid Mech. 71, 145–160.CrossRefGoogle Scholar
Awbi, H. B. & Tan, S. H. 1981 Effect of wind-tunnel walls on the drag of a sphere. J. Fluids Engng 103, 461–465.CrossRefGoogle Scholar
Bearman, P. W. 1967 On vortex street wakes. J. Fluid Mech. 28, 625–841.Google Scholar
Bearman, P. W. 1971 An investigation of the forces on flat plates normal to a turbulent flow. J. Fluid Mech. 46, 177–198.Google Scholar
Bearman, P. W. 1998 Developments in the understanding of bluff body flows. JSME B 41, 103–114.Google Scholar
Bearman, P. W. & Fackrell, J. E. 1975 Calculation of two-dimensional and axi-symmetric bluff-body potential flow. J. Fluid Mech. 72, 229–241.CrossRefGoogle Scholar
Calvert, J. R. 1967 a Experiments on the low-speed flow past cones. J. Fluid Mech. 27, 273–289.CrossRefGoogle Scholar
Calvert, J. R. 1967 b Experiments on the flow past an inclined disk. J. Fluid Mech. 29, 691–703.CrossRefGoogle Scholar
Calvert, J. R. 1972 Some experiments on the flow past a sphere. Aeronaut. J. 76, 248–250.Google Scholar
Carmody, T. 1964 Establishment of the wake behind a disk. Trans. ASME: J. Fluids Engng 86, 869–882.CrossRefGoogle Scholar
Durbin, P. A. & Hunt, J. C. R. 1980 On surface pressure fluctuations beneath flow round bluff bodies. J. Fluid Mech. 100, 161–184.CrossRefGoogle Scholar
Eppler, R. 1954 Contributions to the theory and applications of discontinuous flows. J. Ration. Tech. Anal. 3, 591–644.Google Scholar
Fage, A. 1937 Experiments on a sphere at critical Reynolds numbers. Aero. Res. Counc. Rep. and Memo. no. 1766 (see Goldstein S. 1965 Modern developments in fluid dynamics, vol. 2, 497).Google Scholar
Fage, A. & Johansen, F. C. 1927 On the flow of air behind an inclined flat plate of infinite span. Proc. R. Soc. Lond. A 116, 170–197.Google Scholar
Fail, R., Lawford, J. A. & Eyre, R. C. W. 1957. Low-speed experiments on the wake characteristics of flat plates normal to an air stream. Aero. Res. Counc. R. & M. no. 3120.Google Scholar
Flachsbart, O. 1927. Neue Untersuchungen über den Luftwiderstand con Kugeln. Physikalische Zeitschrift, 28, 461–469 (see NACA TM 475).Google Scholar
Fornberg, B. 1988. Steady viscous flow past a sphere at high Reynolds numbers. J. Fluid Mech. 190, 471–489.Google Scholar
Garabedian, P. R. 1956 Calculation of axially symmetric cavities and jets. Pac. J. Math. 6, 611–684.CrossRefGoogle Scholar
Gaster, M. & Ponsford, P. J. 1984. The flows over tapered flat plates normal to the stream. Aeronaut. J. 88, 206–212.CrossRefGoogle Scholar
Hoerner, S. F. 1965. Fluid-Dynamic Drag. Hoerner Fluid Dynamics.Google Scholar
Hoffman, J. 2006 Adaptive simulation of the subcritical flow past a sphere. J. Fluid Mech. 568, 77–88.CrossRefGoogle Scholar
Holst, H. 1984. Wind tunnel wall interference in closed, ventilated and adaptive test sections. NASA CP-2319, 61–78.Google Scholar
Hunt, J. C. R. & Eames, I. 2002 The disappearance of laminar and turbulent wakes in complex flows. J. Fluid Mech. 457, 111–132.Google Scholar
Lee, B. E. 1975 The effect of turbulence on the surface pressure field of a square prism. J. Fluid Mech. 69, 263–282.Google Scholar
Macha, J. M., Buffington, R. J. & Henfling, J. F. 1991 Slotted-wall blockage corrections for disks and parachutes. J. Aircr. 28, 592–597.CrossRefGoogle Scholar
Maskell, E. C. 1963 A theory of the blockage effects on bluff bodies and stalled wings in a closed wind tunnel. Aero. Res. Counc. R. & M. no. 3400.Google Scholar
Masliyah, J. H. & Epstein, N. 1970 Numerical study of steady flow past spheroids. J. Fluid Mech. 44, 493–512.CrossRefGoogle Scholar
Maxworthy, T. 1969 Experiments on the flow around a sphere at high Reynolds numbers. J. Appl. Mech., Trans. ASME E 36, 598–607.CrossRefGoogle Scholar
McKeon, R. J. & Melbourne, W. H. 1971 Wind tunnel blockage effects and drag on bluff bodies in a rough wall boundary layer. In Proceedings of the Third International Conference of Wind Effects on Buildings and Structures, Tokyo, Japan, 263–272.Google Scholar
Miau, J. J. & Liu, T. W. 1990 Vortex flowmeter designed with wall pressure measurement. Rev. Sci. Instrum. 61 (10), 2676–2681.Google Scholar
Möller, W. 1938 Experimentelle Untersuchung zur Hydromechanik der Kugel. Phys. Z. 39, 57–80.Google Scholar
Morel, T. & Bohn, M. 1980 Flow over two circular disks in tandem. Trans. ASME I: J. Fluids Engng 102, 104–111.Google Scholar
Parkinson, G. V. & Jandali, T. 1970 A wake source model for bluff body potential flow. J. Fluid Mech. 40, 577–594.CrossRefGoogle Scholar
Pitter, R. L., Pruppacher, H. R. & Hamielec, A. E. 1973 A numerical study of viscous flow past thin oblate spheroid at low and intermediate Reynolds numbers. J. Atmos. Sci., 30, 125–134.Google Scholar
Platt, R. C. 1937 Turbulence factors of N.A.C.A. wind tunnels as determined by sphere tests. NACA Report 558.Google Scholar
Pucher, P. 1978 Experimetelle Untersuchung an Würfeln und Quadern zur Bestimmung des Versperrungseinflusses in Windkanälen mit offener Meßstrecke. PhD thesis, TU MÜnchen, (see Kramer, C., Gerhardt, H. J. & Regenscheit, B. J. Wind Engng Ind. Aerodyn. 16 (1984), 225–264).Google Scholar
Richter, A. & Naudascher, E. 1976 Fluctuating forces on a rigid cylinder in confined flow. J. Fluid Mech. 78, 561–576.CrossRefGoogle Scholar
Roberts, B. 1980 Drag and pressure distribution on a family of porous, slotted disks. J. Aircr. 17, 393–401.CrossRefGoogle Scholar
Roshko, A. 1954 On the drag and shedding frequency of two-dimensional bluff bodies. NACA TN 3169.Google Scholar
Roshko, A. 1961 Experiments on the flow past a circular cylinder at very high Reynolds number. J. Fluid Mech. 10, 345–356.Google Scholar
Roshko, A. 1993 Perspectives on bluff body aerodynamics. J. Wind Engng Ind. Aerodyn. 49, 79–100.Google Scholar
Roshko, A. & Lau, J. C. 1965 Some observation on transition and reattachment of a free shear layer in incompressible flow. In Proceedings of the Heat Transfer and Fluid Mechanics Institute, 157.Google Scholar
Saunders, W. S. 1966 Apparatus for reducing linear and lateral wind resistance in a tractor–trailer combination vehicle. U.S. Patent No. 3241876.Google Scholar
Schouveiler, L. & Boudaoud, A. 2006 The rolling up of sheets in a steady flow. J. Fluid Mech. 563, 71–80.CrossRefGoogle Scholar
Shaw, T. L. 1971 Wake dynamics of two-dimensional structures in confined flows. In 14th Congress of International Association of Hydraulic Research, vol. 2, Paris, France (see Richter A. & Naudascher E. 1976, J. Fluid Mech. 78, 561–576).Google Scholar
Simmons, J. E. L. 1977. Similarities between two-dimensional and axi-symmetric vortex wakes. Aeronaut. Q. 28, 15–20.CrossRefGoogle Scholar
Sumner, D. & Brundrett, E. 1995. Testing three-dimensional bluff-body models in a low-speed two-dimensional adaptive wall test section. Trans. ASME: J. Fluids Engng 117, 546–551.Google Scholar
Tomboulides, A. & Orszag, S. A. 2000 Numerical investigation of transitional and weak turbulent flow past a sphere. J. Fluid Mech. 416, 45–73.CrossRefGoogle Scholar
Yeung, W. W. H. 2008 Self-similarity of confined flow past a bluff body. J. Wind Engng Ind. Aerodyn. 96, 369–388.Google Scholar
Yeung, W. W. H. & Parkinson, G. V. 2000. Base pressure prediction in bluff-body potential-flow models. J. Fluid Mech. 423, 381–394.Google Scholar