Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-10T06:36:03.075Z Has data issue: false hasContentIssue false
  • English
  • Français

Experimental determination of the main features of the viscous flow in the wake of a circular cylinder in uniform translation. Part 1. Steady flow

Published online by Cambridge University Press:  11 April 2006

Madeleine Coutanceau  and
Roger Bouard
Madeleine Coutanceau
Affiliation:
Laboratoire de Mécanique des Fluides, Université de Poitiers, France
Roger Bouard
Affiliation:
Laboratoire de Mécanique des Fluides, Université de Poitiers, France
Get access Rights & Permissions [Opens in a new window]

Abstract

A visualization method is used to obtain the main features of the hydrodynamic field for flow past a circular cylinder moving at a uniform speed in a direction perpendicular to its generating lines in a tank filled with a viscous liquid. Photographs are presented to show the particular fineness of the experimental technique. More especially, the closed wake and the velocity distribution behind the obstacle are investigated; the changes in the geometrical parameters describing the eddies with Reynolds number (5 < Re < 40) and with the ratio λ between the diameters of the cylinder and tank are given. A comparison with existing numerical and experimental results is presented and some remarks are made about the calculation techniques proposed up to the present. The limits of the Reynolds-number range for which the twin vortices exist and adhere stably to the cylinder are determined.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 79 , Issue 2 , 22 February 1977 , pp. 231 - 256
Copyright
© 1977 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Acrivos, A., Leal, L. G., Snowden, D. D. & Pan, F. 1968 Further experiments on steady separated flows past bluff objects. J. Fluid Mech. 34, 25.Google Scholar
Allen, D. N. de G. & Southwell, R. V. 1955 Relaxation methods applied to determine the motion, in two dimensions, of a viscous fluid past a fixed cylinder. Quart. J. Mech. Appl. Math. 8, 129.Google Scholar
Apelt, C. J. 1958 The steady flow of a viscous fluid past a circular cylinder at Reynolds numbers 40 and 44. Aero. Res. Counc. R. & M. no. 3175.Google Scholar
Bourot, J. M., Coutanceau, M. & Moreau, J. J. 1962 Sur l'étude théorique et expérimentale des phénomènes d'orientation présentés par une suspension lamellaire dans un écoulement de Stokes. C.R. Acad. Sci. 255, 1377.Google Scholar
Bourot, J. M. & Moreau, J. J. 1949 Sur les zones d'inégale luminosité observées dans certaines visualisations d'écoulements. C.R. Acad. Sci. 228, 1567.Google Scholar
Chartier, C. 1937 Chronophotogrammétrie plane et stéréoscopique. Ministère de l'Air, Publ. Sci. Tech. no. 114.
Collins, W. M. & Dennis, S. C. R. 1973 Flow past an impulsively started circular cylinder. J. Fluid Mech. 60, 105.Google Scholar
Coutanceau, M. 1962 Etude théorique et expérimentale de l'orientation des particules lamellaires mises en suspension dans un écoulement méridien. Thèse de Doctorat de Troisième Cycle.
Coutanceau, M. 1968 Mouvement d'une sphère dans l'axe d'un cylindre contenant un liquide visqueux. J. Méc. 7, 49.Google Scholar
Coutanceau, M. 1971 Contribution à l'étude théorique et expérimentale de l'écoulement autour d'une sphère qui se déplace dans l'axe d'un cylindre, à faible nombre de Reynolds ou en régime irrotationnel. Thèse de Doctorat d'Etat.
Coutanceau, M. 1972 Sur l'étude expérimentale de l'écoulement engendré par une sphère qui se déplace dans l'axe d'un cylindre au-delà du régime de Stokes. C.R. Acad. Sci. A 274, 853.Google Scholar
Dennis, S. C. R. & Chang, G. Z. 1970 Numerical solutions for steady flow past a circular cylinder at Reynolds numbers up to 100. J. Fluid Mech. 42, 471.Google Scholar
Dennis, S. C. R. & Shimshoni, M. 1965 The steady flow of a viscous fluid past a circular cylinder. Aero. Res. Counc. Current Papers, no. 797.Google Scholar
Dimopoulos, H. G. & Hanratty, T. J. 1968 Velocity gradients at the wall for flow around a cylinder for Reynolds numbers between 60 and 360. J. Fluid Mech. 33, 303.Google Scholar
Dupin, P. & Teissie-Solier, M. 1928 Rev. Gén. Elec. 24, 53.
Fage, A. 1934 Photographs of fluid flow revealed with an ultramicroscope. Proc. Roy. Soc. 144, 381.Google Scholar
Grove, A. S., Shair, F. H., Petersen, E. E. & Acrivos, A. 1964 An experimental investigation of the steady separated flow past a circular cylinder. J. Fluid Mech. 19, 60.Google Scholar
Hamielec, A. E. & Raal, J. D. 1969 Numerical studies of viscous flow around circular cylinders. Phys. Fluids, 12, 11.Google Scholar
Hirota, I. & Miyakoda, K. 1965 Numerical solution of Kármán vortex street behind a circular cylinder. J. Met. Soc. Japan, 43, 30.Google Scholar
Homann, F. 1936 Der Einfluss grosser Zähigkeit bei der Strömung um den Zylinder und um die Kugel. Z. angew. Math. Mech. 16, 153.Google Scholar
Imai, I. 1951 On the asymptotic behaviour of viscous fluid flow at a great distance from a cylindrical body, with special reference to Filon's paradox. Proc. Roy. Soc. A 208, 487.Google Scholar
Ingham, D. B. 1968 Note on the numerical solution for unsteady viscous flow past a circular cylinder. J. Fluid Mech. 31, 815.Google Scholar
Jain, P. C. & Rao, K. S. 1969 Numerical solution of unsteady viscous incompressible fluid flow past a circular cylinder. Phys. Fluids Suppl. 12, II 57.Google Scholar
Kaplun, S. 1967 Low Reynolds number flow past a circular cylinder. J. Math. Mech. 6, 595.Google Scholar
Kawaguti, M. 1953 Numerical solution of the Navier–Stokes equations for the flow around a circular cylinder at Reynolds number 40. J. Phys. Soc. Japan, 8, 747.Google Scholar
Kawaguti, M. & Jain, P. C. 1966 Numerical study of a viscous fluid flow past a circular cylinder. J. Phys. Soc. Japan, 21, 2055.Google Scholar
Kovasznay, L. S. G. 1949 Hot-wire investigation of the wake behind cylinders at low Reynolds numbers. Proc. Roy. Soc. A 198, 174.Google Scholar
Lagerstrom, P. A. & Cole, J. D. 1955 Examples illustrating expansion procedures for the Navier–Stokes equations. J. Rat. Mech. Anal. 4, 817.Google Scholar
Nieuwstadt, F. & Keller, H. B. 1973 Viscous flow past circular cylinders. Computers & Fluids, 1, 59.Google Scholar
Nishioka, M. 1973 Hot-wire investigation of the steady laminar wake behind a circular cylinder. Bull. Univ. Osaka Prefecture, 21, 205.Google Scholar
Nishioka, M. & Sato, H. 1974 Measurements of velocity distributions in the wake of a circular cylinder at low Reynolds numbers. J. Fluid Mech. 65, 97.Google Scholar
Nisi, H. & Porter, A. W. 1923 On eddies in air. Phil. Mag. 46 (6), 754.Google Scholar
Payard, M. & Coutanceau, M. 1974 Sur l'étude expérimentale de la naissance et de l'évolution du tourbillon attaché à l'arrière d'une sphère qui se déplace, à vitesse uniforme, dans un fluide visqueux. C.R. Acad. Sci. B 278, 369.Google Scholar
Proudmann, I. & Pearson, J. R. A. 1957 Expansion at small Reynolds numbers for the flow past a sphere and a circular cylinder. J. Fluid Mech. 2, 237.Google Scholar
Pruppacher, H. R., Le Clair, B. P. & Hamielec, A. E. 1970 Some relation between drag and flow pattern of viscous flow past a sphere and a cylinder at low and intermediate Reynolds numbers. J. Fluid Mech. 44, 781.Google Scholar
Roshko, A. 1954 N.A.C.A. Rep. no. 1191.
Shair, F. H., Grove, A. S., Petersen, E. E. & Acrivos, A. 1963 The effect of confining walls on the stability of the steady wake behind a circular cylinder. J. Fluid Mech. 17, 546.Google Scholar
Son, J. S. & Hanratty, T. J. 1969 Numerical solution for the flow around a cylinder at Reynolds numbers of 40, 200 and 500. J. Fluid Mech. 35, 369.Google Scholar
Takaisi, Y. 1969 Numerical studies of a viscous liquid past a circular cylinder. Phys. Fluids Suppl. 12, II 86.Google Scholar
Takami, H. & Keller, H. B. 1969 Steady two-dimensional viscous flow of an incompressible fluid past a circular cylinder. Phys. Fluids Suppl. 12, II 51.Google Scholar
Taneda, S. 1956a Experimental investigation of the wakes behind cylinders and plates at low Reynolds numbers. J. Phys. Soc. Japan, 11, 302.Google Scholar
Taneda, S. 1956b Experimental investigation of the wakes behind a sphere at low Reynolds numbers. J. Phys. Soc. Japan, 11, 1104.Google Scholar
Taneda, S. 1964 Experimental investigation of the wall-effect on a cylindrical obstacle moving in a viscous fluid at low Reynolds numbers. J. Phys. Soc. Japan, 19, 1024.Google Scholar
Taneda, S. 1965 Experimental investigation of vortex streets. J. Phys. Soc. Japan, 20, 1714.Google Scholar
Ta Phoc Loc 1975 Etude numérique de l'écoulement d'un fluide visqueux incompressible autour d'un cylindre fixe ou en rotation. Effet Magnus. J. Méc. 14, 109.Google Scholar
Thom, A. 1928 Aero. Res. Counc. R. & M. no. 1194.
Thom, A. 1933 The flow past circular cylinders at low speeds. Proc. Roy. Soc. A 141, 651.Google Scholar
Thoman, D. C. & Szewczyk, A. A. 1969 Time-dependent viscous flow over a circular cylinder. Phys. Fluids Suppl. 12, II 76.Google Scholar
Tritton, D. J. 1959 Experiments on the flow past a circular cylinder at low Reynolds numbers. J. Fluid Mech. 6, 547.Google Scholar
Underwood, R. L. 1968 Calculation of incompressible flow past a circular cylinder at moderate Reynolds numbers. J. Fluid Mech. 37, 95.Google Scholar
Van Dyke, M. 1964 Perturbation methods in fluid mechanics. Appl. Math. Mech. 8, 149.Google Scholar
Zandbergen, P. J. 1971 The viscous flow around a circular cylinder. Lecture Notes in Physics, vol. 8, p. 144. Springer.