Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-22T07:26:14.039Z Has data issue: false hasContentIssue false
  • English
  • Français

Viscous flow normal to a flat plate at moderate Reynolds numbers

Published online by Cambridge University Press:  26 April 2006

S. C. R. Dennis ,
Wang Qiang ,
M. Coutanceau  and
J.-L. Launay
S. C. R. Dennis
Affiliation:
Department of Applied Mathematics, University of Western Ontario, London, Ontario, Canada
Wang Qiang
Affiliation:
Department of Applied Mathematics, University of Western Ontario, London, Ontario, Canada
M. Coutanceau
Affiliation:
Laboratoire de Mécanique des Fluides, Université de Poitiers, Poitiers, France
J.-L. Launay
Affiliation:
Laboratoire de Mécanique des Fluides, Université de Poitiers, Poitiers, France
Get access Rights & Permissions [Opens in a new window]

Abstract

An experimental and numerical investigation of the two-dimensional flow normal to a flat plate is described. In the experiments, the plate is started impulsively from rest in a channel for Reynolds numbers, based on the breadth of the plate, in the range 5 ≤ Re ≤ 20. Over this range of Re the flow remains symmetrical and stable and tends to a steady state but is shown to depend strongly on the ratio λ of the plate to channel breadth. The evolution of the experimental flow with time and Reynolds number is studied and the variation with λ in the range 0.05 ≤ λ ≤ 0.2 is investigated sufficiently to enable an estimate of properties of the flow as λ → 0 to be obtained for the steady-state flow. The numerical results are obtained for steady flow normal to a flat plate in an unbounded fluid for Reynolds numbers up to Re = 100. They supplement and extend results for this flow obtained for values of Re up to 20 by Hudson & Dennis (1985). The present solutions have been found using a vorticity-stream function formulation rather than the primitive-variable approach of Hudson & Dennis and provide an independent check on these results. A comparison of the theoretical results for Re ≤ 20 with the limit λ → 0 of the experimental results is, generally speaking, extremely satisfactory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 248 , March 1993 , pp. 605 - 635
Copyright
© 1993 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
Arakaki, G. 1968 The growth and development of the wake behind inclined flat plates at low Reynold numbers. J. Sci. Hiroshima Univ. Ser. A-II, 32 (2), 191.Google Scholar
Belotserkovskii, O. M., Gushchin, V. A. & Shchennikov, V. V. 1975 Use of the splitting method to solve problems of the dynamics of a viscous fluid. USSR Comput. Maths Math. Phys. 15, 190.Google Scholar
Coutanceau, M. & BOUARD, R. 1977a Experimental determination of the main features of the viscous flow in the wake of a circular cylinder in uniform translation. Part 1. Steady flow. J. Fluid Mech. 79, 231.Google Scholar
Coutanceau, M. & Bouard, R. 1997b Experimental determination of the main features of the viscous flow in the wake of a circular cylinder in uniform translation. Part 2. Unsteady flow. J. Fluid Mech. 79, 257.Google Scholar
Dennis, S. C. R. 1960 Finite differences associated with second-order differential equations. Q. J. Mech. Appl. Maths 13, 487.Google Scholar
Dennis, S. C. R. & Chang, G.-Z. 1969 Numerical integration of the Navier–Stokes equations for steady two-dimensional flows. Phys. Fluids 12, Suppl. II-88.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. & Hudson, J. D. 1978 A difference method for solving the Navier–Stokes equations. In Proc. of the First Intl Conf. on Numerical Methods in Laminar and Turbulent Flow, p. 69. London: Pentech Press.
Dennis, S. C. R. & Hudson, J. D. 1989 Compact h4 finite-difference approximations to operators of Navier–Stokes type. J. Comput. Phys. 85, 390.Google Scholar
Dennis, S. C. R., Hudson, J. D. & Smith, N. 1968 Steady laminar forced convection from a circular cylinder at low Reynolds numbers. Phys. Fluids 11, 933.Google Scholar
Dennis, S. C. R. & Quartapelle, L. 1989 Some uses of Green's theorem in solving the Navier–Stokes equations. Intl J. Numer. Meth. Fluids 9, 871.Google Scholar
Dennis, S. C. R. & Smith, F. T. 1980 Steady flow through a channel with a symmetrical constriction in the form of a step. Proc. R. Soc. Lond. A 372, 393.Google Scholar
Fornberg, B. 1980 A numerical study of steady viscous flow past a circular cylinder. J. Fluid Mech. 98, 819.Google Scholar
Fornberg, B. 1985 Steady viscous flow past a circular cylinder up to Reynolds numbers 600. J. Comput. Phys. 61, 297.Google Scholar
Hartree, D. R. 1958 Numerical Analysis. Oxford: Clarendon.
Hudson, J. D. & Dennis, S. C. R. 1985 The flow of a viscous incompressible fluid past a normal flat plate at low and intermediate Reynolds numbers: the wake. J. Fluid Mech. 160, 369.CrossRefGoogle 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. R. Soc. Lond. A 208, 487.Google Scholar
Ingham, D. B., Tang, T. & Morton, B. R. 1990 Steady two-dimensional flow through a row of normal flat plates. J. Fluid Mech. 210, 281.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
Maalouf, A. & Bouard, R. 1987 Étude de l’écoulement plan d’un fluide visqueux et incompressible autour et au travers de coques cylindriques poreuses, à faibles nombres de Reynolds. Z. angew Math. Phys. 38, 522.Google Scholar
Ohmi, K., Coutanceau, M., Ta Phuoc, L. & Dulieu, A. 1990 Vortex formation around an oscillating and translating airfoil at large incidences. J. Fluid Mech. 211, 37.Google Scholar
Peregrine, D. H. 1985 A note on the steady high-Reynolds-number flow about a circular cylinder. J. Fluid Mech. 157, 493.Google Scholar
Prandtl, L. & Tietjens, O. G. 1934 Applied Hydro- and Aeromechanics. McGraw-Hill.
Smith, F. T. 1979 Laminar flow of an incompressible fluid past a bluff body: the separation reattachment, eddy properties and drag. J. Fluid Mech. 92, 171.Google Scholar
Smith, F. T. 1985 On large-scale eddy closure. J. Math. Phys. Sci. 19, 1.Google Scholar
Taneda, S. 1968 Standing twin-vortices behind a thin flat plate normal to the flow. Rep. Res. Inst. Appl. Mech. Kyushu Univ. 16 (54), 155.Google Scholar
Taneda, S. & Honji, H. 1971 Unsteady flow past a flat plate normal to the direction of motion. J. Phys. Soc. Japan 30 (1), 262.Google Scholar
Woods, L. C. 1954 A note on the numerical solution of fourth order differential equations. Aero. Q. 5, 176.Google Scholar