Skip to main content Accessibility help
×
Home

The steady separated flow past a circular cylinder at large Reynolds numbers

  • Andreas Acrivos (a1), D. D. Snowden (a1), A. S. Grove (a2) (a3) and E. E. Petersen (a2)

Abstract

This paper is concerned with deducing the most important features of the steady separated flow past a circular cylinder in the limit of vanishing viscosity. First of all, it is shown that the experimental results reported in an earlier article cannot be reconciled with the notion that, as the Reynolds number Re is increased, the flow becomes inviscid everywhere and that viscous effects remain confined within infinitesimally thin shear layers. In contrast, the limiting solution is visualized as exhibiting three essential features: a viscous, closed ‘wake bubble’ of finite width but with a length increasing linearly with Re in which inertial and viscous effects are everywhere of equal order of magnitude; an outer inviscid flow; and, separating the two regions, a diffuse viscous layer covering large sections of the external field. Further properties of this asymptotic solution include: a finite form drag, a negative rear pressure coefficient at the rear stagnation point of the cylinder, and a Nusselt number for heat transfer which becomes independent of Re along the non-wetted portion of the cylinder surface. This model is shown to be consistent with all the experimental data presently available, including some new heat transfer results that are presented in this paper.

An approximate technique is also proposed which takes into account the asymptotic character of the flow in the vicinity of the cylinder and which predicts the pressure distribution around the cylinder in good agreement with the experiments.

Copyright

References

Hide All
Acrivos, A. 1960 Solution of the laminar boundary layer energy equation at high Prandtl numbers. Phys. Fluids, 3, 657.
Batchelor, G. K. 1956 A proposal concerning laminar wakes behind bluff bodies at large Reynolds number. J. Fluid Mech. 1, 388.
Curl, N. 1960 The estimation of laminar skin friction, including the effects of distributed suction. Aero. Quart. 11, 1.
Grove, A. S. 1963 Ph.D. thesis, University of California, Berkeley.
Grove, A. S., Shair, F. H., Petersen, E. E. & Acrivos, Andreas 1964 An experimental investigation of the steady separated flow past a circular cylinder. J. Fluid Mech. 19, 60.
Lighthill, M. J. 1950 Contributions to the theory of heat transfer through a laminar boundary layer. Proc. Roy. Soc. A, 202, 369.
Morgan, G. W. & Warner, W. H. 1956 On heat transfer in laminar boundary layers at high Prandtl number. J. Aero. Sci. 23, 937.
Potter, O. E. 1957 Laminar boundary layers at the interface of co-current parallel streams. Quart. J. Mech. Appl. Math. 10, 302.
Proudman, I. 1960 An example of steady laminar flow at large Reynolds number. J. Fluid Mech. 9, 593.
Riabouchinsky, D. 1920 On the steady flow motions with free surfaces. Proc. Lond. Math. Soc. 19, 206.
Riegels, F. W. 1948 Das Umströmungsproblem bei inkompressiblen Potentialströmungen. Ingenieur-Archiv. 16, 373.
Riegels, F. W. 1961 Aerofoil Sections. London: Butterworths.
Roshko, A. 1954 A new hodograph for free-streamline theory. NACA TN 3168.
Shah, M. J., Petersen, E. E. & Acrivos, A. 1962 Heat transfer from a cylinder to a power-law non-Newtonian fluid. A.I.Ch.E.J. 8, 542.
Shair, F. H. 1963 Ph.D. thesis, University of California, Berkeley.
Squire, H. B. 1934 On the laminar flow of a viscous fluid with vanishing viscosity. Phil. Mag. 7, 1150.
Taneda, S. 1956 Experimental investigation of the wakes behind cylinders and plates at low Reynolds numbers. J. Phys. Soc. Japan, 11, 302.
Thwaites, B. (Ed.) 1960 Incompressible Aerodynamics, p. 131. Oxford: Clarendon Press.
Woods, L. C. 1955 Two-dimensional flow of a compressible fluid past given curved obstacles with wakes. Proc. Roy. Soc. A, 227, 367.
Woods, L. C. 1961 The Theory of Subsonic Plane Flow. Cambridge University Press.
Wu, T. Y. 1962 A wake model for free-streamline flow theory. J. Fluid Mech. 13, 161.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

The steady separated flow past a circular cylinder at large Reynolds numbers

  • Andreas Acrivos (a1), D. D. Snowden (a1), A. S. Grove (a2) (a3) and E. E. Petersen (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed