Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-19T00:26:05.061Z Has data issue: false hasContentIssue false
  • English
  • Français

Axially symmetric turbulent boundary layers on cylinders: mean velocity profiles and wall pressure fluctuations

Published online by Cambridge University Press:  11 April 2006

W. W. Willmarth ,
R. E. Winkel ,
L. K. Sharma  and
T. J. Bogar
W. W. Willmarth
Affiliation:
Department of Aerospace Engineering, University of Michigan, Ann Arbor
R. E. Winkel
Affiliation:
Department of Aerospace Engineering, University of Michigan, Ann Arbor
L. K. Sharma
Affiliation:
Department of Aerospace Engineering, University of Michigan, Ann Arbor
T. J. Bogar
Affiliation:
Department of Physics, Westminster College, Pennsylvania
Get access Rights & Permissions [Opens in a new window]

Abstract

Experimental measurements of the mean velocity profiles produced by axially symmetric turbulent boundary layers on cylinders of various diameters are described. The profile measurements were made with very small hot wires developed for this investigation. Measurements of the wall shear stress on cylinders ranging from 0.02 to 2.0 in. in diameter are also reported. In the boundary layer on cylinders, well-defined regions exist in which the two-dimensional law of the wall and a three-dimensional wake law are valid. There was no evidence that the boundary layer was not fully turbulent even on the cylinders of smallest diameter. Measurements of wall pressure fluctuations beneath the boundary layer on a 1 in. diameter cylinder are also described. The results were much the same as those previously reported by Willmarth & Yang (1970) for a 3 in. diameter cylinder. The only difference was the discovery that the wall pressure was correlated in the transverse direction approximately half-way around the cylinder. This was not true on the 3 in. diameter cylinder.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 76 , Issue 1 , 14 July 1976 , pp. 35 - 64
Copyright
© 1976 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

Cebeci, T. 1970 Laminar and turbulent incompressible boundary layers on slender bodies of revolution in axial flow. J. Basic Engng, Trans. A.S.M.E. D 92, 545.Google Scholar
Chase, D. M. 1972 Mean velocity profile of a thick turbulent boundary layer along a long cylinder. A.I.A.A. J. 10, 849.Google Scholar
Clauser, F. H. 1956 The turbulent boundary layer. Adv. Appl. Mech. 4, 1.Google Scholar
Coles, D. E. 1955 The law of the wall in turbulent shear flow. 50 Jahre Grenzschicht-forschung, Braunschweig: F. Vieweg. 153.
Coles, D. E. 1956 The law of the wake in a turbulent boundary layer. J. Fluid Mech. 1, 191.Google Scholar
Glauert, M. B. & Lighthill, M. J. 1955 Axisymmetric boundary layer on a long thin cylinder. Proc. Roy. Soc. A 203, 188.Google Scholar
Moore, F. K. 1952 Displacement effect of a three-dimensional boundary layer. N.A.C.A. Tech. Note, no. 2722.
Patel, V. C. 1965 Calibration of a Preston tube and limitations on its use in pressure gradients. J. Fluid Mech. 23, 185.Google Scholar
Patel, V. C. 1973 A unified view of the law of the wall using mixing-length theory. Aero. Quart. 24, 55.Google Scholar
Preston, J. H. 1954 The determination of turbulent skin friction by means of Pitot tubes. J. Roy. Aero. Soc. 58, 109.Google Scholar
Rao, G. N. V. 1967 The law of the wall in a thick axisymmetric turbulent boundary layer. J. Appl. Mech. 34, 237.Google Scholar
Rao, G. N. V. & Keshavan, N. R. 1972 Axisymmetric turbulent boundary layers in zero pressure gradient flows. J. Appl. Mech. 39, 25.Google Scholar
Reid, R. O. & Wilson, B. W. 1963 Boundary flow along a circular cylinder. J. Hydraul. Div., Proc. A.S.C.E. 3, 21.Google Scholar
Richmond, R. L. 1957 Experimental investigation of thick axially symmetric boundary layers on cylinders at subsonic and hypersonic speeds. Thesis, California Institute of Technology. (See also Hypersonic Res. Proj. Memo. no. 39.)
White, F. M. 1972 An analysis of axisymmetric turbulent flow past a long cylinder. J. Basic Engng, Trans. A.S.M.E. D 94, 200.Google Scholar
White, F. M., Lessmann, G. H. & Christoph, G. H. 1973 Skin friction in thick axisymmetric boundary layers. A.I.A.A. J. 11, 6, 821.Google Scholar
Willmarth, W. W. 1975a Pressure fluctuations beneath turbulent boundary layers. Ann. Rev. Fluid Mech. 7, 13.Google Scholar
Willmarth, W. W. 1975b Structure of turbulence in boundary layers. Adv. Appl. Mech. 15, 159.Google Scholar
Willmarth, W. W., Winkel, R. E., Bogar, T. J. & Sharma, L. K. 1975 Axially symmetric turbulent boundary layers on cylinders. Dept. Aerospace Engng, Univ. Michigan, Rep. no. 021490—3–T.
Willmarth, W. W. & Yang, C. S. 1970 Wall pressure fluctuations beneath turbulent boundary layers on a flat plate and a cylinder. J. Fluid Mech. 41, 47.Google Scholar
Wills, J. A. B. 1962 The correction of hot-wire readings for proximity to a solid boundary. J. Fluid Mech. 12, 388.Google Scholar
Yu, Y. S. 1958 Effect of transverse curvature on turbulent-boundary-layer characteristics. J. Ship Res. 3, 33.Google Scholar