Hostname: page-component-5c6d5d7d68-txr5j Total loading time: 0 Render date: 2024-08-13T17:59:30.135Z Has data issue: false hasContentIssue false
  • English
  • Français

The thick turbulent boundary layer on a long fine cylinder in axial flow

Published online by Cambridge University Press:  04 July 2016

R. E. Luxton ,
M. K. Bull  and
S. Rajagopalan
R. E. Luxton
Affiliation:
Department of Mechanical Engineering, University of Adelaide
M. K. Bull
Affiliation:
Department of Mechanical Engineering, University of Adelaide
S. Rajagopalan
Affiliation:
Department of Mechanical Engineering, University of Adelaide
Get access Rights & Permissions [Opens in a new window]

Summary

Transverse curvature effects in axi-symmetric flow on a circulai cylinder are discussed and it is deduced that for small δ/a, where δ is the boundary layer thickness and a is the cylinder radius, transverse curvature effects are small, for δ/a = 0(1) the effect is felt mainly in the outer region and for δ/a » 1, both the inner and the outer regions are affected. It is argued that the last case can only be achieved experimentally in the laboratory if the radius Reynolds number Ra= U1a/v is small and the streamwise Reynolds number Rx=U1xlv is large, implying x/a large. New experimental data are presented for this case. The data show that both the mean and turbulent flow field scale on outer variables throughout the layer and, for Ra≥455, exhibit Reynolds number independence. No logarithmic region is found in the mean profiles, a result which is echoed by the absence of a shoulder in the streamwise turbulence profiles which clearly evidence that the flow in the layer is fully turbulent. A flow model is suggested, in physical terms, to explain the very high turbulence levels found close to the cylinder at values of Ra which should, according to stability theory, be bordering on laminar flow.

Type
Research Article
Information
The Aeronautical Journal , Volume 88 , Issue 875 , May 1984 , pp. 186 - 199
Copyright
Copyright © Royal Aeronautical Society 1984 

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

1. Young, A. D. The calculation of the total and skin friction drag of bodies of revolution at 0° incidence. ARC R and M No 1874, April 1939.Google Scholar
2. Huffman, G. D. and Bradshaw, P. A note on von Karman's constant in low Reynolds number turbulent flows. J Fluid Mechanics, 1972, 53, 45–60.Google Scholar
3. Richmond, R. Experimental investigations of thick axially symmetric boundary layers on cylinders at subsonic and Hypersonic speeds. PhD Thesis, California Institute of Technology, 1957.Google Scholar
4. Yu, Y. S. Effect on transverse curvature on turbulent boundary layer characteristics. J Ship Research, 1958, 3, 33–51.Google Scholar
5. Yasuhara, M. Experiments of axi-symmetric boundary layers along a cylinder in incompressible flow. Trans Japan Society of Aerospace Sciences, 1959, 2, 33–72.Google Scholar
6. Chin, Y. T., Hulesbos, J. and Hunnicutt, G. H. Effect of lateral curvature on the characteristics and skin friction of a turbulent air boundary layer with or without helium addition. Proc Heat Transfer and Fluids Mechanics Institute, 1967, 394–409.Google Scholar
7. Willmarth, W. W. and Yang, C. S. Wall pressure fluctuations beneath turbulent boundary layers on a flat plate and a cylinder. J Fluid Mechanics, 1970, 41, 47–80.Google Scholar
8. Rao, G. N. V. and Keshavan, N. R. Axi-symmetric turbulent boundary layers in zero pressure gradient flows. J Applied Mechanics, Trans ASME, 1972, 94, 25–32.Google Scholar
9. Afzal, N. and Singh, K. P. Measurements in an axi-symmetric turbulent boundary layer along a circular cylinder. Aero Quarterly, 1976, 27, 217–228.Google Scholar
10. Afzal, N. and Narasimha, R. Axi-symmetric turbulent boundary layer along a circular cylinder at constant pressure. J Fluid Mechanics, 1976, 74, 113–128.Google Scholar
11. Coles, D. E. The law of the wall in turbulent shear flow. 50 Jahre Grenzschichtforschung (Ed Görtler, H. and Tollmein, W.) Friedr. Vieweg, Braunschweig, 1955, 153–163.Google Scholar
12. Rao, G. N. V. The law of the wall in a thick axi-symmetric turbulent boundary layer. J Applied Mechanics, Trans. ASME, 1967, 89, 237–238.Google Scholar
13. Chase, D. M. Mean velocity profiles of a thick turbulent boundary layer along a circular cylinder, AIAA Jnl, 1972, 10, 849–850.(See also subsequent discussion).Google Scholar
14. White, F. M. An analysis of axi-symmetric turbulent flow past a long cylinder. J Basic Engineering, Trans ASME, 1972, 94, 200–206.Google Scholar
15. Ackroyd, J. A.D. On the analysis of turbulent boundary layers on slender cylinders. J Fluids Engineering, Trans ASME, 1982, 104, 185–190.Google Scholar
16. Willmarth, W. W., Winkel, R. E., Sharma, L. K. and Bogar, T. J. Axially symmetric turbulent boundary layers on cylinders: Mean velocity profiles and wall pressure fluctuations. J Fluid Mechanics, 1976, 76, 35–64.Google Scholar
17. Sparrow, E. M., Eckert, E. R. G. and Minkowycz, W. J. Heat transfer and skin friction for turbulent boundary layer flow longitudinal to a circular cylinder. J Applied Mechanics, Trans ASME, 1963, 30, 37–43.Google Scholar
18. Cebeci, T. Laminar and turbulent incompressible boundary layers on slender bodies of revolution in axial flow, (including discussion). J Basic Engineering, Trans ASME, 1970, 92, 545–554.Google Scholar
19. White, F. M., Lessmann, R. C. and Christoph, G. H. Analysis of turbulent skin friction in thick axi-symmetric boundary layers. AIAA Jnl. 1973, 11, 821–825.Google Scholar
20. Patel, V. C. A. A unified view of the law of the wall using mixing length theory. Aero Quarterly, 1973, 24, 55–70.Google Scholar
21. Denli, N. and Landweber, L. Thick axi-symmetric turbulent boundary layer on a circular cylinder.J Hydronautics 1979, 13, 92–104.Google Scholar
22. Shanebrook, R. and Sumner, W. J. Entrapment theory for axi-symmetric, turbulent, incompressible boundary layers. J Hydronautics, 1970, 4, 159–160.Google Scholar
23. Glauert, M. B. and Lighthill, M. J. Axi-symmetric boundary layer on a long thin cylinder. Proc Royal Society London, 1955, A230, 188–203.Google Scholar
24. Willmarth, W. W., Sharma, L. K. and Inglis, S. The effect of cross flow and isolated roughness elements on the boundary layer and wall pressure fluctuations on circular cylinders. Univ. Michigan, Dept. Aerospace Engineering, Report 014439-01, 1977.Google Scholar
25. Patel, V. C. A., Nakayama, A. and Damian, R. Measurements in the thick turbulent boundary layer near the tail of a body of revolution. J Fluid Mechanics, 1974, 63, 345–367.Google Scholar
26. Perry, A. E. and Abell, C. J. Scaling laws for pipe-flow turbulence. J Fluid Mechanics, 1975, 67, 257–271.Google Scholar
27. Willmarth, W. W. Structure of turbulence in boundary layers. Adv Appl Mech, 15, 159–254. (see page 221).Google Scholar
28. Gould, J. and Smith, F. S. Air-drag on synthetic-fibre textile monofilmaments and yarns in axial flow at speeds of 100 m/s. J Textile Institute, 1980, 71, 38–49.Google Scholar