Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-09T20:21:54.289Z Has data issue: false hasContentIssue false
  • English
  • Français

The Calculation of Three-Dimensional Turbulent Boundary Layers: Part I: Flow over the Rear of an Infinite Swept Wing

Published online by Cambridge University Press:  07 June 2016

N. A. Cumpsty  and
M. R. Head
N. A. Cumpsty
Affiliation:
Cambridge University Engineering Laboratory
M. R. Head
Affiliation:
Cambridge University Engineering Laboratory
Get access

Summary

A method of calculation has been developed in which all terms in the momentum integral equations in the streamwise and cross-flow directions are taken into account so that no restriction to small cross-flows is imposed. The essential feature of the method is the use of an entrainment equation which enables the development of the streamwise form parameter to be calculated along with the streamwise and cross-flow momentum thicknesses. Mager’s quadratic expression is used to relate streamwise and cross-flow profiles. The method has been applied to the idealised case of an infinite swept wing with free-stream velocity over the forward part of the chord and a linear adverse velocity gradient over the rear. The position of separation, the directions of the surface streamlines and the development of streamwise and cross-flow profiles have been calculated for a series of angles of sweep and for adverse pressure gradients of varying severity.

Type
Research Article
Information
Aeronautical Quarterly , Volume 18 , Issue 1 , February 1967 , pp. 55 - 84
Copyright
Copyright © Royal Aeronautical Society. 1967

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. Cooke, J. C. A calculation method for three-dimensional boundary layers. ARC R & M 3199, 1958.Google Scholar
2. Cooke, J. C. An axially symmetric analogue for general three-dimensional boundary layers. ARC R & M 3200, 1959.Google Scholar
3. Becker, E. Berechnung von Reibungschichten mit Schwacher Sekundärströmung nach dem Impulsverfahren. Zeitschrift für Flugwissenschaften, Vol. 7, No. 6, p. 163, 1959.Google Scholar
4. Mager, A. Generalization of boundary layer momentum integral equations to three-dimensional flows including those of rotating systems. NACA Report 1067, 1952.Google Scholar
5. Head, M. R. Entrainment in the turbulent boundary layer. ARC R & M 3152, 1958.Google Scholar
6. Spalding, D. B. A unified theory of friction, heat transfer and mass transfer in the turbulent boundary layer and wall jet. ARC 25 925. (Unpublished.) Google Scholar
7. Thompson, B. G. J. The calculation of the turbulent boundary layer. PhD Dissertation, Cambridge University, 1963.Google Scholar
8. Timman, R. The theory of three-dimensional laminar boundary layers. Proceedings of a Symposium on Boundary Layer Effects in Aerodynamics, held at the National Physical Laboratory. HMSO, London, 1955.Google Scholar
9. Cooke, J. C. and Hall, M. G. Boundary layers in three dimensions. A paper in Progress in Aeronautical Sciences, Vol. 2. Pergamon Press, London, 1962.Google Scholar
10. Thompson, B. G. J. A new two-parameter family of mean velocity profiles for incompressible turbulent boundary layers on smooth walls. ARC 26 830. (To be published.) Google Scholar
11. Gruschwitz, E. Turbulente Reibungschichten mit Sekundärströmung. Ingenieur Archiv, Vol. VI, p. 355, 1935.CrossRefGoogle Scholar
12. Johnston, J. P. On the three-dimensional boundary layer generated by secondary flow. Journal of Basic Engineering, Series D in Transactions of the American Society of Mechanical Engineers, Vol. 82, p. 233, 1960.Google Scholar
13. Bradshaw, P. and Ferris, D. H. The response of a retarded equilibrium turbulent boundary layer to the sudden removal of pressure gradient. ARC 26 758. (Unpublished.) Google Scholar
14. Hornung, H. G. and Joubert, P. N. The mean velocity profile in three-dimensional turbulent boundary layers. Journal of Fluid Mechanics, Vol. 15, p. 368, 1963.CrossRefGoogle Scholar
15. Hall, M. G. Recent developments in boundary layer research. AGARDograph 97, pp. 8–9, 1965.Google Scholar