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The Estimation of Laminar Skin Friction, including the Effects of Distributed Suction

Published online by Cambridge University Press:  07 June 2016

N. Curle
N. Curle*
Affiliation:
Aerodynamics Division, National Physical Laboratory
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Summary

Stratford's analysis of the laminar boundary layer near separation uses two physical ideas. In the outer part of the boundary layer, where viscous effects are small, the development is given by the condition that the total head is constant along streamlines, apart from a second-order correction for viscosity. Near the wall, however, viscous forces must balance the pressure forces, and the profile adjusts itself accordingly. Quantitatively these ideas yield a simple formula for predicting separation, which has been found to be particularly accurate.

In this paper it is indicated how the same approach may be used to yield the full distribution of skin friction along the wall. Further, the effects of suction may be incorporated into the method. Physically, suction affects the outer part of the boundary layer in that the streamlines are drawn towards the wall when suction is applied. At the wall, the balance between viscous and pressure forces is influenced by the momentum of the fluid which is sucked away. When these effects are accounted for quantitatively, the resulting formula for the skin friction is still very simple.

Several examples are considered, and comparison is made with exact theory and with approximate results by other methods. It is indicated that the method has a useful range of validity.

Type
Research Article
Information
Aeronautical Quarterly , Volume 11 , Issue 1 , February 1960 , pp. 1 - 21
Copyright
Copyright © Royal Aeronautical Society. 1960

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References

1. Gadd, G. E., Jones, C. W. and Watson, E. J. Laminar Boundary Layers. Chapter VI. Unpublished manuscript.Google Scholar
2. Stratford, B. S. Flow in the Laminar Boundary Layer near Separation. R.& M. 3002, November 1954.Google Scholar
3. Thwaites, B. Approximate Calculation of the Laminar Boundary Layer. Aeronautical Quarterly, Vol. I, p. 245, November 1949.Google Scholar
4. Curle, N. and Skan, S. W. Approximate Methods for Predicting Separation Properties of Laminar Boundary Layers. Aeronautical Quarterly, Vol. VIII, p. 257, August 1957.Google Scholar
5. Head, M. R. An Approximate Method of Calculating the Laminar Boundary Layer in Two-Dimensional Incompressible Flow. R.& M. 3123, March 1957.Google Scholar
6. Thwaites, B. Investigations into the Effect of Continuous Suction on Laminar Boundary-Layer Flow under Adverse Pressure Gradients. R.& M. 2514, April 1946.Google Scholar
7. Thwaites, B. The Development of Laminar Boundary Layers under Conditions of Continuous Suction. Part II. Approximate Methods of Solution. A.R.C. 12,699, F.M.1296a, November 1949.Google Scholar
8. Schlichting, H. Ein Näherungsverfahren zur Berechnung der laminaren Grenzschicht mit Absaugung bei beliebiger Korperform. Aerodynamisches Institut der Technischen Hochschule, Braunschweig. Bericht 43/13, 1943. Translation N.A.C.A. T.M. 1216, 1949.Google Scholar
9. Pohlhausen, K. Zur Integration der Differential-gleichung der laminaren Grenzschicht. Zeitschrijt für angewandte Mathematik und Mechanik. Vol. I, p. 252, 1921.Google Scholar
10. Howarth, L. On the Solution of the Laminar Boundary Layer Equations. Proc. Roy. Soc. A. 164, p. 542, 1938.Google Scholar
11. Hartree, D. R. The Solution of the Equations of the Laminar Boundary Layer for Schubauer's Observed Pressure Distribution for an Elliptic Cylinder. R. & M. 2427, April 1939.Google Scholar
12. Falkner, V. M. and Skan, S. W. Some Approximate Solutions of the Boundary Layer Equations. R. & M. 1314, 1930.Google Scholar
13. Head, M. R. Approximate Calculations of the Laminar Boundary Layer with Suction, with Particular Reference to the Suction Requirements for Boundary Layer Stability on Aerofoils of Different Thickness/Chord Ratios. R. & M. 3124, September 1957.Google Scholar
14. Iglisch, R. Exakte Berechnung der laminaren Grenzschicht an der langsangestromten ebenen Platte mit homogener Absaugung. Schriften der Deutschen Akademie der Luftfahrtforschung, Band 8B, 1944. Translation N.A.C.A. T.M. 1205, 1949.Google Scholar
15. Prandtl, L. The Mechanics of Viscous Fluids. Vol. III, Aerodynamic Theory, p. 118, Springer, Berlin, 1935.Google Scholar
16. Preston, J. H. The Boundary Layer Flow over a Permeable Surface through which Suction is Applied. R. & M. 2244, February 1946.Google Scholar
17. Watson, E. J. Private Communication.Google Scholar