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The Effects of Heat Transfer on Laminar-Boundary-Layer Separation in Supersonic Flow

Published online by Cambridge University Press:  07 June 2016

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

By generalising earlier work, an approximate method is derived for calculating compressible laminar boundary layers with an unfavourable pressure gradient, with the wall temperature and Prandtl number arbitrary and some allowance made for the viscosity-temperature law. The method merely requires two quadratures and uses tables of universal functions. On the basis of this method it is suggested that when the wall is at uniform temperature the viscosity-temperature law should make little difference to the results, and that, when the wall temperature varies spatially by a factor of two, the use of a linear relationship may introduce errors of order 4 per cent in the momentum thickness. It is further suggested that the effects of Prandtl number differing from unity will increase as either the Mach number is increased or the wall is cooled. These general conclusions are borne out by detailed numerical calculations in a few selected cases.

Type
Research Article
Information
Aeronautical Quarterly , Volume 12 , Issue 4 , November 1961 , pp. 309 - 336
Copyright
Copyright © Royal Aeronautical Society. 1961

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References

1. Gadd, G. E. Interactions between Wholly Laminar or Wholly Turbulent Boundary Layers and Shock Waves Strong Enough to Cause Separation. Journal of the Aeronautical Sciences, Vol. 20, p. 729,1953.CrossRefGoogle Scholar
2. Gadd, G. E. A Theoretical Investigation of Laminar Separation in Supersonic Flow. Journal of the Aeronautical Sciences, Vol. 24, p. 759,1957.CrossRefGoogle Scholar
3. Stratford, B. S. Flow in the Laminar Boundary Layer near Separation. R. & M. 3002, 1954.Google Scholar
4. Gadd, G. E. An Experimental Investigation of Heat Transfer Effects on Boundary-Layer Separation in Supersonic Flow. Journal of Fluid Mechanics, Vol. 2, p. 105, 1957.CrossRefGoogle Scholar
5. Crocco, L. and Lees, L. A Mixing Theory for the Interaction between Dissipative Flows and Nearly Isentropic Streams. Journal of the Aeronautical Sciences, Vol. 19, p. 649, 1952.CrossRefGoogle Scholar
6. Bray, K. N. C, Gadd, G. E. and Woodger, M. Some Calculations by the Crocco-Lees and Other Methods of Interactions between Shock Waves and Laminar Boundary Layers, including Effects of Heat Transfer and Suction. A.R.C. Current Paper 556, 1960.Google Scholar
7. Curle, N. The Steady Compressible Laminar Boundary Layer, with Arbitrary Pressure Gradient and Uniform Wall Temperature. Proc. Roy. Soc. A. 249, p. 206, 1958.Google Scholar
8. Curle, N. Heat Transfer and Laminar Boundary-Layer Separation in Steady Com pressible Flow Past a Wall with Non-Uniform Temperature. R. & M. 3179, 1958.Google Scholar
9. Gadd, G. E. Some Aspects of Laminar Boundary Layer Separation in Compressible Flow with No Heat Transfer to the Wall. Aeronautical Quarterly, Vol. IV, p. 123, 1953.CrossRefGoogle Scholar
10. Young, A. D. Skin Friction in Compressible Flow. Aeronautical Quarterly, Vol. I, p. 137,1949.CrossRefGoogle Scholar
11. Monaghan, R. J. An Approximate Solution of the Compressible Laminar Boundary Layer on a Flat Plate. R. & M. 2760, 1949.Google Scholar
12. Howarth, L. Concerning the Effect of Compressibility on Laminar Boundary Layers and Their Separation. Proc. Roy. Soc. A. 194, p. 16, 1948.Google Scholar
13. Chapman, D. R. and Rubesin, M. W. Temperature and Velocity Profiles in the Com pressible Laminar Boundary Layer with Arbitrary Distribution of Surface Temperature. Journal of the Aeronautical Sciences, Vol. 16, p. 547, 1949.CrossRefGoogle Scholar
14. Truckenbrodt, E. Ein Quadraturrerfahren zur Berechnung der laminaren und turbulenten Reibungsschichten bei ebener und rotationssymmetrischer Stromung. Ingenieur-Archiv, Vol. 20, p. 211, 1952.CrossRefGoogle Scholar
15. Curle, N. and Skan, S. W. Approximate Methods for Predicting Separation Properties of Laminar Boundary Layers. Aeronautical Quarterly, Vol. VIII, p. 257, 1957.CrossRefGoogle Scholar
16. Chapman, D. R., Kuehn, D. M. and Larson, H. K. Investigation of Separated Flows in Supersonic and Subsonic Streams with Emphasis on the Effect of Transition. N.A.C.A. Report 1356, 1958.Google Scholar
17. Hakkinen, R. J., Greber, I., Trilling, L. and Abarbanel, S. S. The Interaction of an Oblique Shock Wave with a Laminar Boundary Layer. N.A.S.A. Memo. 2-18-59W, 1959.Google Scholar
18. Gadd, G. E. and Attridge, J. L. A Note on the Effects of Heat Transfer on the Separation of a Laminar Boundary Layer. A.R.C. Current Paper 569, 1961.Google Scholar
19. Pohlhausen, K. Zur Integration der Differential-gleichung der laminaren Grenschicht. Zeitschrift fiir Angewandte Mathematik und Mechanik, Vol. 1, p. 252, 1921.CrossRefGoogle Scholar
20. Timman, R. A One Parameter Method for the Calculation of Laminar Boundary Layers. N.L.L. (Amsterdam) Report F. 35, 1949.Google Scholar
21. Falkner, V. M. and Skan, S. W. Some Approximate Solutions of the Boundary-Layer Equations. R. & M. 1314, 1930.Google Scholar
22. Stewartson, K. Further Solutions of the Falkner-Skan Equation. Proceedings of the Cambridge Philosophical Society, Vol. 50, p. 454, 1954.CrossRefGoogle Scholar