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An Analysis of the Turbulent Base Pressure Problem in Supersonic Axisymmetric Flow

Published online by Cambridge University Press:  07 June 2016

H. McDonald
H. McDonald*
Affiliation:
British Aircraft Corporation (Operating) Limited, Preston Division
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Summary

The problem of predicting the turbulent supersonic base pressure in axisymmetric flow is treated by an extension of a method of solution to the two-dimensional problem given in Ref. 1. The solution consists principally in tracing the boundary-layer development from upstream of the base to downstream of the recompression region for a given base pressure. A unique solution is obtained by specifying the shape of the rehabilitated boundary-layer velocity profile.

A comparison with experiment in the case of the step-down cylinder problem (the sting-support problem) yields some very favourable results. It is pointed out that, while it has not been found possible to obtain a solution to the problem of a vanishingly small sting, the base pressure does not vary appreciably while the sting is decreased from about 0-3 of the base diameter down to zero. It would appear that the present analysis is capable of giving accurate results down to sting/diameter ratios of the order of 0·3.

Type
Research Article
Information
Aeronautical Quarterly , Volume 16 , Issue 2 , May 1965 , pp. 97 - 121
Copyright
Copyright © Royal Aeronautical Society. 1965

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References

1. McDonald, H. Turbulent Shear Layer Re-attachment with Special Emphasis on the Base Pressure Problem. Aeronautical Quarterly, Vol. XV p. 247, August 1964.CrossRefGoogle Scholar
2. Korst, H. H., Chow, W. L. and Zumwalt, G. W. Research on Transonic and Supersonic Flow of a Real Fluid at Abrupt Increases in Cross Section. University of Illinois M.E. T.N. 392-2, December 1959.Google Scholar
3. Mangler, W. Compressible Boundary Layers on Bodies of Revolution. A.R.C. Reports and Translations No. F.M. 949, March 1946.Google Scholar
4. McDonald, H. A Study of the Turbulent Separated Flow Region Occurring at a Compression Corner in Supersonic Flow. English Electric Aviation, Aerodynamics Technical Note Ae.210, 1963. (To be published in the Journal of Fluid Mechanics?)Google Scholar
5. McIntyre, R. W., Hall, D. M., Bauchop, P. and Lang, I. A Characteristic Interpretative Programme. Bristol Siddeley (Engines) Ltd., Report No. 5054, November 1962.Google Scholar
6. Ferri, A. Elements of Aerodynamics of Supersonic Flows. Macmillan, 1949.Google Scholar
7. Schlichting, H. Boundary Layer Theory, 4th Edition p. 584. McGraw-Hill, 1960.Google Scholar
8. Mager, A. Transformation of the Compressible Turbulent Boundary Layer. Journal of the Aeronautical Sciences, May 1958.Google Scholar
9. Nash, J. F. An Analysis of Two-Dimensional Turbulent Base Flow including the Effect of the Approaching Boundary Layer. National Physical Laboratory Aero. Report 1036, July 1962.Google Scholar
10. Nash, J. F. The Effect of an Initial Boundary Layer on the Development of a Turbulent Free Shear Layer. National Physical Laboratory Aero. Report 1019, June 1962.Google Scholar
11. Kirk, F. N. An Approximate Theory of Base Pressures in Two-Dimensional Flow at Supersonic Speeds. R.A.E. Technical Note Aero. 2377, December 1959.Google Scholar
12. Reshotko, E. and Tucker, M. Effect of a Discontinuity on Turbulent Boundary-Layer Thickness Parameters with Application to Shock-Induced Separation. N.A.C.A. T.N. 3454, April 1955.Google Scholar
13. Maskell, E. C. Approximate Calculation of the Turbulent Boundary Layer in Two-Dimensional Incompressible Flow. R.A.E. Report Aero. 2443, November 1951.Google Scholar
14. Ludwieg, H. and Tillmann, W. Investigations of the Wall Shearing Stress in Turbulent Boundary Layers. N.A.C.A. T.M. 1285, 1950.Google Scholar
15. Chapman, D. R. An Analysis of Base Pressure at Supersonic Velocities and Comparison with Experiment. N.A.C.A. Report 1051, November 1956.Google Scholar
16. Reid, J. and Hastings, R. C. Experiments on the Axi-symmetric Flow over Afterbodies and Bases at M = 20. R.A.E. Report Aero. 2628, October 1959.Google Scholar
17. Donaldson, I. S. The Effect of Sting Supports on the Base Pressure of a Blunt-Based Body in a Supersonic Stream. Aeronautical Quarterly, Vol. VI p. 221, August 1955.Google Scholar