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Turbulent Shear Layer Re-Attachment with Special Emphasis on the Base Pressure Problem

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

An analysis is presented which enables the boundary-layer thickness parameters of a re-attaching shear layer to be determined when the free-stream flow upstream of the base is supersonic, the base pressure is known, and die initial boundary layer is turbulent. The application of this analysis to some experimental results, on the flow behind blunt-trailing-edge wings and over a back-step where both the base pressure and the initial boundary layer are known, would appear to indicate that the re-attached profile could be specified by one parameter, namely the transformed shape parameter, the transformation used being a turbulent analogue of the well-known Stewartson-Illingworth transformation of the laminar boundary layer and where the shape parameter is defined as the ratio of boundary-layer displacement to momentum thickness. By adopting a value of the shape parameter in advance, it is possible to use the analysis to determine the base pressure by an iterative process and so, on this basis, it is suggested that this analysis is used to replace the existing recompression criterion of the Chapman-Korst model of separated flow which aims to predict base pressures and is known to be capable of improvement.

As part of this investigation, an improvement had to be made to the existing compressible turbulent shear layer velocity profiles of Korst and others and this was achieved by means of the compressibility transformation.

Type
Research Article
Information
Aeronautical Quarterly , Volume 15 , Issue 3 , August 1964 , pp. 247 - 280
Copyright
Copyright © Royal Aeronautical Society 1964 

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References

1. Chapman, D. R., Kuehn, D. M. and Larson, H. K. Investigation of Separated Flows in Supersonic Streams with Emphasis on the Effect of Transition. N.A.C.A. Report 1356, 1958.Google Scholar
2. Korst, H. H., Page, R. H. and Childs, M. W. A Theory for Base Pressures in Transonic and Supersonic Flow. University of Illinois ME-TN-392-2, December 1959.Google Scholar
3. Nash, J. F. An Analysis of Two-Dimensional Turbulent Base Flow Including the Effect of the Approaching Boundary Layer. N.P.L. Aero. Report 1036, July 1962.Google Scholar
4. Squire, H. B. and Young, A. D. The Calculation of the Profile Drag of Aerofoils. R. & M. 1838, November 1937. (Also in Boundary Layer Theory (4th Edition) by Schlichting, H.. McGraw-Hill, 1960.)Google Scholar
5. 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
6. Ananda Murthy, K. R. and Hammitt, A. G. Investigation of the Interaction of a Turbulent Boundary Layer with Prandtl-Meyer Expansion Fans at M = l·88. Princeton University Report No. 434, August 1958.Google Scholar
7. Toixmien, W. Calculation of Turbulent Expansion Processes. N.A.C.A. T.N. 1085, 1945.Google Scholar
8. Nash, J. F. The Effect of the Initial Boundary Layer on the Development of a Turbulent Free Shear Layer. N.P.L. Aero. Report 1019, June 1962.Google Scholar
9. Kirk, F. N. An Approximate Theory of Base Pressure in Two-Dimensional Flow at Supersonic Speeds. R.A.E. Tech. Note Aero. 2377, December 1959.Google Scholar
10. Coles, D. E. The Turbulent Boundary Layer in a Compressible Fluid. A.R.C. 24,497, September 1962.Google Scholar
11. Mager, A. Transformation of the Compressible Turbulent Boundary Layer. Journal of the Aeronautical Sciences, Vol. 25, No. 5, p. 305, 1958.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.M. 3454, 1955.Google Scholar
13. Charwat, A. F. and Yakura, J. K. An Investigation of Two-Dimensional Supersonic Base Pressure. Journal of the Aeronautical Sciences, Vol. 25, No. 2, p. 122, 1958.Google Scholar
14. Reichardt, H. Gesetzmassigkeiten der Freien Turbulenz. A.R.C. 6670, May 1942.Google Scholar
15. Liepmann, H. W. and Laufer, J. Investigation of Free Turbulent Mixing. N.A.C.A. T.N. 1257, 1947.Google Scholar
16. Crane, L. J. The Laminar and Turbulent Mixing of Jets of Compressible Fluid. Journal of Fluid Mechanics, Vol. 3, Pt. 1, p. 81, October 1957.Google Scholar
17. Johannesen, N. H. The Mixing of Free Axially Symmetric Jets of Mach Number 1·4. A.R.C. 18,967, January 1957.Google Scholar
18. Gooderum, P. B., Wood, G. P. and Brevoort, M. J. Investigation with an Interferometer of the Turbulent Mixing of a Free Supersonic Jet. N.A.C.A. Report 963, 1950.Google Scholar
19. Pitkin, E. T. and Glassman, I. Experimental Mixing Profiles of a Mach 2·6 Free Jet. Journal of the Aeronautical Sciences, Vol. 25, No. 12, p. 791, 1958.Google Scholar
20. Cary, B. An Optical Study of 2-D Jet Mixing. Ph.D. Thesis, University of Maryland, 1954.Google Scholar
21. Berstader, D. and Pai, S. I. On Turbulent Jet Mixing in Two-Dimensional Supersonic Flow. Journal of Applied Physics, Vol. 21, No. 6, 1950.Google Scholar
22. Unpublished work by Zumwalt. University of Illinois. Reported in Ref. 23, 1962.Google Scholar
23. Maydew, R. C and Reed, J. F. Turbulent Mixing of Compressible Free Jets. American Institute of Aeronautics and Astronautics Journal, June 1963.Google Scholar
24. Chapman, D. R., Wimbrow, W. R. and Kesler, R. H. Experimental Investigation of Base Pressure on Blunt Trailing Edge Wings at Supersonic Velocities. N.A.C.A. T.N. 2611, 1952.Google Scholar
25. Hastings, R. C. Turbulent Flow Past Two-Dimensional Bases in Supersonic Streams. R.A.E. Tech. Note Aero. 2931, December 1963.Google Scholar
26. Sirieux, M. Pression de Culot et Processus de Melange Turbulent en Écoulement Supersonique Plan. La Recherche Aéronautique, Septembre/Octobre 1960.Google Scholar
27. Beastall, D. and Eggwk, H. Some Experiments on Breakaway in Supersonic Flow. Part II. R.A.E. Tech. Note Aero. 2061, November 1951.Google Scholar
28. Goin, K. L. Effects of Plan Form, Airfoil Section and Angle of Attack on the Pressures Along the Base of Blunt Trailing Edge Wings at Mach Numbers of 1·41, 1·62 and 1·96. N.A.C.A. R.M. L52D21 (Ministry of Aviation T.I.B. 3324), 1952.Google Scholar
29. Gadd, G. E., Holder, D. W. and Regan, J. D. Base Pressures in Supersonic Flow. A.R.C. 17,490, March 1955.Google Scholar
30. Van Hise, V. Investigation of Variation in Base Pressure over the Reynolds Number Range in which Wake Transition Occurs for Two-Dimensional Bodies at Mach Numbers from 1·95 to 2·92. N.A.S.A. T.N. D-167, November 1959.Google Scholar
31. Morrow, J. D. and Ellis, Katz. Flight Investigation at Mach Numbers from 0·6 to 1·7 to Determine Drag and Base Pressures on a Blunt Trailing Edge Airfoil and Drag of Diamond and Circular Arc Airfoils at Zero Lift. N.A.C.A. T.N. 3548, 1955.Google Scholar
32. Fuller, L. and Reid, J. Experiments on Two-Dimensional Base Flow at M = 2A. R.A.E. Aero. Report 2569, February 1956.Google Scholar
33. Thomann, H. Measurements of Heat Transfer and Recovery Temperature in Regions of Separated Flow at a Mach Number of 1·8. F.F.A. (Stockholm) Report 82, November 1958.Google Scholar
34. Badrinarayanan, M. A. An Experimental Investigation of Base Flows at Supersonic Speeds. Journal of the Royal Aeronautical Society, Vol. 65, p. 475, July 1961.Google Scholar
35. Hughes, P. F. Estimation of Boundary Layer Thickness Parameters Downstream of a Back-Step in Supersonic Flow. English Electric Aviation Ltd., Alpha-Code Programme No. 127, 1963.Google Scholar
36. 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
37. Mueller, T. J. and Robertson, J. M. A Study of the Mean Motion and Turbulence Downstream of a Roughness Element. Modern Developments in Theoretical and Applied Mechanics, Vol. 1. Plenum Press, 1963.Google Scholar