Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-10T00:58:21.716Z Has data issue: false hasContentIssue false
  • English
  • Français

The Prediction of Turbulent, Supersonic, Two-Dimensional, Boundary-Layer Flows

Published online by Cambridge University Press:  07 June 2016

S. Sivasegaram  and
J. H. Whitelaw
S. Sivasegaram
Affiliation:
Imperial College, London
J. H. Whitelaw
Affiliation:
Imperial College, London
Get access

Summary

The prediction procedures of Bradshaw and Ferriss and Spalding and Patankar are compared with a wide range of experimental data obtained in turbulent, supersonic, two-dimensional flow. Both procedures are shown to result in satisfactory predictions of mean velocity profiles and wall shear stress in adiabatic-wall situations: in addition, the procedure of Spalding and Patankar is shown to be satisfactory in heat transfer situations. The Bradshaw and Ferriss procedure employs a turbulent energy hypothesis in contrast to the mixing-length assumptions used in the present version of the Spalding and Patankar procedure. The close agreement between the predictions of the two procedures indicates a lack of experimental data obtained in flow configurations with suddenly imposed or relaxed pressure gradients.

Type
Research Article
Information
Aeronautical Quarterly , Volume 22 , Issue 3 , August 1971 , pp. 274 - 294
Copyright
Copyright © Royal Aeronautical Society. 1971

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. Spalding, D. B. and Patankar, S. V.: Heat and mass transfer in boundary layers. Morgan Grampian Press, London, 1967.Google Scholar
2. Bradshaw, P. and Ferriss, D. H. : Calculation of boundary layer development using the turbulent energy equation. II—Compressible boundary layers. NPL Aero Report 1217, 1966.Google Scholar
3. Thompson, B. G. J. : A critical review of existing methods of calculating the turbulent boundary layer. ARC 26 109, 1964.Google Scholar
4. Herring, H. J. and Mellor, G. L. : A method of calculating compressible turbulent boundary layers. NASA CR-114, 1968.Google Scholar
5. Smith, A. M. O. and Cebeci, J. : Numerical solutions of the turbulent boundary layer equations. Douglas Aircraft Report DAC 33 735, 1967.Google Scholar
6. Rotta, J. C. : Statistische Theorie nicht homogener Turbulenz. Zeitschrift für Physik, Bd. 129, p. 547 and Bd. 131, p. 51, 1957.Google Scholar
7. Rodi, W. and Spaldino, D. B. : A two-parameter model of turbulence and its application to free jets, Department of Mechanical Engineering, Imperial College, London, BL/TN/B/12, 1969.Google Scholar
8. Ng, K. H. and Spalding, D. B. : Some applications of a model of turbulence to boundary layers near walls. Department of Mechanical Engineering, Imperial College, London, BL/TN/A/14, 1969.Google Scholar
9. Sivasegaram, S. : A review of the literature pertaining to experimental investigation of the two-dimensional, compressible, turbulent boundary layer. Department of Mechanical Engineering, Imperial College, London, TWF/TN/44, 1968.Google Scholar
10. Spalding, D. B. and Chi, S. W. : The drag of a compressible turbulent boundary layer on a smooth flat plate with and without heat transfer. Journal of Fluid Mechanics, Vol. 18, Part 1, p. 117, 1964.CrossRefGoogle Scholar
11. Chi, S. W. and Spalding, D. B.: Influence of temperature ratio on heat transfer to a flat plate through a turbulent boundary layer in air. Proceedings, Third International Heat Transfer Conference, August 7-12, Vol. 3, American Institute of Chemical Engineers, New York, 1964.Google Scholar
12. Wilson, R. E. : Turbulent boundary layer characteristics at supersonic speeds—Theory and experiment. Journal of the Aeronautical Sciences, Vol. 17, No. 9, p. 585, 1950.Google Scholar
13. Coles, D.: Measurements in the boundary layer on a smooth flat plate in supersonic flow. Report Nos. 20-69, 20-70, 20-71, Jet Propulsion Laboratories, Pasadena, June 1953.Google Scholar
14. Brinich, P. F. and Diaconis, N. S. : Boundary layer development and skin friction at Mach number 3·05. NACA TN 2742, 1952.Google Scholar
15. Rubesin, M. W., Maydew, R. C. and Varga, S. A.: An analytical and experimental investigation of the skin friction of the turbulent boundary layer on a flat plate at supersonic speeds, NACA TN 2305, 1951.Google Scholar
16. Chapman, D. R. and Kester, R. H. : Turbulent boundary layer and skin friction measurements in axial flow along cylinders at Mach number between 0·5 and 3·6. NACA TN 3097, 1954.Google Scholar
17. Adcock, J. B., Peterson, J. B. and McRee, I.: Experimental investigation of a turbulent boundary layer at Mach 6, high Reynolds number and zero heat transfer. NASA TN D-3882, 1967.Google Scholar
18. Matting, F. W., Chapman, D. B., Nyholm, J. R. and Thomas, A. G.: Turbulent skin friction at high Mach numbers and Reynolds numbers in air and helium. NASA TR-R-82, 1961.Google Scholar
19. Lobb, R. K., Winkler, E. H. and Persh, J. : Experimental investigation of turbulent boundary layers in hypersonic flow. Navord Report 3880, 1955.Google Scholar
20. Winkler, E. M. and Cha, M. H.: Investigation of the flat plate hypersonic boundary layers with heat transfer at a Mach number of 5·2. Navord Report 6631, 1959.Google Scholar
21. Samuels, R. D., Peterson, J. B. and Adcock, J. B.: Experimental investigation of the turbulent boundary layers at a Mach number of 6 with heat transfer at high Reynolds number. NASA TN D-3858, 1967.Google Scholar
22. Hill, F. K. : Boundary layer measurements in hypersonic flow. Journal of the Aeronautical Sciences, Vol. 23, p. 35, 1956.Google Scholar
23. Hill, F. K. : Turbulent boundary layer measurements at Mach numbers from 8-10. Physics of Fluids, Vol. 2, p. 668, 1959.Google Scholar
24. Pasiuk, L., Hastings, S. H. and Chatham, R. : Experimental Reynolds analogy factor for a compressible turbulent boundary layer with a pressure gradient. Naval Ordnance Laboratories, NOL TR 64-200, 1964.Google Scholar
25. Edwards, B. and Sivasegaram, S. : An experimental investigation of Mach 2·2, turbulent boundary layers in nominally zero pressure gradients. Department of Mechanical Engineering, Imperial College, London, BL/TN/3, 1968.Google Scholar
26. Meier, H. U. : Messungen von turbulenten Grenzschichten an einer wärmeisolierten Wand im kleinen Uberschallwindkanal der AVA. Zeitschrift für Flugwissenschaften, 17th year, Book 1, January 1969.Google Scholar
27. Sivasegaram, S. : An experimental investigation of supersonic boundary layer flows with pressure gradients. ARC Report 31 586, 1970.Google Scholar
28. Crocco, L. : As quoted in Ref. 29.Google Scholar
29. Rotta, J. C. : Kritische Durchsicht experimentaller Wärmübergangzahlen und Temperaturverteilungen in turbulenten Grenzschichten bei Uber und Hyperschallströmung. Deutsche Luft-und Raumfahrt ((DLR), FB 66-51, 1966.Google Scholar
30. Maise, G. and McDonald, H. : Mixing length and kinematic eddy viscosity in compressible boundary layers. AIAA Journal, Vol. 6, p. 73, 1968.Google Scholar
31. Spalding, D. B. : Unpublished work at Imperial College, 1969.Google Scholar
32. Meier, H. U. : Eine kombinierte Sonde für Temperatur und Druckmessungen in Grenzschichten bei kompressiblen Strömungen. AVA, Göttingen 68 G03, 1968.Google Scholar
33. Michel, R. : Resultats sur la couche limite turbulente aux grandes vitesses. ONERA Publication 102, 1961.Google Scholar
34. Mclafferty, G. H. and Barber, R. E. : Turbulent boundary layer characteristics in supersonic streams having adverse pressure gradients. Journal of the Aerospace Sciences, Vol. 29, p. 1, 1962.Google Scholar
35. Nothwang, G. J. : An evaluation of four experimental methods for measuring mean properties of a supersonic turbulent boundary layer. NACA Report 1320, 1957.Google Scholar
36. Laufer, J. : Opening address at Symposium on Compressible Turbulent Boundary Layers, NASA Langley Research Center, December 1968.Google Scholar