Hostname: page-component-7479d7b7d-k7p5g Total loading time: 0 Render date: 2024-07-15T22:03:04.791Z Has data issue: false hasContentIssue false
  • English
  • Français

Reynolds number effects on the prediction of mean flow data for adiabatic 2-D compressible boundary layers

Published online by Cambridge University Press:  04 July 2016

F. Motallebi
F. Motallebi*
Affiliation:
University of Technology , The Netherlands
Get access Rights & Permissions [Opens in a new window]

Abstract

The paper presents a method for the prediction of mean flow data (i.e. skin friction, velocity profile and shape parameter) for adiabatic two-dimensional compressible turbulent boundary layers at zero pressure gradient. The transformed law of the wall, law of the wake, the van Driest model for the complete inner region and a correlation between the Reynolds number based on the boundary layer integral length scale (ReΔ*.) and the Reynolds number based on the boundary layer momentum thickness (Reθw) were used to predict the mean flow quantities. The results for skin friction coefficient show good agreement with a number of existing theories including the van Driest II and the Huang et al. Comparison with a large number of experimental data suggests that at least for transonic and supersonic flows, the velocity profile as described by van Driest and Coles is Reynolds number dependent and should not be presumed universal. Extra information or perhaps a better physical approach to the formulation of the mean structure of compressible turbulent boundary layers even in zero pressure gradient and adiabatic condition, is required in order to achieve complete (physical and mathematical) convergence when it is applied in any prediction methods.

Type
Research Article
Information
The Aeronautical Journal , Volume 100 , Issue 992 , February 1996 , pp. 53 - 59
Copyright
Copyright © Royal Aeronautical Society 1996 

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.)

Footnotes

†

Formerly assistant professor of Tehran University, Iran

References

1. Schlichting, H. Boundary-Layer Theory, 7th edition, McGraw-Hill Book Company, New-York, 1979, pp 587–589.Google Scholar
2. Fernholz, H.H. A critical commentary on mean flow data for two-dimensional compressible turbulent boundary layers, AGARDo-graph No 253, May 1980.Google Scholar
3. Van Driest, E.R. Turbulent boundary layer in compressible fluids, J Aeronaut Sci, March 1951, 18, (5), pp 145–160.Google Scholar
4. Van Driest, E.R. Turbulent Flows with Heat Transfer, Lin, C.C. (Ed), Princeton University Press, Princeton, NJ, 1959, pp 339–427.Google Scholar
5. Coles, D.E. The turbulent boundary layer in compressible fluid, Rand Corp, Report R-403-PR, Santa Monica, September 1962.Google Scholar
6. Coles, D.E. The law of the wake in the turbulent boundary layers, J Fluid Mech, July 1956, 1, (2), pp 191–226.Google Scholar
7. Cebecci, T. and Smith, A.M.O. Analysis of Turbulent Boundary Layers, 1st Ed, Academic Press, New York, 1974, pp 146–148.Google Scholar
8. Huang, P.G., Bradshaw, P. and Coakley, T.J. Skin friction and velocity profile family for compressible turbulent boundary layers, AIAA J, Sept 1993, 31, (9), pp 1600–1604.Google Scholar
9. Van Driest, E.R. On turbulent flow near a wall, J Aeronaut Sciences, 1956, 23, pp 1007–1012.Google Scholar
10. Fernholz, H.H. Private communication, Technische Universitat Berlin, Hermann-Fottinger-Institut fur Thermo-und Fluiddynamik, Berlin, Germany, November 1991.Google Scholar
11. Motallebi, F. Experimental investigation of the flow quality in the GLT20 subsonic-transonic boundary layer wind tunnel, Faculty of Aerospace Engineering, Delft University of Technology, Report LR-720, April 1993.Google Scholar
12. Motallebi, F. Mean flow study of 2-D subsonic turbulent boundary layers, AIAA J, November 1994, 32, (11), pp 2153–2161.Google Scholar
13. Winter, K.G. and Gaudet, L. Turbulent boundary layer studies at high Reynolds numbers at Mach numbers between 0.2 and 2.8, Aeronautical Research Council, ARC R & M No 3712, London, UK, December 1970.Google Scholar
14. Gaudet, L. Experimental investigation of the turbulent boundary layer at high Reynolds numbers and a Mach number of 0.8, Royal Aircraft Establishment, RAE Report, TR-84094, Bedford, UK, September 1984.Google Scholar
15. Collins, D.J., Coles, D.E. and Hicks, J.W. Measurements in the turbulent boundary layer at constant pressure in subsonic and supersonic flow, Part I: Mean flow, Jet Propulsion Laboratory, California Institute of Technology, AEDC-TR-78-21, Pasadena, California, May 1978.Google Scholar
16. Motallebi, F. Prediction of mean flow data for adiabatic 2-D compressible turbulent boundary layers, Faculty of Aerospace Engineering, Report LR-784, Delft, The Netherlands, February 1995.Google Scholar
17. Van Driest, E.R. Problem of aerodynamic heating, Aeronaut Engineering Review, October 1956, 15, (10), pp 26–41.Google Scholar
18. Spalding, D.B. and Chi, S.W. The drag of a compressible boundary layer on a smooth flat plate with and without heat transfer, J Fluid Mech, January 1964, 8, (1), pp 117–143.Google Scholar
19. Von Karman, T. Turbulence and skin friction, J Aeronaut Sciences, January 1934, 1, (1),pp 1–20.Google Scholar
20. Schoenherr, K.E. Resistance of flat surfaces moving through a fluid, Transaction of Society of Naval Architects and Marine Engineers, 1932, 40, pp 279–313.Google Scholar
21. Gad-El-Hak, M. and Bandyopadhyay, P.R. Reynolds number effects in wall-bounded turbulent flows, ASME J Applied Mechanic Review, August 1994, 47, (8), pp 307–365.Google Scholar
22. Gad-El-Hak, M. Does a turbulent boundary layer ever achieve self-preservation?, Lecture given at the Department of Aerospace Engineering, Delft University of Technology, June 1994.Google Scholar
23. Motallebi, F. Comments on skin friction and velocity profile family for compressible turbulent boundary layers, AIAA J, September 1994, 32, (9), pp 1938.Google Scholar
24. Fernholz, H.H. and Finley, P.J. (eds) A critical compilation of compressible boundary layer data, AGARDograph No 223, June 1977.Google Scholar
25. Fernholz, H.H. and Finley, P.J. (eds) A further compilation of compressible boundary layer data with a survey of turbulence data, AGARDograph No 263, November 1981.Google Scholar