Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-26T18:27:35.406Z Has data issue: false hasContentIssue false
  • English
  • Français

The Turbulent Wall Jet in an Arbitrary Pressure Gradient

Published online by Cambridge University Press:  07 June 2016

I. S. Gartshore  and
B. G. Newman
I. S. Gartshore
Affiliation:
McGill University, Montreal
B. G. Newman
Affiliation:
McGill University, Montreal
Get access

Summary

A method for calculating the growth of a turbulent wall jet in streaming flow has been developed. The flow is assumed to be two-dimensional, incompressible and over a plane, smooth wall. Downstream variations of pressure are permitted and separation in an adverse pressure gradient may be predicted. The method incorporates procedures for matching the flow to that at the blowing slot, although it is postulated that the upstream boundary layer there is thin enough that the wall jet develops without an unmixed wake (i.e. there is not a minimum in the mean-velocity profile).

The method incorporates four integral momentum equations taken from the wall to various points in the flow. The calculation of the outer shearing stress, although empirical, is based on the large-eddy equilibrium hypothesis and therefore has some foundation. The remaining empiricism in the method is based on measurements in self-preserving wall jets.

The method has been used to predict the jet-momentum coefficient required to suppress separation over a trailing-edge flap attached to a thin aerofoil. Plausible curves have been obtained Using assumed values of upstream boundary layer at the slot. Of some practical interest is the indication that large savings in power are possible if the upstream boundary layer is removed. This indicates that blowing combined with upstream suction, or multiple-slot blowing, may give useful savings in the application of blowing to prevent separation.

Type
Research Article
Information
Aeronautical Quarterly , Volume 20 , Issue 1 , February 1969 , pp. 25 - 56
Copyright
Copyright © Royal Aeronautical Society. 1969

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. Lachmann, G. V. (Ed.) Boundary layer and flow control, Vol. I, Pergamon, 1961.Google Scholar
2. Carriere, P., Eichelbrenner, E. and Poisson-Quinton, Ph. Contribution théoretique et experimentale a l’étude du contrôle de la couche limite par soufflage; Advances in Aeronautical Sciences, Vol. 2, MacMillan, New York, 1959.Google Scholar
3. Eichelbrenner, E. A. and Dumargue, P. Le problème du “jet pariétal” plan en régime turbulent pour un écoulement extérieur de vitesse Ue constante. Journal de Mécanique, Vol. I, No. 1, p. 109, and Vol. I, No. 2, p. 123,1962.Google Scholar
4. Patel, R. P. and Newman, B. G. Self-preserving, two-dimensional turbulent jets and wall jets in a moving stream. MERL Report Ae 5, McGill University, 1961.Google Scholar
5. Newman, B. G. Turbulent jets and wakes in a pressure gradient. Proceedings, General Motors Conference, Detroit. Elsevier, Amsterdam, 1965.Google Scholar
6. Glauert, M. B. The wall jet. Journal of Fluid Mechanics, Vol. I, p. 625, 1956.Google Scholar
7. Bradshaw, P. and Gee, M. T. Turbulent wall jets with and without an external stream. ARC R & M 3252, 1962.Google Scholar
8. Harris, G. L. The two-dimensional, incompressible, turbulent wall jet beneath an external stream of arbitrary pressure gradient. Thesis submitted to L’Université Libre de Bruxelles for the degree of Docteur en Sciences Appliquées, May 1965.Google Scholar
9. Kruka, V. and Eskinazi, S. The wall-jet in a moving stream. Journal of Fluid Mechanics, Vol. 20, p. 555, 1964.Google Scholar
10. KÜChemann, D. and Weber, J. Aerodynamics of propulsion. McGraw-Hill Publications in Aeronautical Science, p. 237, 1953.Google Scholar
11. Nicoll, W. B. and Escudier, M. P. The entrainment function in turbulent boundary layer and wall-jet calculations. Imperial College of Science and Technology, London, Department of Mechanical Engineering, TWF/R/1, 1965.Google Scholar
12. Nicoll, W. B. The turbulent wall jet: its development and film-cooling effectiveness. Thesis submitted for PhD degree, University of London, 1967.Google Scholar
13. Squire, H. B. and Trouncer, J. Round jets in a general stream. ARC R & M 1974, 1944.Google Scholar
14. Duncan, W. J., Thom, A. S. and Young, A. D. The mechanics of fluids. Edward Arnold, London, 1960.Google Scholar
15. Patel, R. P. Self-preserving, two-dimensional turbulent jets and wall jets in a moving stream. MEng Thesis, McGill University, 1962.Google Scholar
16. Townsend, A. A. The properties of equilibrium boundary layers. Journal of Fluid Mechanics, Vol. 1, p. 561, 1956.Google Scholar
17. Clauser, F. M. The turbulent boundary layer. Advances in Applied Mechanics, Vol. 4, Academic Press, New York, 1956.Google Scholar
18. Meixor, G. L. and Gibson, D. M. Equilibrium turbulent boundary layers. Journal of Fluid Mechanics, Vol. 24, 1966.Google Scholar
19. Kline, S. J., Lisin, A. V. and Waitman, B. A. Preliminary experimental investigation of effect of free stream turbulence on turbulent boundary layer growth. NASA TN D-368, 1960.Google Scholar
20. Gartshore, I. S. An experimental examination of the large-eddy equilibrium hypothesis. Journal of Fluid Mechanics, Vol 24, p. 89, 1966.Google Scholar
21. Townsend, A. A. The structure of turbulent shear flow. Cambridge University Press, 1956.Google Scholar
22. Gartshore, I. S. Two-dimensional turbulent wakes. Journal of Fluid Mechanics, Vol. 30, p. 547, 1967.CrossRefGoogle Scholar
23. Gartshore, I. S. and Hawaleshka, O. The design of a two-dimensional blowing slot and its application to a turbulent wall jet in still air. MERL Technical Note 64-5, McGill University, 1964.Google Scholar
24. Townsend, A. A. Turbulence. Handbook of fluid dynamics, McGraw-Hill, 1961.Google Scholar
25. Glauert, H. The elements of aerofoil and airscrew theory. Second Edition, Cambridge University Press, 1948.Google Scholar
26. Newman, B. G. Some contributions to the study of the turbulent boundary layer near separation. Australian Department of Supply Report ACA-53, 1951.Google Scholar
27. Thompson, B. G. J. A critical review of existing methods of calculating the turbulent boundary layer. ARC R & M 3447, 1964.Google Scholar
28. Bradshaw, P. The response of a retarded equilibrium boundary layer to the sudden removal of pressure gradient. NPL Aero Report 1145, ARC 26, 758, FM 3577, 1965.Google Scholar
29. Lohr, R. Erhohung des Maximalauftriebes eines Rechteckflugels in Bodenahe durch kombiniertes Ausblasen an der Flugelnase und an der Hinterkantenklappe. Deutsche Versuchsanstalt für Luft-und Raumfahrt, DLR, FB 64-02, 1964.Google Scholar
30. Kelly, M. W. Analysis of some parameters used in correlating blowing type boundary layer control data. NACA RM A56F12, 1956.Google Scholar
31. Bradbury, L. J. S. and Riley, J. Spread of a turbulent plane jet. Journal of Fluid Mechanics, Vol. 27, p. 381, 1967.Google Scholar