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The Effect of Jet Entrainment on Lift and Moment for a Thin Aerofoil with Blowing

Published online by Cambridge University Press:  07 June 2016

I . Wygnanski
Affiliation:
Mechanical Engineering Research Laboratories, McGill University
B. G. Newman
Affiliation:
Mechanical Engineering Research Laboratories, McGill University
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Summary

Jet flap theory for thin aerofoils has been extended to include the effect of jet entrainment on the external flow when the jet is blown over the upper surface of the aerofoil. The effective camber of the aerofoil is increased by the sink effect due to entrainment and the increase of lift at zero incidence is proportional to the square root of the jet momentum coefficient. Formulae and charts are presented to facilitate the determination of the increments of lift and pitching moment due to this effect. The theory is shown to be in first-order agreement with the exact solution for a circular-arc aerofoil of small camber with distributed sinks on the upper surface.

The new theory is compared with four old sets and one new set of experimental data. It greatly improves the accuracy of prediction for cases where the incidence and flap angle are small. The new theory substantiates the usefulness of a small flap in applications of the jet flap principle.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society. 1964

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References

1. Malavard, L., Poisson-quinton, PH. and Jousserandot, P. Theoretical and Experimental Investigations of Circulation Control. Translated by Berthoff and Hazen. Princeton University Report No. 358, 1956.Google Scholar
2. Stratford, B. S. Early Thoughts on the Jet Flap. Aeronautical Quarterly, Vol. VII, p. 45, February 1956.Google Scholar
3. Helmbold, H. B. The Lift of a Blowing Wing in a Parallel Stream. Journal of the Aeronautical Sciences, Vol. 22, p. 341, 1955.Google Scholar
4. Spence, D. A. The Lift Coefficient of a Jet-Flapped Wing. Proc. Roy. Soc. A, Vol. 238, p. 46, 1956.Google Scholar
5. Legendre, R. Influence de l'Emission d'un Jet au bord de Fuite d'un Profil sur l'Ecoulement autour de ce Profil. Comptes Rendus, Academie des Sciences, Paris, 1956.Google Scholar
6. Woods, L. C. Some Contributions to Jet-Flap Theory and to the Theory of Source Flow from Aerofoils. A.R.C. Current Paper 388, 1958.Google Scholar
7. Malavard, L. Sur une Théorie Lineaire du Soufflage au bord de Fuite d'un Profil d'Aile. Comptes Rendus, Académie des Sciences, Paris, 1956.Google Scholar
8. Taylor, G. I. Flow Induced by Jets. Journal of the Aeronautical Sciences, Vol. 25, p. 464, 1958.Google Scholar
9. Schlichting, H. Boundary Layer Theory, p. 605. 4th edition, McGraw-Hill, 1960.Google Scholar
10. Newman, B. G. Deflection of Plane Jets by Adjacent Boundaries—Coanda Effect. Boundary Layer and Flow Control, Vol. I. Edited by Lachmann, . Pergamon Press, 1961.Google Scholar
11. Carriere, P. and Eichelbrenner, E. A. Theory of Flow Reattachment. Boundary Layer and Flow Control, Vol. I, p. 212. Edited by Lachmann, . Pergamon Press, 1961.Google Scholar
12. Reichardt, H. On a New Theory of Free Turbulence. Journal of the Royal Aeronautical Society, Vol. 47, p. 167, 1943.Google Scholar
13. Förthmann, E. Uber Turbulente Strahlausbreitung. Ingenieur Archiv, Vol. 5, p. 42, 1934. Also N.A.C.A. T.N. 789, 1936.Google Scholar
14. Knystautas, R. The Turbulent Jet From a Series of Holes in Line. Aeronautical Quarterly, Vol. XV, p. 1, February 1964.Google Scholar
15. Von glahn, U. H. Use of the Coanda Effect for Jet Deflection and Vertical Lift with Multiple Flat-Plate and Curved Plate Deflection Surface. N.A.C.A. T.N. 4377, 1958.Google Scholar
16. Libby, P. A. and Ting, L. Remarks on the Eddy Viscosity in Compressible Mixing Flows. Journal of the Aeronautical Sciences, Vol. 27, p. 797, 1960.Google Scholar
17. Mager, A. Transformation of the Compressible Turbulent Boundary Layer. Journal of the Aeronautical Sciences, Vol. 25, p. 305, 1958.Google Scholar
18. Pai, S. Fluid Dynamics of Jets, p. 148. Von Nostrand, 1954.Google Scholar
19. Crane, L. J., The Laminar and Turbulent Mixing of Jets of Compressible Fluid. Part II, The Mixing of Two Semi-Infinite Streams. Journal of Fluid Mechanics, Vol. 3, p. 81, 1957.Google Scholar
20. Myers, G. E., Schauer, J. J. and Eustis, R. H. The Plane Turbulent Wall Jet, Part I. Jet Development and Friction Factor. Department of Mechanical Engineering, Stanford University, Technical Report No. 1, June 1961.Google Scholar
21. Schwarz, W. H. and Cosart, W. P. The Two-Dimensional Turbulent Wall Jet. Journal of Fluid Mechanics, Vol. 10, Part 4, p. 481, 1961.Google Scholar
22. Patel, R. P. Self-Preserving Two-Dimensional Turbulent Jets and Wall Jets in a Moving Stream. McGill University, M.Eng. Thesis, 1962.Google Scholar
23. Patel, R. P. and Newman, B. G. Self-Preserving Two-Dimensional Turbulent Jets and Wall Jets in a Moving Stream. McGill University, Mechanical Engineering Research Laboratories, Aeronautical Report No. 5, 1961.Google Scholar
24. Sawyer, R. A. Two-Dimensional Turbulent Jets with Adjacent Boundaries. Cambridge University, Ph.D. Thesis, 1962.Google Scholar
25. Stratford, B. S., Jawor, Z. M. and Golesworthy, G. T. The Mixing with Ambient Air of a Cold Airstream in a Centrifugal Field. N.G.T.E. Memo 355, 1962.Google Scholar
26. Fekete, G. I. Coanda Flow of a Two-Dimensional Wall Jet on the Outside of a Circular Cylinder. McGill University, Mechanical Engineering Department, Report No. 63-11, 1963.Google Scholar
27. Spence, D. A. The Lift on a Thin Aerofoil with a Jet-Augmented Flap. Aeronautical Quarterly, Vol. IX, p. 287, 1958.Google Scholar
28. Spence, D. A. Simple Results for a Two-Dimensional Jet Flap Aerofoil. Aeronautical Quarterly, Vol. IX, p. 395, 1958.Google Scholar
29. Thomas, F. Untersuchungen über die Erhohung des Auftriebes von Tragflugeln mittels Grenzschichtbeeinflussung durch Ausblasen. Zeitschrift für Flugwissenschaften, Vol. 2, No. 10, p. 46, 1962.Google Scholar
30. Attinello, J. S. Design and Engineering Features of Flap Blowing Installations. Boundary Layer and Flow Control, Vol. I, p. 488. Edited by Lachmann, . Pergamon Press, 1961.Google Scholar
31. Milne-thomson, L. M. Theoretical Hydrodynamics, 4th Edition. Macmillan, 1960.Google Scholar
32. Glauert, H. The Elements of Aerofoil and Airscrew Theory. Cambridge University Press, 1926.Google Scholar
33. Gröbner, W. and Hofreiter, N. Integral Tables, p. 75. Springer, 1961.Google Scholar
34. Jahnke, E., Emde, F. and Lösch, F. Tables of Higher Functions. 6th Edition, McGraw-Hill, 1960.Google Scholar
35. Peirce, B. O. A Short Table of Integrals. Ginn, London, 1956.Google Scholar
36. Hough, G. R. Cambered Jet-Flap Aerofoil Theory. Cornell University, Graduate School of Aeronautical Engineering Report, 1959.Google Scholar
37. Siestrunck, R. General Theory of the Jet-Flap in Two-Dimensional Flow. Boundary Layer and Flow Control, Vol. I, p. 358. Edited by Lachmann, . Pergamon Press, 1961.Google Scholar
38. Poisson-quinton, PH. Recherches Théoriques et Expérimentales sur le Controle de la Couche Limite. Seventh International Congress of Applied Mechanics, Vol. II, Part 2, p. 365, 1948.Google Scholar
39. Mandl, P. Effect of Standing Vortex on Flow About Suction Aerofoils with Split Flaps. N.R.C. (Canada), Aero. Report LR-239, 1959.Google Scholar
40. Wygnanski, I. and Newman, B. G. General Description and Calibration of the McGill 3 ft x 2 ft Low Speed Wind Tunnel. McGill University Mechanical Engineering Research Laboratories, Aeronautical Report No. 4, 1961.Google Scholar