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Planar flows past thin multi-blade configurations

Published online by Cambridge University Press:  26 April 2006

F. T. Smith
Affiliation:
Mathematics Department, University College, Gower St., London, WC1E 6BT, UK
S. N. Timoshin
Affiliation:
Mathematics Department, University College, Gower St., London, WC1E 6BT, UK

Abstract

Two-dimensional steady laminar flows past multiple thin blades positioned in near or exact sequence are examined for large Reynolds numbers. Symmetric configurations require solution of the boundary-layer equations alone, in parabolic fashion, over the successive blades. Non-symmetric configurations in contrast yield a new global inner–outer interaction in which the boundary layers, the wakes and the potential flow outside have to be determined together, to satisfy pressure-continuity conditions along each successive gap or wake. A robust computational scheme is used to obtain numerical solutions in direct or design mode, followed by analysis. Among other extremes, many-blade analysis shows a double viscous structure downstream with two streamwise length scales operating there. Lift and drag are also considered. Another new global interaction is found further downstream. All the interactions involved seem peculiar to multi-blade flows.

Type
Research Article
Copyright
© 1996 Cambridge University Press

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References

Brown, S. N. & Stewartson, K. 1970 J. Fluid Mech. 42, 561584.
Brown, S. N. & Stewartson, K. 1975 Aero. Q., Nov., 275280.
Davis, S. S. & Chang, I.-C. 1986 Invited survey paper, AIAA 24th Aerosp. Sci. Mtg., Jan. 6–9 Reno, Nevada, USA. Paper 86–0336.
Glauert, H. 1948 The Elements of Aerofoil and Airscrew Theory, 2nd edition. Cambridge University Press.
Goldstein, S. 1930 Proc. Camb. Phil. Soc. 26, 130.
Hawkings, D. L. & Lowson, M. V. 1974 J. Sound Vib. 36, 120.
Messiter, A. F. & Stewartson, K. 1972 AIAA J. 10, 719.
Moore, D. W. & Saffman, P. G. 1973 Proc. R. Soc. Lond. A 333, 491508.
Muskhelishvili, N. I. 1946 Singular Integral Equations. P. Noordhoff (English transl. 1953).
Parry, A. B. & Crighton, D. G. 1989 AIAA J. 27, 11841190.
Riley, N. 1996 Handbook of Acoustics, chap. 30. Wiley.
Seddon, J. 1990 Basic Helicopter Dynamics, BSP Professional Books. Oxford.
Smith, F. T. 1976 J. Fluid Mech. 78, 709736.
Smith, F. T. 1983 J. Fluid Mech. 131, 219249.
Smith, F. T. & Timoshin, S. N. 1996 Proc. R. Soc. Lond. A 452, 13011329.
Spence, D. A. 1970 J. Fluid Mech. 44, 625636.
Stewartson, K. 1974 Adv. Appl. Mech. 14, 145.
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. Academic Press.
Wake, B. E. & Baeder, J. D. 1994 Am. Helicopter Soc. Aeromech. Specialists Conf., San Fransisco, CA, USA, Jan. 19–21.