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Short-length instabilities, breakdown and initial value problems in dynamic stall

Published online by Cambridge University Press:  26 February 2010

O. S. Ryzhov  and
F. T. Smith
O. S. Ryzhov
Affiliation:
Computing Centre of the Academy of Sciences of the USSR, 40 Vavilov Street, 117333 Moscow, USSR.
F. T. Smith
Affiliation:
Mathematics Department, University College London, Gower Street, London. WC1E 6BT
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Summary

A recent paper [1] indicates that the beginnings of dynamic stall, near an aerofoil's leading edge, for instance, can be regarded as the finite-time nonlinear breakdown of a boundary layer subjected to an angle of attack above the critical value for the existence of a steady solution. The present theoretical study shows that the same non-linear breakdown can occur even in the below-critical regime. This happens particularly when reversed flow is present since short wavelength disturbances are then unstable and accumulate, for certain confined initial conditions, to force the finite-time collapse. A number of marginal cases with forward or reversed, subsonic or supersonic, oncoming motion are also noted and shed extra light on the instability and subsequent breakdown.

Type
Research Article
Information
Mathematika , Volume 31 , Issue 2 , December 1984 , pp. 163 - 177
Copyright
Copyright © University College London 1984

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References

1.Smith, F. T.. Aero. Quart., (1982), 331.CrossRefGoogle Scholar
2.Stewartson, K., Smith, F. T. and Kaups, K.. Studies Appl. Math., 67 (1982), 45.CrossRefGoogle Scholar
3.Smith, F. T. and Daniels, P. G.. J. Fluid Mech., 110 (1981), 1.CrossRefGoogle Scholar
4.Brown, S. N. and Stewartson, K.. S.I.A.M. J. Appl. Math., 43 (1983), 1119.CrossRefGoogle Scholar
5.Ryzhov, O. S. and , V. I.Zhuk. Proc. 1th Internal. Con). Numr. Methods Fluid Dynam., Stanford 1980. Lecture Notes in Physics No. 141.Google Scholar
6.Ruban, A. I.. Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, 6 (1982), 55.Google Scholar
7.Elliott, J. W. and Smith, F. T.. In preparation.Google Scholar