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Remarks on the nonlinear dynamics of a typical aerofoil section in dynamic stall

Published online by Cambridge University Press:  03 February 2016

U. Galvanetto ,
J. Peirò  and
C. Chantharasenawong
U. Galvanetto
Affiliation:
Department of Aeronautics, Imperial College, London, UK
J. Peirò
Affiliation:
Department of Aeronautics, Imperial College, London, UK
C. Chantharasenawong
Affiliation:
Department of Aeronautics, Imperial College, London, UK
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Abstract

We use standard tools of the theory of dynamical systems such as phase plots, bifurcation diagrams and basins of attraction to analyse and understand the dynamic behaviour of a typical aerofoil section under dynamic stall conditions. The structural model is linear and the aerodynamic loading is represented by the Leishman-Beddoes semi-empirical dynamic stall model. The loads given by this model are nonlinear and non-smooth, therefore we have integrated the equation of motion using a Runge-Kutta-Fehlberg (RKF45) algorithm equipped with event detection. We perform simulations of the motion for a range of Mach numbers and show that the model is very sensitive to small variations. This is evidenced by the presence in the bifurcation diagram of co-existing attractors or, in other words, by the existence of more than one steady-state motion for a given Mach number. The mechanisms for the appearance and disappearance of the co-existing attractors are elucidated by analysing the evolution of their basins of attraction as the Mach number changes.

Type
Research Article
Information
The Aeronautical Journal , Volume 111 , Issue 1125 , November 2007 , pp. 731 - 739
Copyright
Copyright © Royal Aeronautical Society 2007 

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