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Compressible-flow channel flutter

Published online by Cambridge University Press:  20 April 2006

J. B. Grotberg  and
T. R. Shee
J. B. Grotberg
Affiliation:
Department of Engineering Sciences and Applied Mathematics, The Technological Institute, Northwestern University, Evanston, Illinois 60201
T. R. Shee
Affiliation:
Department of Engineering Sciences and Applied Mathematics, The Technological Institute, Northwestern University, Evanston, Illinois 60201
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Abstract

The effect of fluid compressibility on the dynamic stability of a two-dimensional flow through a flexible channel is analysed. The compressibility parameter Q is defined as the ratio of a reference elastic wave speed of the wall to the local speed of sound. As the fluid speed increases, the walls become dynamically unstable at the critical fluid speed S0 and start to flutter at critical frequency ω0. The effect of three other dimensionless parameters on the critical condition is also analysed. These are the ratio γ of fluid damping to wall damping, the ratio B of wall bending resistance to elastance, and the ratio μ of wall to fluid mass. Nonlinear analysis using the Poincaré–Lindstedt method shows stiffening at supercritical speeds. Further stability analysis using the method of multiple scales shows that the amplitude growth is finite and the nonlinear fluttering state is stable. Both symmetric and antisymmetric modes of oscillation are analysed. A frictionless system is found to be a singular case in the nonlinear theory. The hydraulic approximation employed in the analysis is shown to be a particular limiting form of the corresponding Orr–Sommerfeld system.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 159 , October 1985 , pp. 175 - 193
Copyright
© 1985 Cambridge University Press

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