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Unsteady flow in a supersonic cascade with strong in-passage shocks

Published online by Cambridge University Press:  12 April 2006

M. E. Goldstein ,
Willis Braun  and
J. J. Adamczyk
M. E. Goldstein
Affiliation:
National Aeronautics and Space Administration, Lewis Research Center, Cleveland, Ohio 44135
Willis Braun
Affiliation:
National Aeronautics and Space Administration, Lewis Research Center, Cleveland, Ohio 44135
J. J. Adamczyk
Affiliation:
National Aeronautics and Space Administration, Lewis Research Center, Cleveland, Ohio 44135
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Abstract

Linearized theory is used to study the unsteady flow in a supersonic cascade with in-passage shock waves. We use the Wiener–Hopf technique to obtain a closed-form analytical solution for the supersonic region. To obtain a solution for the rotational flow in the subsonic region we must solve an infinite set of linear algebraic equations. The analysis shows that it is possible to correlate quantitatively the oscillatory shock motion with the Kutta condition at the trailing edges of the blades. This feature allows us to account for the effect of shock motion on the stability of the cascade.

Unlike the theory for a completely supersonic flow, the present study predicts the occurrence of supersonic bending flutter. It therefore provides a possible explanation for the bending flutter that has recently been detected in aircraft-engine compressors at higher blade loadings.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 83 , Issue 3 , 5 December 1977 , pp. 569 - 604
Copyright
© 1977 Cambridge University Press

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