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Linear instability analysis of low-pressure turbine flows

Published online by Cambridge University Press:  01 June 2009

N. ABDESSEMED ,
S. J. SHERWIN  and
V. THEOFILIS
N. ABDESSEMED
Affiliation:
Department of Aeronautics, South Kensington Campus, Imperial College London, London SW7 2AZ, UK
S. J. SHERWIN
Affiliation:
Department of Aeronautics, South Kensington Campus, Imperial College London, London SW7 2AZ, UK
V. THEOFILIS*
Affiliation:
School of Aeronautics, Universidad Politécnica de Madrid, Pza. Cardenal Cisneros 3, E28040 Madrid, Spain
*
†Email address for correspondence: [email protected]
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Abstract

Three-dimensional linear BiGlobal instability of two-dimensional states over a periodic array of T-106/300 low-pressure turbine (LPT) blades is investigated for Reynolds numbers below 5000. The analyses are based on a high-order spectral/hp element discretization using a hybrid mesh. Steady basic states are investigated by solution of the partial-derivative eigenvalue problem, while Floquet theory is used to analyse time-periodic flow set-up past the first bifurcation. The leading mode is associated with the wake and long-wavelength perturbations, while a second short-wavelength mode can be associated with the separation bubble at the trailing edge. The leading eigenvalues and Floquet multipliers of the LPT flow have been obtained in a range of spanwise wavenumbers. For the most general configuration all secondary modes were observed to be stable in the Reynolds number regime considered. When a single LPT blade with top to bottom periodicity is considered as a base flow, the imposed periodicity forces the wakes of adjacent blades to be synchronized. This enforced synchronization can produce a linear instability due to long-wavelength disturbances. However, relaxing the periodic restrictions is shown to remove this instability. A pseudo-spectrum analysis shows that the eigenvalues can become unstable due to the non-orthogonal properties of the eigenmodes. Three-dimensional direct numerical simulations confirm all perturbations identified herein. An optimum growth analysis based on singular-value decomposition identifies perturbations with energy growths O(105).

Type
Papers
Information
Journal of Fluid Mechanics , Volume 628 , 10 June 2009 , pp. 57 - 83
Copyright
Copyright © Cambridge University Press 2009

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