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Research Papers

# A Conceptual Flutter Analysis of a Packet of Vanes Using a Mass-Spring Model

[+] Author and Article Information
Roque Corral1

Technology and Methods Department, Industria de TurboPropulsores S.A., 28830 Madrid, Spainroque.corral@itp.es

Juan Manuel Gallardo

Technology and Methods Department, Industria de TurboPropulsores S.A., 28830 Madrid, Spainjuan.gallardo@itp.es

Carlos Martel

1

Also: Associate Professor at the Department of Engine Propulsion and Fluid Dynamics of the School of Aeronautics, Universidad Politécnica de Madrid (UPM).

J. Turbomach 131(2), 021016 (Jan 29, 2009) (7 pages) doi:10.1115/1.2952364 History: Received August 01, 2007; Revised December 05, 2007; Published January 29, 2009

## Abstract

The linear aeroelastic stability of a simplified mass-spring model representing the basic dynamics of a packet of $Na$ airfoils has been used to uncover a new type of coupled mode flutter. This simple model retains an essential dynamical feature of the vane packet: the presence of a cluster of $Na−1$ nearly identical purely structural natural frequencies due to the much larger stiffness of the lower platform as compared to that of the airfoil. Using this model it may be seen that this degeneracy makes the $Na−1$ associated mode shapes extremely sensible to the addition of small perturbations such as the aerodynamic forces. Since the determination of the aerodynamic vibrational correction (damping and frequency) requires knowing the mode shape, the aerodynamic corrections of the $Na−1$ cluster modes are now unavoidably coupled together. Moreover, the computation of the aerodynamic correction independently for each structural mode shape leads typically to dangerously overpredicting the stabilizing effect of vane packing. It is shown that the expected stabilizing effect due to the packets may be negligible, depending on the relative frequency split associated with the strength of the aerodynamic forces and realistic structural effects such as the finite stiffness of the lower platform. It is also shown that in these cases, the most unstable mode may be, in a first approximation, very similar to that obtained modeling the stator as a continuous ring.

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## Figures

Figure 1

Typical geometry and mode shape of a LPT vane packet

Figure 2

Mode frequency distribution of a realistic vane packet for a fixed nodal diameter

Figure 3

Mass-spring model of a packet of Na vanes with an infinitely stiff platform

Figure 4

Aerodynamic nondimensional frequency correction (top) and damping, expressed as a fraction of the critical damping (bottom) for traveling wave with the indicated number of nodal diameters and computed at the cluster frequency ωa

Figure 5

Top: Advanced mass-spring model of a packet of Na vanes, with flexible platform and hook. Bottom: Vibration frequencies versus nodal diameter for a stator of completely independent vane packets for the parameter values given in the text (insets show the in-sector vane displacements for the modes in the frequency cluster).

Figure 6

Stability of the vane packet using realistic aerodynamics. (Symbols: ×, structural eigenvalues; ●, aeroelastic eigenvalues; ○, most unstable mode. Top: Packet model; bottom: continuous ring).

Figure 7

Representation of the most unstable mode shape for the tuned and realistic aerodynamics (top: physical space with vertical lines marking each packet; bottom: traveling-wave decomposition)

Figure 8

Effect of the density variation in the damping of the continuous ring model

Figure 9

Stability of the vane packet using mild aerodynamics. (Symbols: ×, structural eigenvalues: ●, aeroelastic eigenvalues; ○, most unstable mode. Top: packet model; bottom: continuous ring).

Figure 10

Fourier representation of the less stable mode for the complex model and mild aerodynamics (Top: physical space with vertical lines marking each packet; bottom: traveling-wave decomposition)

Figure 11

Comparison of the fully coupled (dots) and uncoupled (open circles) approaches. Top: Packet model; bottom: continuous ring.

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