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Research Papers

Aeroelastic Analysis of Rotors With Flexible Disks and Alternate Blade Mistuning

[+] Author and Article Information
James M. Bleeg

 Pratt & Whitney, 400 Main Street, East Hartford, CT 06108james.bleeg@pw.utc.com

Ming-Ta Yang

 Pratt & Whitney, 400 Main Street, East Hartford, CT 06108ming-ta.yang@pw.utc.com

James A. Eley

 Pratt & Whitney, 400 Main Street, East Hartford, CT 06108james.eley@pw.utc.com

In the case of a tuned rotor, N is the number of blades. In the case of a rotor with ABM, N is the number of blades divided by 2.

For tuned rotors with stiff disks, mode families are usually isolated with large frequency differences between modes at the same nodal diameter. However, ABM rotors with flexible disks can have two or more modes per nodal diameter within a relatively narrow frequency range. Dyadic modes are discussed further in Sec. 3.

Significant geometric differences between the two blade types are not evident in the contour plots because all the contour plots presented herein are mapped to rectangles to protect proprietary rotor designs.

For this application, the PSMs were constructed in pairs: For the first PSM of a given pair, the A blade deflects and the B blade is stationary and vice versa for the second PSM. Constructing the PSM in this way allowed for a more straightforward implementation of the method.

Nodal diameters>0 travel in the direction of the rotor spin. Nodal diameters<0 travel in the opposite direction.

Predicted damping levels vary significantly with mode (e.g., Fig. 1). In this paper, modes with predicted aerodynamic damping levels clearly below the damping distribution mean are labeled lightly damped. Modes with predicted damping levels clearly above the mean are labeled heavily damped.

J. Turbomach 131(1), 011011 (Oct 17, 2008) (9 pages) doi:10.1115/1.2812957 History: Received June 20, 2007; Revised July 19, 2007; Published October 17, 2008

A new reduced-order aeroelastic model using the principal shapes (AMPSs) of modes is presented. Rotors with flexible disks and alternate blade mistuning can challenge the fidelity of flutter prediction techniques that assume uniform blade-to-blade geometry and mode shape invariance with nodal diameter pattern. The AMPS method, however, accounts for alternating blade geometry as well as varying blade mode shapes, providing accurate flutter predictions for a large number of modes from a small number of computational fluid dynamics simulations. AMPS calculations on rotors with alternate blade mistuning are presented and compared to other prediction techniques. The results provide insight into how alternate blade mistuning affects aerodynamic coupling and the flutter characteristics of a rotor.

Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Nodal diameter map and mode shapes, ABM Rotor X

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Figure 2

Singular values of PSM, ABM Rotor X

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Figure 3

Errors of mode shapes approximated by PSM, ABM Rotor X. The normalized error for the rth mode is defined as ‖ϕr−ϕr‖∕maxr‖ϕr‖ where ϕr is the mode shape approximated by PSM and ϕr is the baseline mode shape. ‖∙‖ is the Euclidean norm of a vector.

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Figure 4

IC CFD Models for ABM rotors

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Figure 5

Pressure ratio versus flow, Rotor X

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Figure 6

Aerodynamic damping, ABM Rotor X

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Figure 7

Magnitude of unsteady pressure, ABM Rotor X, B blade, 5 ND mode

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Figure 8

Aerodynamic damping density, ABM Rotor X, B BLADE, 5 ND mode

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Figure 9

Comparison of AMPS and direct method, ABM Rotor X

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Figure 10

(a) Comparison of aerodynamic damping, Rotor X, not aliased and (b) comparison of aerodynamic damping, Rotor X, aliased

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Figure 11

(a) Blade-by-blade damping breakdown, −4 ND mode, lightly damped, tuned Rotor X and (b) blade-by-blade damping breakdown, −4 ND mode, lightly damped, ABM Rotor X

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Figure 12

(a) Blade-by-blade damping breakdown, −4 ND mode, heavily damped, tuned Rotor X and (b) blade-by-blade damping breakdown, −4 ND mode, heavily damped, ABM Rotor X

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Figure 13

Ratios of maximum blade deflection amplitude, ABM Rotor X

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Figure 14

(a) Blade-by-blade damping breakdown, −3 ND mode, lightly damped, tuned Rotor X and (b) blade-by-blade damping breakdown, −3 ND mode, lightly damped, ABM Rotor X

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Figure 15

ND map of tuned Rotor X

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Figure 16

Ratios of maximum blade deflection amplitude, ABM Rotor X

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Figure 17

Aerodynamic damping, Rotor X. Aerodynamic input for the CH and KF methods is provided by AMPS analysis of tuned Rotor X.

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Figure 18

ND map, tuned Rotor Y (38 blades)

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Figure 19

Aerodynamic damping, Rotor Y. Aerodynamic input for the CH and KF methods is provided by AMPS analysis of tuned Rotor Y.

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Figure 20

Ratios of maximum blade deflection amplitude, ABM Rotor Y

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