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Research Papers: Gas Turbines: Structures and Dynamics

A Fast Influence Coefficient Method for Aerodynamically Mistuned Disks Aeroelasticity Analysis

[+] Author and Article Information
Kwen Hsu1

 Rolls-Royce Corporation, Aerothermal Method Group, 2001 South Tibbs Avenue, Indianapolis, IN 46241kwen.hsu@rolls-royce.com

Daniel Hoyniak

 Rolls-Royce Corporation, Dynamics Group, 2001 South Tibbs Avenue, Indianapolis, IN 46241

1

Corresponding author.

J. Eng. Gas Turbines Power 133(12), 122502 (Aug 26, 2011) (10 pages) doi:10.1115/1.4004110 History: Received July 08, 2010; Revised March 11, 2011; Published August 26, 2011; Online August 26, 2011

The blade geometric variations are usually ignored in the prediction of bladed disk aerodynamic damping values. This situation is the result of the high computational cost associated with the full-annulus unsteady flow CFD models required to account for these blade geometric differences. This paper presents an approach that can account for these geometric differences with high fidelity and at a reasonable one-time cost. The approach is based on the use of the influence-coefficient (IC) method together with a set of sensitivity coefficients defined for the blade geometry changing effects. The sensitivity coefficients make use of a set of principal component analysis (PCA) modes that describe the measured blade geometry variation. Once the sensitivity coefficients are determined, they are used to construct the IC matrices and to predict the aerodynamic damping values associated with the geometrically mistuned disk. The currently proposed method is unique in two aspects. The first is to follow the observed physics while making assumptions in the linearization process to reduce the number of required sensitivity coefficients. The second is to construct the multiblade CFD model, with blades of different geometries, in a unique way to reduce the data generation costs. Two IC approximation formulas were developed. If NP denotes the number of PCA modes used to describe the blade geometric variation, one formula reduces the number of required multiblade unsteady CFD models from (NP +1) [3] to (NP +1) [2], the other reduces the number of CFD models from (NP +1) [2] to NP +1. Results obtained from these two formulas are compared and validated.

FIGURES IN THIS ARTICLE
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Copyright © 2011 by American Society of Mechanical Engineers
Topics: Disks , Blades , Geometry , Shapes
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References

Figures

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Figure 1

The DOE table for all 7-blade models we need for 10 PCA modes

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Figure 2

The chosen 7-blade model design

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Figure 3

Comparison of blade shape p0 with blade shape p6: discrepancy in trailing edges. Blue line is for p6 shape and red line is for p0 shape.

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Figure 4

Pressure contours on the blade surfaces. Seven-blade model steady-state solution, p0p6 case, suction side. Unit: Pa.

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Figure 5

(a) A bladed disk design used for methodology validation. Case 1. (b) First quadrant of validation case 2. (c) First quadrant of validation case 3.

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Figure 6

Comparison of the seven IC values for blade-5 and blade-9 of the 12-blade model

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Figure 7

Comparison of errors on the predicted middle three IC values for blade-9 of the 12-blade model. % error = (prediction value - target value)/target value.

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Figure 8

Frequency mistuning pattern used in the MISER computation of aeroelastic eigenvalues for this 24-blade fan rotor. Random seed = 3, standard deviation = 1%. Tuned blade frequency is 192.4 Hz.

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Figure 9

Comparison of MISER predicted aeroelastic eigenvalues for aero-mistuned case 1

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Figure 10

Comparison of MISER predicted aeroelastic eigenvalues for aero-mistuned case 2

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Figure 11

Comparison of MISER predicted aeroelastic eigenvalues for aero-mistuned case 3

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