Research Papers

Forced Response Sensitivity of a Mistuned Rotor From an Embedded Compressor Stage

[+] Author and Article Information
Fanny M. Besem

Department of Mechanical Engineering,
Duke University,
Durham, NC 27708
e-mail: fanny.besem@duke.edu

Robert E. Kielb

Department of Mechanical Engineering,
Duke University,
Durham, NC 27708

Nicole L. Key

Zucrow Laboratories,
School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47907

1Corresponding author.

2Present address: NUMECA USA, 1044 Larkin St., San Francisco, CA 94115.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received September 15, 2015; final manuscript received September 17, 2015; published online November 17, 2015. Editor: Kenneth C. Hall.

J. Turbomach 138(3), 031002 (Nov 17, 2015) (10 pages) Paper No: TURBO-15-1205; doi: 10.1115/1.4031866 History: Received September 15, 2015; Revised September 17, 2015

The frequency mistuning that occurs due to manufacturing variations and wear and tear of the blades has been shown to significantly affect the flutter and forced response behavior of a blade row. While tuned computational fluid dynamics (CFD) analyses are now an integral part of the design process, designers need a fast method to evaluate the localized high blade responses due to mistuning. In this research, steady and unsteady analyses are conducted on the second-stage rotor of an axial compressor, excited at the first torsion vibratory mode. A deterministic mistuning analysis is conducted using the numerical modal forces and the individual blade frequencies obtained experimentally by tip timing data. The mistuned blade responses are compared in the physical and traveling wave coordinates to the experimental data. The individual and combined impacts of frequency, aerodynamic, and forcing function perturbations on the predictions are assessed, highlighting the need to study mistuned systems probabilistically.

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Fig. 1

Drawing of the compressor located in the Zucrow Laboratories at Purdue University. The air flow comes from left to right. The number of blades is indicated above each row. (Adapted from Ref. [13].)

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Fig. 2

Campbell diagram for the second-stage rotor. The crossing of interest in this paper occurs at 74% corrected speed, at the crossing between the 44/rev coming from the upstream and downstream vanes (inlet guide vanes and first- and second-stage stators) and the first torsion frequency.

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Fig. 3

View of the undeformed and deformed rotor blade from the side (left picture) and the top (right picture). The mode shape is a first torsion. The hub is also represented.

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Fig. 4

Aerodynamic damping versus NDs at the 1T, 44/rev crossing. The circles represent the tuned aerodynamic damping from CFD calculations. The diamonds are the predicted mistuned aerodamping values. The vertical bar represents the range of damping values estimated from the experimental physical blade responses, with the average value shown by the rectangular symbol. The star is the damping estimated from the experimental 211ND traveling wave.

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Fig. 5

Variations from the mean of the experimentally measured natural frequencies for the 33 rotor blades. The mean natural frequency is 2723 Hz.

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Fig. 6

Fourier transform of the experimentally measured natural frequencies of the 33 rotor blades. The zeroth harmonic, or mean, is 2723 Hz. The first 32 harmonics are shown.

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Fig. 7

Blade amplitudes versus frequency with structural and aerodynamic couplings. All results are computational.

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Fig. 8

Comparison of the maximum blade response amplitude through a frequency sweep for all 33 rotor blades. The full line represents the experimental results while the dashed line shows the numerical predictions.

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Fig. 9

Comparison of the response ND content throughout the sweep between the experiments (left) and the predictions (right). The dominant ND in the experiments are −11ND,−14ND, +14ND, and +17ND. The same ND are highlighted in the predictions for comparison.

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Fig. 10

Comparison of the response −11ND content throughout the sweep between the experiments (full line) and the predictions (dashed line)

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Fig. 11

ND content in the experimental (top) and predicted (bottom) blade responses at 2717 Hz

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Fig. 12

Comparison of the mistuned blade amplitude predictions (dashed line) with the experimental blade amplitudes (full line) at 2717 Hz

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Fig. 13

Range of maximum blade response amplitudes from 100 Monte Carlo simulations with a random frequency mistuning of 0.05% of the SD on top of the measured frequencies

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Fig. 14

Range of maximum blade response amplitudes from 100 Monte Carlo simulations with random aerodynamic perturbations of 10% of the SD

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Fig. 15

Range of maximum blade response amplitudes from 100 Monte Carlo simulations with random excitation perturbations of 5% of the SD

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Fig. 16

Range of maximum blade response amplitudes from 100 Monte Carlo simulations with 0.05% SD additional frequency mistuning, 10% SD aerodynamic asymmetries, and 5% excitation perturbation

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Fig. 17

Graphical explanation of the half-power method

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Fig. 18

Blade amplitude versus frequency for blades 5 and 8 of the mistuned system, compared with the tuned blade amplitude

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Fig. 19

Damping values estimated by half-power method for each of the 33 rotor blades in the case of the mistuned system with 0.1% structural damping and no aerodynamic coupling. The horizontal line represents the correct damping value.




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