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Research Papers: Gas Turbines: Structures and Dynamics

A Mistuned Forced Response Analysis of an Embedded Compressor Blisk Using a Reduced-Order Model

[+] Author and Article Information
Mauricio Gutierrez Salas

Heat and Power Technology Royal
Institute of Technology,
Stockholm 10044, Sweden
e-mail: maugut@kth.se

Paul Petrie-Repar

Heat and Power Technology,
Royal Institute of Technology,
Stockholm 10044, Sweden
e-mail: paul.petrie-repar@energy.kth.se

Robert E. Kielb

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

Nicole L. Key

Zucrow Laboratories,
School of Mechanical Engineering,
Purdue University,
Purdue, IN 47907
e-mail: nkey@purdue.edu

1Corresponding author.

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 31, 2018; final manuscript received August 8, 2018; published online October 11, 2018. Editor: Jerzy T. Sawicki.

J. Eng. Gas Turbines Power 141(3), 032505 (Oct 11, 2018) (13 pages) Paper No: GTP-18-1536; doi: 10.1115/1.4041280 History: Received July 31, 2018; Revised August 08, 2018

Accuracy when assessing mistuned forced response analyses is still a major concern. Since a fully coupled analysis is still very computational expensive, several simplifications and reduced-order models (ROMs) are carried out. The use of a reduction method, the assumptions and simplifications, generate different uncertainties that challenge the accuracy of the results. Experimental data are needed for validation and also to understand the propagation of these uncertainties. This paper shows a detailed mistuned forced response analysis of a compressor blisk. The blisk belongs to the Purdue Three-Stage (P3S) Compressor Research Facility. Two different stator–rotor–stator configurations of 38 and 44 upstream stator vanes are taken into consideration. Several loading conditions are analyzed at three different speed lines. A ROM known as subset nominal mode (SNM), has been used for all the analyses. This reduction takes as a basis a set of modes within a selected frequency spectrum. It can consider a complete family of modes to study the disk–blade modal interaction. A detailed comparison between the predicted and measured results has been performed, showing a good agreement for the high loading (HL) conditions.

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References

Craig, R. R. , and Bampton, M. C. C. , 1968, “ Coupling of Substructures for Dynamic Analyses,” AIAA J., 6(7), pp. 1313–1319. [CrossRef]
Bladh, R. , Castanier, M. P. , and Pierre, C. , 2000, “ Component-Mode-Based Reduced Order Modeling Techniques for Mistuned Bladed Disks-Part I: Theoretical Models,” ASME J. Eng. Gas Turbines Power, 123(1), pp. 89–99. [CrossRef]
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Lim, S.-H. , Bladh, R. , and Castanier, M. P. , 2007, “ Compact, Generalized Component Mode Mistuning Representation for Modeling Bladed Disk Vibration,” AIAA J., 45(9), pp. 2285–2298. [CrossRef]
Yang, M.-T. , and Griffin, J. , 2001, “ A Reduced-Order Model of Mistuning Using a Subset of Nominal System Modes,” ASME J. Eng. Gas Turbines Power, 123(4), pp. 893–900. [CrossRef]
Feiner, D. , and Griffin, J. , 2002, “ A Fundamental Model of Mistuning for a Single Family of Modes,” ASME J. Turbomach., 124(4), pp. 597–605. [CrossRef]
Martel, C. , Corral, R. , and Llorens, J. M. , 2008, “ Stability Increase of Aerodynamically Unstable Rotors Using Intentional Mistuning,” ASME J. Turbomach., 130(1), p. 011006. [CrossRef]
Gutierrez Salas, M. , Bladh, R. , Mårtensson, H. , Petrie-Repar, P. , Fransson, T. , and Vogt, D. M. , 2017, “ Forced Response Analysis of a Mistuned, Compressor Blisk Comparing Three Different Reduced Order Model Approaches,” ASME J. Eng. Gas Turbines Power, 139(6), p. 062501. [CrossRef]
Besem, F. M. , Kielb, R. E. , Galpin, P. , Zori, L. , and Key, N. L. , 2016, “ Mistuned Forced Response Predictions of an Embedded Rotor in a Multistage Compressor,” ASME J. Turbomach., 138(6), p. 061003. [CrossRef]
Li, J. , Aye-Addo, N. , Kormanik , N., III , Matthews, D. , Key, N. , and Kielb, R. , 2017, “ Mistuned Higher-Order Mode Forced Response of an Embedded Compressor Rotor, Part I: Steady and Unsteady Aerodynamics,” ASME Paper No. GT2017-64633.
Li, J. , Aye-Addo, N. , Kielb, R. , and Key, N. , 2017, “ Mistuned Higher-Order Mode Forced Response of an Embedded Compressor Rotor, Part II: Mistuned Forced Response Prediction,” ASME J. Turbomach., 140(3), p. 031006. [CrossRef]
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Figures

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Fig. 1

Purdue three-stage (P3S) compressor [10]

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Fig. 2

Compressor map indicating three speed lines [10]

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Fig. 3

ZZenf diagram indicating the resonance points for the three speed lines

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Fig. 4

Two FEMs have been used to study the boundary conditions: (a) long domain and (b) short domain

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Fig. 5

First torsion family (1T) excited by a 38EO (–5ND) at 86% Nc and by a 44EO (–11ND) at 74% Nc for the FEM long domain

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Fig. 6

Mistuned amplitude response for HL @4295 rpm for the FEM long domain

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Fig. 7

Mistuned amplitude response for HL @4295 rpm

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Fig. 8

First chord-wise-bending family (1CWB) excited by a 88EO (11ND) at 68% Nc

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Fig. 9

Normalized Fourier content for the 1CWB mistuned basis @3400 rpm

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Fig. 10

Mistuned amplitude response for LL @3400 rpm

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Fig. 11

Mistuned amplitude response for PE @3400 rpm

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Fig. 12

Mistuned amplitude response for HL @3400 rpm

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Fig. 13

Fourier content of the tuned forced response modes for PE @3400 rpm (contour represents amplitude in mils)

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Fig. 14

Fourier content of the mistuned forced response modes for PE @3400 rpm (contour represents amplitude in mils)

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Fig. 15

Maximum peak-to-peak absolute amplitude for PE @4944 Hz

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Fig. 16

Forced response mistuned blade amplitudes for LL, PE, and HL @3400 rpm

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Fig. 17

Normalized Fourier content for the 1T mistuned basis @3700 rpm

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Fig. 18

First torsion family (1T) excited by a 38EO (–5ND) at 86% Nc and by a 44EO (–11ND) at 74% Nc

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Fig. 19

Fourier content of the forced response modes for PE @3700 rpm (Contour represents amplitude in mils)

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Fig. 20

Mistuned amplitude response for PE @3700 rpm

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Fig. 21

Maximum peak-to-peak absolute amplitude for PE @2723 Hz

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Fig. 22

Mistuned amplitude response for HL @3700 rpm

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Fig. 23

Forced response mistuned blade amplitudes for PE and HL @3700 rpm

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Fig. 24

Normalized Fourier content for the 1T mistuned basis @4295 rpm

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Fig. 25

Normalized Fourier content for the 1T mistuned basis @4295 rpm (Long domain)

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Fig. 26

Mistuned amplitude response for LL @4295 rpm

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Fig. 27

Fourier content of the forced response modes for PE @4295 rpm (Contour represents amplitude in mils)

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Fig. 28

Mistuned amplitude response for PE @4295 rpm

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Fig. 29

Maximum peak-to-peak absolute amplitude for PE @2717 Hz

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Fig. 30

Forced response mistuned blade amplitude for LL, PE, and HL @4295 rpm

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Fig. 31

Experimental and predicted mistuned parameters @3400 rpm (88EO): (a) ratio ((xmax)/(xmean)) and (b) ratio ((xmax)/(xtuned))

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Fig. 32

Experimental and predicted mistuned parameters @3700 rpm (44EO): (a) ratio ((xmax)/(xmean)) and (b) ratio ((xmax)/(xtuned))

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Fig. 33

Experimental and predicted mistuned parameters @4295 rpm (38EO): (a) ratio ((xmax)/(xmean)) and (b) ratio ((xmax)/(xtuned))

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