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Research Papers: Gas Turbines: Structures and Dynamics

Multistage Blisk and Large Mistuning Modeling Using Fourier Constraint Modes and PRIME

[+] Author and Article Information
Eric Kurstak

Gas Turbine Laboratory,
Department of Mechanical and
Aeronautical Engineering,
The Ohio State University,
Columbus, OH 43235
e-mail: kurstak.1@osu.edu

Kiran D'Souza

Gas Turbine Laboratory,
Department of Mechanical and
Aeronautical Engineering,
The Ohio State University,
Columbus, OH 43235
e-mail: dsouza.60@osu.edu

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received August 28, 2017; final manuscript received September 13, 2017; published online April 10, 2018. Editor: David Wisler.

J. Eng. Gas Turbines Power 140(7), 072505 (Apr 10, 2018) (10 pages) Paper No: GTP-17-1483; doi: 10.1115/1.4038613 History: Received August 28, 2017; Revised September 13, 2017

Current efforts to model multistage turbomachinery systems rely on calculating independent constraint modes for each degree-of-freedom (DOF) on the boundary between stages. While this approach works, it is computationally expensive to calculate all the required constraint modes. This paper presents a new way to calculate a reduced set of constraint modes referred to as Fourier constraint modes (FCMs). These FCMs greatly reduce the number of computations required to construct a multistage reduced order model (ROM). The FCM method can also be integrated readily with the component mode mistuning (CMM) method to handle small mistuning and the pristine rogue interface modal expansion (PRIME) method to handle large and/or geometric mistuning. These methods all use sector-level models and calculations, which make them very efficient. This paper demonstrates the efficiency of the FCM method on a multistage system that is tuned and, for the first time, creates a multistage ROM with large mistuning using only sector-level quantities and calculations. The results of the multistage ROM for the tuned and large mistuning cases are compared with full finite element results and are found in good agreement.

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References

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Figures

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Fig. 1

Multistage system comprised of a 25 sector bladed disk and a 23 sector bladed disk

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Fig. 2

Stage 1 (O) and stage 2 (X) boundary node rings of a simplified example system demonstrating the nonconforming meshes

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Fig. 3

Stage 1 (O) and stage 2 (X) displacement set for the inner ring cosine with harmonic 3 (⋯) for the example in Fig. 2

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Fig. 4

23 sector model with a blade having 50% of its mass missing

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Fig. 5

Relative error of the ROM frequencies: (a) frequencies of PRIME ROM (X) and full FEM (O) analysis and (b) relative error of the ROM frequencies

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Fig. 6

Modeshape comparison of the ROM (X) with respect to the full FEM (O) analysis of a localized mode

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Fig. 7

Contour plot showing a shaded region where the average relative error of the frequency values is below 0.05% for the first 200 modes

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Fig. 8

Condition maps for the mass matrix with the shaded region indicating values less than 109

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Fig. 9

Contour plot showing a shaded region where the average error of the frequency values is below 0.05% and both the mass and stiffness matrices have a condition number less than 109

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Fig. 10

Blade tip displacements of pristine (O) and rogue (X) systems for a harmonic 2 displacement

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Fig. 11

Frequency comparison between the FCM ROM and the full multistage analysis: (a) frequencies for FCM ROM (O) and FEM (X) and (b) error in FCM ROM for first 200 modes

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Fig. 12

Forced response analysis for an engine order one excitation for a tuned, multistage system: FCM ROM (O) and full FEM (–): (a) stage 1 and (b) stage 2

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Fig. 13

Frequency comparison between the FCM-PRIME ROM with geometric mistuning present and full multistage FEM: (a) frequency comparison between the FCM-PRIME ROM (O) and the full FEM (X) and (b) error in FCM-PRIME ROM frequency values

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Fig. 14

Modeshape comparison of the FCM-PRIME ROM with respect to the full FEM analysis of mode 24: FCM-PRIME ROM (X) and the full FEM (O): (a) stage 1 and (b) stage 2

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Fig. 15

Forced response analysis for an engine order one excitation for a geometrically mistuned, multistage system: FCM-PRIME ROM (O) and full FEM (–): (a) stage 1 and (b) stage 2

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