Research Papers: Gas Turbines: Structures and Dynamics

Harmonic Convergence Estimation Through Strain Energy Superconvergence

[+] Author and Article Information
Alexander A. Kaszynski

Universal Technology Corporation,
Dayton, OH 45434
e-mail: akascap@gmail.com

Joseph A. Beck, Jeffrey M. Brown

Turbine Engine Division,
U.S. Air Force Research Laboratory,
Wright-Patterson AFB, OH 45431

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received January 15, 2016; final manuscript received February 22, 2016; published online April 12, 2016. Editor: David Wisler.

J. Eng. Gas Turbines Power 138(10), 102501 (Apr 12, 2016) (9 pages) Paper No: GTP-16-1017; doi: 10.1115/1.4033059 History: Received January 15, 2016; Revised February 22, 2016

Grid convergence in finite element analysis (FEA), despite a wide variety of tools available to date, remains an elusive and challenging task. Due to the complex and time-consuming process of remeshing and solving the finite element model (FEM), convergence studies can be a part of the most arduous portion of the modeling process and can even be impossible with FEMs unassociated with CAD. Existing a posteriori methods, such as relative error in the energy norm, provide a near arbitrary indication of the model convergence for eigenfrequencies. This paper proposes a new approach to evaluate the harmonic convergence of an existing model without conducting a convergence study. Strain energy superconvergence (SES) takes advantage of superconvergence points within a FEM and accurately recovers the strain energy within the model using polyharmonic splines, thus providing a more accurate estimate of the system's eigenfrequencies without modification of the FEM. Accurate eigenfrequencies are critical for designing for airfoil resonance avoidance and mistuned rotor response prediction. Traditional error estimation strategies fail to capture harmonic convergence as effectively as SES, potentially leading to a less accurate airfoil resonance and rotor mistuning prediction.

Copyright © 2016 by ASME
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Fig. 1

Cantilever beam SERR (top) and strain energy (bottom)

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Fig. 2

SERR and frequency error with respect to nodal density

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Fig. 3

Twisted cantilever beam strain energy in 3B

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Fig. 4

SERR and frequency error for twisted cantilever beam

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Fig. 5

Improved eigenfrequency estimation comparison

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Fig. 6

Recovered strain energy variation

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Fig. 7

Annulus recovered strain energy variation

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Fig. 8

Annulus eigenfrequency estimation comparison

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Fig. 9

Tetrahedral FEM convergence study results

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Fig. 10

Strain energy in original beam (top) and polyharmonic interpolated beam (bottom)

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Fig. 11

Interpolation accuracy versus PSIM cloud size

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Fig. 12

Interpolation accuracy versus distance to cluster center

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Fig. 13

Production IBR SES convergence study

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Fig. 14

Recovered strain energy variation in first bend for a production IBR sector

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Fig. 15

Nonaxisymmetric incomplete inflated torus

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Fig. 16

Convergence study comparing original and interpolation based eigenvalues




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