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Research Papers

Prediction of Turbomachinery Aeroelastic Behavior From a Set of Representative Modes

[+] Author and Article Information
Damian M. Vogt, Torsten H. Fransson

Royal Institute of Technology,
Heat and Power Technology,
S-100 44 Stockholm, Sweden

Hans Mårtensson

VOLVO Aero Corporation,
S-461 81 Trollhättan, Sweden

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received August 10, 2011; final manuscript received August 23, 2011; published online October 30, 2012. Editor: David Wisler.

J. Turbomach 135(1), 011032 (Oct 30, 2012) (11 pages) Paper No: TURBO-11-1180; doi: 10.1115/1.4006536 History: Received August 10, 2011; Revised August 23, 2011

A method is proposed for the determination of the aeroelastic behavior of a system responding to mode-shapes which are different from the tuned in vacuo ones, due to mistuning, mode family interaction, or any other source of mode-shape perturbation. The method is based on the generation of a data base of unsteady aerodynamic forces arising from the motion of arbitrary modes and uses least square approximations for the prediction of any responding mode. The use of a reduced order technique allows for mistuning analyses and is also applied for the selection of a limited number of arbitrary modes. The application of this method on a transonic compressor blade shows that the method captures the aeroelastic properties well in a wide frequency range. A discussion of the influence of the mode-shapes and frequency on the final stability response is also provided.

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References

Figures

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Fig. 1

Structural rotor blade mesh

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Fig. 2

First seven real modes and frequencies. Frequency range considered: f1 − f7.

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Fig. 3

Steady state mesh domain. Linearized mesh domain is highlighted.

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Fig. 4

100% speed-line. Design point is highlighted.

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Fig. 5

Different number of master nodes (above). MAC of reduced real modes when compared to the full real modes (below).

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Fig. 6

19 GAMs from axial (X) displacement of master nodes. Absolute amplitudes. Eliminated modes are highlighted.

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Fig. 9

Stability from arbitrary modes oscillated at f1

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Fig. 10

SCA (top) and mean (bottom) and its differences with the real modes. Arbitrary modes are oscillated at f1.

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Fig. 11

SCA (top) and mean (bottom) and its differences with the real modes. Arbitrary modes are oscillated at f7.

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Fig. 7

19 Least square error when fitting the 11 X and Z arbitrary modes to the real modes (above). Matched modes (below).

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Fig. 8

Aerodynamic damping from the first seven real modes using the MLS general method. Zoomed-in view of mode 1.

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Fig. 12

Stability from arbitrary modes are oscillated at f4

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Fig. 13

SCA (top) and mean (bottom) and its differences with the real modes. Arbitrary modes are oscillated at f4.

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Fig. 20

Static pressure versus imaginary Cp loading at 90% span. GAM 6Z influence of blade 0. Shock regions are highlighted.

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Fig. 21

Steady versus unsteady loading at 90% span. GAM 6Z influence of blade 1. Shock regions are highlighted.

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Fig. 14

SCA (top) and mean (bottom) and its differences with the real modes. Arbitrary modes are oscillated at f1 and f4.

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Fig. 15

SCA (top) and mean (bottom) and its differences with the real modes. Arbitrary modes are oscillated at f4 and f7.

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Fig. 16

Generalized real (left) and imaginary (right) forces of the 1st mode at different frequencies. Influence coefficient domain; MLS GAMs frequency fit (dashed lines).

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Fig. 17

Influence coefficient generalized forces of all of the GAMs at f1

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Fig. 18

Imaginary pressure coefficient for the X modes 2–5. Influence of blade 0 on itself.

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Fig. 19

Imaginary pressure coefficient for the mode 6 Z. Influence of blade 0.

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