Research Papers

Forced Response Analyses of Mistuned Radial Inflow Turbines

[+] Author and Article Information
Thomas Giersch

Chair of Structural Mechanics and
Vehicle Vibration Technology,
e-mail: gierstho@tu-cottbus.de

Peter Hönisch

e-mail: hoenisch@tu-cottbus.de

Bernd Beirow

e-mail: beirow@tu-cottbus.de

Arnold Kühhorn

e-mail: kuehhorn@tu-cottbus.de
Brandenburg University of Technology Cottbus,
D-03046 Cottbus, Germany

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the Journal of Turbomachinery. Manuscript received July 31, 2012; final manuscript received August 15, 2012; published online March 25, 2013. Editor: David Wisler.

J. Turbomach 135(3), 031034 (Mar 25, 2013) (9 pages) Paper No: TURBO-12-1161; doi: 10.1115/1.4007512 History: Received July 31, 2012; Revised August 15, 2012

Radial turbine wheels designed as blade integrated disks (blisk) are widely used in various industrial applications. However, related to the introduction of exhaust gas turbochargers in the field of small and medium sized engines, a sustainable demand for radial turbine wheels has come along. Despite those blisks being state of the art, a number of fundamental problems, mainly referring to fluid-structure-interaction and, therefore, to the vibration behavior, have been reported. Aiming to achieve an enhanced understanding of fluid-structure-interaction in radial turbine wheels, a numerical method, able to predict forced responses of mistuned blisks due to aerodynamic excitation, is presented. In a first step, the unsteady aerodynamic forcing is determined by modeling the spiral casing, the stator vanes, and the rotor blades of the entire turbine stage. In a second step, the aerodynamic damping induced by blade vibration is computed using a harmonic balance technique. The structure itself is represented by a reduced order model being extended by aerodynamic damping effects and aerodynamic forcings. Mistuning is introduced by adjusting the modal stiffness matrix based on results of blade by blade measurements that have been performed at rest. In order to verify the numerical method, the results are compared with strain-gauge data obtained during rig-tests. As a result, a measured low engine order excitation was found by modeling the spiral casing. Furthermore, a localization phenomenon due to frequency mistuning could be proven. The predicted amplitudes are close to the measured data.

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Fig. 1

Modeled turbine stage: the black line represents the boundary of the rotor's sector mesh used for steady-state flow analyses

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Fig. 2

Nodal diameter map of the tuned FE model and chosen subset of nominal modes for the frequency range of interest. fmean is the mean value of all eigenfrequencies belonging to the first flap mode

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Fig. 3

Undamped eigenfrequencies of the updated model and resonance frequencies of measurements at rest

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Fig. 4

Comparison of measured and computed mode shapes at rest

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Fig. 5

Relative torsional moment and polytropic efficiency with respect to the measured data at 100% speed. Steady-state CFD results versus performance measurements.

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Fig. 6

Time history of relative modal forcing on tuned standing wave modes (first flap) with 6 nodal diameters. Values are divided by the amplitude of modal forcing of nodal diameter 2 (engine order 24).

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Fig. 7

Resulting nodal diameter versus exciting engine order. Rotating direction of traveling waves (BTW: backward traveling wave, FTW: forward traveling wave).

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Fig. 8

Average forcing on first flap blade-sector mode shape related to EO 24 excitation

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Fig. 9

Relative amplitudes of unsteady pressure (a) and interpolated first flap mode shape on CFD-grid (b)

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Fig. 10

Influence coefficients depending on vibrating blade 0 (first flap mode)

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Fig. 11

Aerodynamic damping determined for first flap mode

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Fig. 12

Strain amplitude at s-g position measured data (a), calculated with material and predicted fluid-damping (b), calculated with measured overall-damping at fref (c)

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Fig. 13

Amplitude of operating deflection shape of maximum responding resonance at f=fref

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Fig. 14

Blade individual maximum response frequencies

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Fig. 15

Aerodynamic damping determined for different vibration amplitudes (first flap mode)

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Fig. 16

Aerodynamic damping determined for different mass flows (first flap mode)



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