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Research Papers: Gas Turbines: Structures and Dynamics

A Study of Nonlinear Vibrations in a Frictionally Damped Turbine Bladed Disk With Comprehensive Modeling of Aerodynamic Effects

[+] Author and Article Information
Z.-I. Zachariadis

Mechanical Engineering Department,
Imperial College London,
South Kensington Campus,
London, SW7 2AZ, UK

R. Elliott

Rolls-Royce plc,
P.O. Box 31,
Derby, DE24 8BJ, UK

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the Journal of Engineering for Gas Turbines and Power. Manuscript received September 16, 2012; final manuscript received October 9, 2012; published online February 21, 2013. Editor: Dilip R. Ballal.

J. Eng. Gas Turbines Power 135(3), 032504 (Feb 21, 2013) (11 pages) Paper No: GTP-12-1361; doi: 10.1115/1.4007871 History: Received September 16, 2012; Revised October 09, 2012

A new effective method for comprehensive modeling of gas flow effects on vibration of nonlinear vibration of bladed disks has been developed for a case when the effect of the gas flow on the mode shapes is significant. The method separates completely the structural dynamics calculations from the significantly more computationally expensive computational fluid dynamics (CFD) calculations while providing the high accuracy of modeling for aerodynamic effects. A comprehensive analysis of the forced response using the new method has been performed for a realistic turbine bladed disk with root-disk joints, tip, and under-platform dampers. The full chain of aerodynamic and structural calculations are performed: (i) determination of boundary conditions for CFD, (ii) CFD analysis, (iii) calculation of the aerodynamic characteristics required by the new method, and (iv) nonlinear forced response analysis using the modal aerodynamic influence matrix (MAIM). The efficiency of the friction damping devices has been studied and compared for several resonance frequencies and engine orders. Advantages of the method for aerodynamic effect modeling have been demonstrated.

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Figures

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Fig. 1

Calculation mesh for through-flow solver (a) and relative Mach number contours for the take-off condition (b)

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Fig. 2

The computational mesh of the LP stage (a) and an example of steady-state pressure distribution over vanes and rotor blades (b)

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Fig. 3

Instantaneous pressure contours of the IP/LP stages

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Fig. 4

Modal force values for first 16 modes

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Fig. 5

Modal aerodynamic influence matrix, 26 EO, 100% vibration frequency: (a) real parts and (b) imaginary parts

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Fig. 6

Frequency shifts due to the MAIM

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Fig. 7

Modal damping factors corresponding to the MAIM

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Fig. 8

Comparison of modal damping factors for first modes: from the MAIM and from the conventional approach

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Fig. 10

Dependency of the modal damping factors on the vibration frequency, −26 EO

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Fig. 9

Dependency of the modal damping factors on the vibration frequency, −3 EO

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Fig. 11

Whole bladed disk and its sector with models of two damper types analyzed: TD and UPD

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Fig. 12

Bladed disk with tip dampers: 26 EO effect of the friction coefficient

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Fig. 13

Bladed disk with tip dampers: 5/26 EO effect of the friction coefficient and excitation level

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Fig. 14

Bladed disk with UPDs: effect of the friction coefficient value, 26 EO

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Fig. 15

Bladed disk with u/p dampers: 5/26 EO effect of the friction coefficient and excitation level

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Fig. 16

Bladed disk with u/p dampers: 5/26 EO effect of the friction coefficient and excitation level

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Fig. 17

Resonance amplitudes calculated with different damping devices: a case of friction coefficient 0.3 and normalized excitation level 0.1

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Fig. 18

Effects of the multiharmonic excitation: a case of TDs

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Fig. 19

Bladed disk forced response for different levels of aero-effect modeling MAIM: 1/3 EO

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Fig. 20

Bladed disk forced response for different levels of aero-effect modeling MAIM: 26 EO, root + UPDs

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Fig. 21

Bladed disk forced response for different levels of aero-effect modeling MAIM: 26 EO, root + TDs

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Fig. 22

Bladed disk forced response for different levels of aero-effect modeling MAIM: 26 EO, root + TDs + UPDs

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Fig. 23

Comparison of resonance response levels for different damping devices: 26 EO

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