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Research Papers

Forced Response of a Centrifugal Compressor Stage Due to the Impeller–Diffuser Interaction

[+] Author and Article Information
Edward J. Walton, Choon S. Tan

MIT Gas Turbine Laboratory,
Massachusetts Institute of Technology,
Cambridge, MA 02139

1Present address: GE Aviation, Lynn, MA 01910.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received December 4, 2015; final manuscript received February 11, 2016; published online April 5, 2016. Editor: Kenneth C. Hall.

J. Turbomach 138(9), 091004 (Apr 05, 2016) (13 pages) Paper No: TURBO-15-1293; doi: 10.1115/1.4032838 History: Received December 04, 2015; Revised February 11, 2016

The impact mode coupling between impeller blades and the disk backwall has on the forced response amplitude of impeller blades is assessed. The assessments focus on the forced response of two splitter blade modes to a variety of representative boundary conditions and unsteady loadings. The forcing function is the synchronous unsteady loading generated by the impeller–diffuser interaction at resonance. The results indicate that modal coupling of blade- and disk-dominant modes renders the forced response highly sensitive to small variations in airfoil and disk backwall thickness. As a complement, a reduced-order model based on the forced response of a two mass–spring system is used to elucidate the physical interaction of modal coupling. The practical implication of this finding is that a forced response issue with an impeller blade cannot be addressed adequately by stiffening the structure, such as thickening the blade or disk. Thus, appropriate measures need to be taken to avoid potential blade–disk mode couplings within the manufacturing tolerances of the part.

Copyright © 2016 by ASME
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References

Figures

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Fig. 1

View of the research centrifugal compressor stage showing the impeller and discrete passage diffuser. Adopted from Gould [3].

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Fig. 2

FEM mesh of the centrifugal impeller

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Fig. 3

The splitter blade Campbell diagram showing edgewise modes 5 and 6 crossing with the diffuser engine order

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Fig. 4

Simplified SAFE diagram connecting discrete splitter blade and backwall modes into mode families represented by the horizontal and diagonal curves, respectively. Mode veering exists where the mode family curves cross. Main blade modes are now shown for clarity.

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Fig. 5

Representative impeller mode shapes: (a) splitter blade-dominant mode, (b) backwall-dominant, and (c) splitter blade–backwall coupling in vicinity of a veering point

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Fig. 6

Magnitude and phase of splitter blade surface static pressure found from unsteady CFD analysis, magnitude normalized by maximum value

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Fig. 7

Time-accurate loading on the splitter blade normalized by exducer dynamic head at modes 5 and 6 crossings with stage inlet conditions

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Fig. 8

Splitter blade mode shapes 5 and 6 shown on the sector model

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Fig. 9

Modal pressure distribution of splitter mode 5 with unsteady pressure calculated at mode 5 crossing speed. Results normalized to maximum design point modal pressure.

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Fig. 10

Modal pressure distribution of splitter mode 6 with unsteady pressure calculated at mode 6 crossing speed. Results normalized to maximum design point modal pressure.

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Fig. 11

Modal force amplification calculated for splitter modes 5 and 6 as a function of IBPA or nodal diameter. The calculated modal force at any IBPA is normalized by the modal force at the diffuser engine order for each mode, respectively.

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Fig. 12

Schematic of how the disk's backwall geometry is changed

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Fig. 13

Schematic of how the splitter blade geometry is changed

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Fig. 14

Updated SAFE diagram for the impeller showing the change in backwall mode placement for a 6% thicker backwall at the exducer radius. Horizontal lines, splitter modes; diagonal lines, backwall modes; solid line, nominal geometry; and dashed line, thicker geometry.

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Fig. 15

Frequency map showing interaction of backwall and disk modes as backwall thickness is varied

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Fig. 16

Updated SAFE diagram for the impeller showing the change in backwall mode placement for a 13% thicker airfoil. Horizontal lines, splitter modes; diagonal lines, backwall modes; solid line, nominal geometry; and dashed line, thicker geometry.

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Fig. 17

Frequency map showing the interaction of backwall and disk modes as airfoil thickness is varied

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Fig. 18

Variation in splitter modes 5 and 6 forced responses to increase backwall thickness. Amplification factor of displacement is relative to impeller with no backwall thickness increase. Mode shape magnitude is local magnitude at splitter trailing edge. Mode shape phase angle is the difference in mode shape phase from trailing edge to leading edge.

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Fig. 19

Variation in splitter modes 5 and 6 forced responses to increase airfoil thickness. Amplification factor of displacement is relative to impeller with no airfoil thickness increase. Mode shape magnitude is local magnitude at splitter trailing edge. Mode shape phase angle is the difference in mode shape phase from trailing edge to leading edge.

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Fig. 20

Direct comparison of splitter modes 5 and 6 forced response to increase backwall thickness. Amplification factor of displacement is relative to the forced response of mode 5 with no backwall thickness increase.

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Fig. 21

Direct comparison of splitter modes 5 and 6 forced response to increase airfoil thickness. Amplification factor of displacement is relative to the forced response of mode 5 with no airfoil thickness increase.

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Fig. 22

Two mass–spring system to approximate the blade–disk interaction

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Fig. 23

Comparison of the force response between the representative two mass–spring system and the actual centrifugal impeller mode 6 when the disk is stiffened

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Fig. 24

Comparison of the forced response between the representative two mass–spring system and the actual centrifugal impeller mode 6 when the airfoil is stiffened

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