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Research Papers

Aerodynamic Asymmetry Analysis of Unsteady Flows in Turbomachinery

[+] Author and Article Information
Kivanc Ekici1

Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27708-0300ekici@utk.edu

Robert E. Kielb

Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27708-0300rkielb@duke.edu

Kenneth C. Hall

Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27708-0300kenneth.c.hall@duke.edu

1

Corresponding author. Present address: Department of Mechanical, Aerospace, and Biomedical Engineering, University of Tennessee, 315 Perkins Hall, Knoxville, TN 37996-2030.

J. Turbomach 132(1), 011006 (Sep 15, 2009) (11 pages) doi:10.1115/1.3103922 History: Received July 02, 2008; Revised January 26, 2009; Published September 15, 2009

A nonlinear harmonic balance technique for the analysis of aerodynamic asymmetry of unsteady flows in turbomachinery is presented. The present method uses a mixed time-domain/frequency-domain approach that allows one to compute the unsteady aerodynamic response of turbomachinery blades to self-excited vibrations. Traditionally, researchers have investigated the unsteady response of a blade row with the assumption that all the blades in the row are identical. With this assumption the entire wheel can be modeled using complex periodic boundary conditions and a computational grid spanning a single blade passage. In this study, the steady/unsteady aerodynamic asymmetry is modeled using multiple passages. Specifically, the method has been applied to aerodynamically asymmetric flutter problems for a rotor with a symmetry group of 2. The effect of geometric asymmetries on the unsteady aerodynamic response of a blade row is illustrated. For the cases investigated in this paper, the change in the diagonal terms (blade on itself) dominated the change in stability. Very little mode coupling effect caused by the off-diagonal terms was found.

Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Representative computational grid for a compressor with a symmetry group of 2

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Figure 2

Steady pressure distribution on the blade surface

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Figure 3

Real part of computed unsteady surface pressure. The rotor blades vibrate in pitch with a reduced frequency of 0.3 and an interblade phase angle of 36 deg.

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Figure 4

Imaginary part of computed unsteady surface pressure. The rotor blades vibrate in pitch with a reduced frequency of 0.3 and an interblade phase angle of 36 deg.

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Figure 5

Modal force for the aerodynamically symmetric cascade

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Figure 6

Diagonal terms of the aerodynamic matrix for 0.9–0.7 blade-to-blade spacing

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Figure 7

Off-diagonal terms of the aerodynamic matrix for 0.9–0.7 blade-to-blade spacing

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Figure 8

Diagonal terms of the aerodynamic matrix for 1.0–0.6 blade-to-blade spacing

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Figure 9

Off-diagonal terms of the aerodynamic matrix for 1.0–0.6 blade-to-blade spacing

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Figure 10

Comparison of eigenvalues for symmetric and alternate blade-to-blade spacing cases

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Figure 11

Off-diagonal terms of the aerodynamic matrix for 0/−2 stagger angle case

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Figure 12

Diagonal terms of the aerodynamic matrix for 0/+2 stagger angle case

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Figure 13

Comparison of eigenvalues for symmetric and alternate stagger cases

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Figure 14

Diagonal terms of the aerodynamic matrix for 0/−5 stagger angle case

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Figure 15

Diagonal terms of the aerodynamic matrix for 0/+5 stagger angle case

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Figure 16

Off-diagonal terms of the aerodynamic matrix for 0/−5 stagger angle case

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Figure 17

Off-diagonal terms of the aerodynamic matrix for 0/+5 stagger angle case

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Figure 18

Comparison of eigenvalues for symmetric and alternate stagger cases

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Figure 19

Effect of stagger angle variation on the steady flow

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Figure 20

Comparison of eigenvalues for symmetric and alternate stagger cases

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