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Research Papers

Quasi-Steady Prediction of Coupled Bending-Torsion Flutter Under Classic Surge

[+] Author and Article Information
S. M. Ananth

e-mail: ananthsm@iitk.ac.in

A. Kushari

e-mail: akushari@iitk.ac.in
Department of Aerospace Engineering,
Indian Institute of Technology Kanpur,
Kanpur, Uttar Pradesh 208016, India

Manuscript received May 14, 2012; final manuscript received January 27, 2013; accepted manuscript posted February 11, 2013; published online July 12, 2013. Assoc. Editor: Nesreen Ghaddar.

J. Appl. Mech 80(5), 051010 (Jul 12, 2013) (15 pages) Paper No: JAM-12-1190; doi: 10.1115/1.4023617 History: Received May 14, 2012; Accepted January 11, 2013; Revised January 27, 2013

In this paper, a quasi-steady method is developed for predicting the coupled bending-torsion flutter in a compressor cascade during classic surge. The classic surge is one of the major compressor flow field instabilities involving pulsation of the main flow through the compressor. The primary reason for the occurrence of the classic surge is the stalling of the blade rows and if the conditions are favorable this can trigger flutter, which is a self-excited aero elastic instability. The classic surge flow is modeled by using the well-established model of Moore and Greitzer and the obtained flow condition is used to determine the aerodynamic loads of the cascade using the linearized Whitehead's theory. The cascade stability is then examined by solving the two dimensional structural model by treating it as a complex eigenvalue problem. The structural stability is analyzed for a range of values of the frequency ratio and primary emphasis is given for the frequency ratio value of 0.9 as many interesting features could be revealed. The cascade shows a bifurcation from bending flutter to the torsional one signifying that only one of the flutter modes are favored at any instant in time. The torsional flutter is found to be the dominant flutter mode for a range of frequency ratios during classic surge whereas the bending flutter is found to occur only for some values of frequency ratio very close to unity as the torsional loads acting on the blades are found to be orders of magnitude higher than the bending loads. A rapid initiation of torsional flutter is seen to occur during classic surge for frequency ratio values very close to unity and it is perceived that during blade design, frequency ratios should be kept below 0.9 to prevent the flutter possibilities. An estimate of structural energy variation with time indicates that even if the total structural energy is negative one of the modes can go unstable during classic surge.

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Figures

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Fig. 1

Schematic of the compressor showing nondimensional lengths [18]

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Fig. 2

Cubic axisymmetric characteristic of Moore and Greitzer [13]

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Fig. 3

Unsteady variation of flow property

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Fig. 4

(a) Schematic of the cascade geometry, (b) blade geometry and structural model [10]

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Fig. 5

Effect of variation in frequency ratio (γω) on system behavior for different inter blade phase angle (β): variation of damping with time in bending mode for different γω- (a) γω = 0.1, (b) γω = 0.5, (c) γω = 0.8, (d) γω = 0.9, (e) γω = 1.0, and (f) γω = 1.5

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Fig. 6

Effect of variation in frequency ratio (γω) on system behavior for different inter blade phase angle (β): variation of damping with time in torsional mode for different γω- (a) γω = 0.1, (b) γω = 0.5, (c) γω = 0.8, (d) γω = 0.9, (e) γω = 1.0, and (f) γω = 1.5

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Fig. 7

Unsteady variation of aerodynamic loads (a) bending mode, and (b) torsional mode

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Fig. 8

Cascade system behavior in bending mode for γω = 0.9 and n = 7: (a) temporal variation of lift coefficient and damping coefficient, (b) temporal variation of moment coefficient and damping coefficient, (c) temporal variation of lift coefficient and nondimensional frequency, and (d) temporal variation of moment coefficient and nondimensional frequency

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Fig. 9

Cascade system behavior in bending mode: (a) flutter boundary plot-variation of nondimensional flutter velocity with frequency ratio for n = 0, 10, 20, (b) flutter boundary plot-variation of nondimensional flutter velocity with frequency ratio for n = 30, 39, and (c) unsteady variation of reduced stall velocity showing the flutter onset points for γω = 0.9

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Fig. 10

Cascade system behavior in torsional mode for γω = 0.9 and n = 24: (a) temporal variation of lift coefficient and damping coefficient, (b) temporal variation of moment coefficient and damping coefficient, (c) variation of nondimensional frequency with lift coefficient, and (d) variation of nondimensional frequency with moment coefficient

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Fig. 11

Cascade system behavior in torsional mode: flutter boundary plot-variation of nondimensional flutter velocity with frequency ratio for (a) n = 0, n = 10, n = 20, and (b) n = 30, n = 39

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Fig. 12

Cascade system behavior in torsional mode for n = 0, n = 10, n = 20, n = 30, and n = 39: unsteady variation of reduced stall velocity showing the flutter onset points for (a) γω = 0.9, (b) γω = 0.92, (c) γω = 0.94, and (d) γω = 0.96

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Fig. 13

Cascade system behavior in torsional mode for n = 0, n = 10, n = 20, n = 30, and n = 39: unsteady variation of reduced stall velocity showing the flutter onset points for (a) γω = 0.98, (b) γω = 1.2, (c) γω = 1.8, and (d) γω = 2.6

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Fig. 14

Temporal variation of structural properties in bending and torsional mode: (a) damping coefficient for γω = 0.9 and n = 7, (b) nondimensional frequency for γω = 0.9 and n = 7, (c) damping coefficient for γω = 0.9 and n = 24, and (d) nondimensional frequency for γω = 0.9 and n = 24

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Fig. 15

Cascade structural energy variation with time: (a) bending energy and torsional energy for γω = 0.9 and n = 7, (b) total structural energy for γω = 0.9 and n = 7, (c) bending energy and torsional energy for γω = 0.9 and n = 24, and (d) total structural energy for γω = 0.9 and n = 24

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