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Research Papers

The Impact of Blade Loading and Unsteady Pressure Bifurcations on Low-Pressure Turbine Flutter Boundaries

[+] Author and Article Information
Joshua J. Waite

Department of Mechanical Engineering,
Duke University,
Durham, NC 27708
e-mail: joshua.waite@duke.edu

Robert E. Kielb

Department of Mechanical Engineering,
Duke University,
Durham, NC 27708
e-mail: rkielb@duke.edu

1Corresponding author.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received October 1, 2015; final manuscript received November 10, 2015; published online December 29, 2015. Editor: Kenneth C. Hall.

J. Turbomach 138(4), 041002 (Dec 29, 2015) (9 pages) Paper No: TURBO-15-1218; doi: 10.1115/1.4032043 History: Received October 01, 2015; Revised November 10, 2015

The three major aeroelastic issues in the turbomachinery blades of jet engines and power turbines are forced response, nonsynchronous vibrations, and flutter. Flutter primarily affects high-aspect ratio blades found in the fan, fore high-pressure compressor stages, and aft low-pressure turbine (LPT) stages as low natural frequencies and high axial velocities create smaller reduced frequencies. Often with LPT flutter analyses, physical insights are lost in the exhaustive quest for determining whether the aerodynamic damping is positive or negative. This paper underlines some well-known causes of the LPT flutter in addition to one novel catalyst. In particular, an emphasis is placed on revealing how local aerodynamic damping contributions change as a function of unsteady (e.g., mode shape, reduced frequency) and steady (e.g., blade torque, pressure ratio) parameters. To this end, frequency domain Reynolds-averaged Navier–Stokes (RANS) CFD analyses are used as computational wind tunnels to investigate how aerodynamic loading variations affect flutter boundaries. Preliminary results show clear trends between the aerodynamic work influence coefficients and variations in exit Mach number and back pressure, especially for torsional mode shapes affecting the passage throat. Additionally, visualizations of qualitative bifurcations in the unsteady pressure phases around the airfoil shed light on how local damping contributions evolve with steady loading. Final results indicate a sharp drop in aeroelastic stability near specific regions of the pressure ratio, indicating a strong correlation between blade loading and flutter. Passage throat shock behavior is shown to be a controlling factor near the trailing edge, and as with critical reduced frequency, this phenomenon is shown to be highly dependent on the vibratory mode shape.

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References

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Tchernycheva, O. V. , Fransson, T. , Kielb, R. E. , and Barter, J. , 2001, “ Comparative Analysis of Blade Mode Shape Influence on Flutter of Two-Dimensional Turbine Blades,” 15th International Symposium on Air Breathing Machines (ISABE), Bangalore, India, Sept. 3–7, ISABE Paper No. ISABE-2001-1243.
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Figures

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Fig. 1

TD plot of STCF 4: M2 = 0.90. Neighboring blades shown for cascade orientation. ξ and η normalized by the chord. Used with permission [14].

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Fig. 2

Investigation of torsion instability boundaries as a function of torque by Cardinale et al. [12]

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Fig. 4

Fundamental mode shapes considered. Displacements exaggerated 10 × for depiction. (a) Flex mode and (b) leading edge pitch mode.

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Fig. 5

Minimum nondimensional damping coefficient over all IBPAs as a function of reduced frequency. p2/p* = 1.21.

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Fig. 6

Magnitude of the GF influence coefficients for subsonic exit flow at four different reduced frequencies. (a) Flex mode and (b) LE pitch mode.

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Fig. 7

Work-per-cycle contributions from the reference and neighboring blades at σ = −72 deg as a function of reduced frequency. (a) Flex: σ = −72 deg and (b) LE pitch: σ = −72 deg.

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Fig. 8

Variation of inlet/exit Mach number, enforced blade vibrational frequency, exit flow angle, and torque as a function of normalized back pressure for a constant reduced frequency of k = 0.1

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Fig. 9

Work-per-cycle contributions of the reference and neighbor blades as a function of steady loading. (a) Flex: k = 0.1, σ = –54 deg and (b) LE pitch: k = 0.3, σ = −72 deg.

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Fig. 10

Minimum damping over all IBPAs as a function of normalized back pressure for k = 0.1 flex, k = 0.3 leading edge pitch, k = 0.3 midchord pitch, and k = 0.1 edgewise bending

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Fig. 11

Least stable IBPA as a function of mode shape, reduced frequency, and critical choking pressure ratio (refinement of σ = 18 deg)

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Fig. 12

Density gradient contours in the O-block for back pressures on opposite sides of the critical choking pressure. (a)p2/p* = 1.01 and (b) p2/p* = 0.95.

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Fig. 13

Coefficient of pressure distribution across airfoil as a function of load. Increasing load (decreasing back pressure) in the downward-right direction. Highest (lowest) p2/p* value shown is 1.31 (0.48).

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Fig. 14

SS unsteady pressure bifurcations as a function of increased loading: k = 0.1, flex mode, σ = −54 deg. (a) SS: |p̂| and (b) SS: p̂ phase.

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Fig. 15

Pressure side unsteady pressure bifurcations as a function of increased loading: k = 0.1, flex mode, σ = −54 deg. (a) Pressure side: |p̂| and (b) PS: p̂ phase.

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