Research Papers

Geometrical Modification of the Unsteady Pressure to Reduce Low-Pressure Turbine Flutter

[+] Author and Article Information
Christian Peeren

Siemens AG/TU Dresden,
Mellinghofer Strasse 55,
Mülheim a.d. Ruhr 45473, Germany
e-mail: christian.peeren@siemens.com

Konrad Vogeler

TU Dresden,
George-Bähr-Strasse 3c,
Dresden 01069, Germany
e-mail: konrad.vogeler@tu-dresden.de

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received September 14, 2016; final manuscript received March 17, 2017; published online May 2, 2017. Assoc. Editor: Li He.

J. Turbomach 139(9), 091011 (May 02, 2017) (11 pages) Paper No: TURBO-16-1239; doi: 10.1115/1.4036343 History: Received September 14, 2016; Revised March 17, 2017

In this work, the impact of the airfoil shape on flutter is investigated. Flutter occurs when the blade structure is absorbing energy from its surrounding fluid leading to hazardous amplification of vibrations. The key for a more stable design is the local modification of the blade motion induces unsteady pressure, which is responsible for local stability. Especially for free-standing blades, where most exciting aerodynamic work transfer is found at the upper tip sections, a reshaping of the airfoil is expected to beneficially influence stability. Two approaches are pursued in this work. This first approach is based on flow physics considerations. The unsteady pressure field is decomposed into four physical mechanisms or effects and each effect investigated. The second approach is used to validate the conclusions made in the theoretical part by numerical optimizing the geometry of a representative turbine blade. Selected optimized designs are picked and compared with each other in terms of local stability, aerodynamics, and robustness with respect to the boundary conditions. Both approaches are applied for a freestanding and interlocked turbine blade section. The found design potential is discussed and the link to the differences mechanisms, introduced in the first part, established. Based on the observations made, design recommendations are made for a flutter-reduced turbine design.

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Fig. 1

Unsteady pressure caused by the motion of the blades: (a) pressure amplitude numerical simulation σ=90 deg and (b) sketched unsteady pressure sources

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Fig. 2

Isentropic flow as function of A/A* for γ=1.4

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Fig. 3

Channel kinematic model. Dashed: deformed geometry. Solid (left figure): part of the deformation which effect area: (a) steady and deflected airfoils and (b) change of the area due to blade deformation. Note that A0 is perpendicular to the blade surface.

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Fig. 4

Channel kinematic amplitude, phase and theor. work over the IBPA for a real mode shape. Dashed: λ=0.6. Blue, SSβR=±180 deg and Δβ=0 deg. Red: PS βR=0 deg and Δβ=±180 deg: (a) Â (V-shape), (b) ϕA (Z-shape), and (c) wretheor. (S-shape).

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Fig. 5

NACA0008 cascade steady Mach contour plot: (a) Mach contour plot (unstaggered) γ=0 deg and (b) Mach contour plot (staggered) γ=60 deg

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Fig. 6

gc sign weighted unsteady pressure phase of the staggered and unstaggered case for all reduced frequencies: (a) Φpgc unstaggered case k1 = 2.8 × 10−3, (b) Φpgc unstaggered case k2 = 0.140, (c) Φpgc unstaggered case k3 = 0.280, (d) Φpgc staggered case k1 = 2.8 × 10−3, (e) Φpgc staggered case k2 = 0.140, and (f) Φpgc staggered case k3 = 0.280

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Fig. 7

Unsteady pressure phase at x = 0.5

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Fig. 8

Modification of shock systems: (a) normal shock modifications and (b) fish tail shock modifications

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Fig. 9

Classic flutter excitation sketched as function of the isentropic exit Mach number. The blue line corresponds to a baseline design (design A) and the red one to flutter excitation minimized design (design B).

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Fig. 10

Sketch of the real and imaginary rotational center used for the freestanding and interlocked case

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Fig. 11

Mach contour plots of the baseline (NB = 16) for both operating points: (a) operating point 1 (OP1, normal shock) and (b) operating point 2 (OP2, reflected shock)

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Fig. 12

Optimization results of all three configurations. A negative value of Ξmin corresponds to flutter excitation and a high value of ζ to increased aerodynamic losses. The solid thick line denotes the Pareto front, which links the members with the best aerodynamic damping and loss behavior: (a) NB = 16, ζOP1 over ΞminOP1, (b) NB = 16, ΞminOP2 over ΞminOP1, (c) NB = 16, ζOP2 over ζOP1, (d) NB = 18, ζOP1 over ΞminOP1, (e) fNB = 18, ΞminOP2 over ΞminOP1, (f) NB = 18, ζOP2 over ζOP1, (g) fNB = 20, ζOP1 over ΞminOP1, (h) NB = 20, ΞminOP2 over ΞminOP1, and (i) NB = 20, ζOP2 over ζOP1.

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Fig. 13

Airfoil geometry, aerodynamic damping curve, isentropic Mach number, and unsteady aerodynamic work distribution for the critical IPBA of the Pareto members for OP1: (a) geometry Nb = 16, (b) aero. damping curve, (c) isentropic Mach number Nb = 16, (d) unsteady aero. work at critical IBPA, (e) geometry Nb = 18, (f) aero. damping curve, (g) isentropic Mach numberNb = 18, (h) unsteady aero. work at critical IBPA, (i) geometry Nb = 20, (j) aero. damping curve, (k) isentropic Mach number Nb = 20, and (l) unsteady aero. work at critical IBPA.

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Fig. 14

Robustness of the optimized geometries case NB = 16. Minimum aerodynamic damping and aerodynamic losses are plotted over Misen,2 and β1. The total temperature is constant (Tt1=330 K): (a) min. aero. damping design I, (b) min. aero. damping baseline B, (c) min. aero. damping design IV, (d) aero. losses design I, (e) aero. losses baseline B, and (f) aero. losses design IV.

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Fig. 15

Composition of the critical aerodynamic work for the baseline and optimized designs for OP1 and NB = 16

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Fig. 16

Optimization results for the whole three-dimensional domain with tip gap: (a) spanwise aerodynamic work for the critical IBPA and (b) isentropic Mach number for 85% span



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