INFLUENCE OF A VIBRATION AMPLITUDE DISTRIBUTION ON THE AERODYNAMIC STABILITY OF A LOW-PRESSURE TURBINE SECTORED VANE

Olga V. Chernysheva,1 Torsten H. Fransson,1 RobertE. Kielb,2 and John Barter3

1 Royal Institute of Technology S-100 44 Stockholm, Sweden olga@egi. kth. se fransson@egi. kth. se

2

Duke University Durham, NC 27708-0300, USA rkielb@duke. edu

3

3 GE Aircraft Engines,

Cincinnati, OH 45215-1988, USA john. Barter@ae. ge. com

Abstract A parametrical analysis summarizing the effect of the reduced frequency and sector mode shape is carried out for a low-pressure sectored vane cascade for different vibration amplitude distributions between the airfoils in sector as well as the numbers of the airfoils in sector. Critical reduced frequency maps are provided for torsion – and bending-dominated sector mode shapes.

Despite the different absolute values of the average aerodynamic work be­tween four-, five – and six-airfoil sectors a high risk for instability still exists in the neighborhood of realistic reduced frequencies of modern low-pressure tur­bine. Based on the cases studied it is observed that a sectored vane mode shape with the edge airfoils in the sector dominant provides the most unstable critical reduced frequency map.

Keywords: Flutter, sectored vane, sector mode shape, vibration amplitude distribution, crit­

ical reduced frequency.

17

K. C. Hall et al. (eds.),

Unsteady Aerodynamics, Aeroacoustics and Aeroelasticity of Turbomachines, 17-29. © 2006 Springer. Printed in the Netherlands.

Nomenclature
C	chord length	[m]
к	reduced frequency based on half-chord and outlet fbw velocity, wc/( 2F2)	[-]
M	Mach number	[-]
V	fbw velocity	[m/s]
X	cascade axial co-ordinate	[-]
Y Greek	cascade tangential co-ordinate	[-]
p	absolute fbw angle	[deg]
oj Subscripts	circular frequency	[rad/s]
IS	isentropic
1	inlet
2	outlet

1. Introduction

In order to eliminate or reduce blade vibration problems in turbomachines, the adjacent airfoils around the wheel are often mechanically connected to­gether with either lacing wires, tip shrouds or part-span shrouds in a number of identical sectors. Such mechanical connections make the vibratory mode shapes much more complex. At the same time it allows a significant improve­ment in the stability margin of the design.

Numerical (see, for example, [1-3]) and experimental aerodynamic analy­sis has demonstrated the stabilizing effect. The numerical studies for sectored vanes presented in [1-2] were conducted with all blades in the sector vibrat­ing with the same frequency and amplitude and at different real mode shapes. The method used in [1] utilized the possibility of superposition for a linear system, the approach in [2] required calculations on a domain that covered as many passages as airfoils belonging to one sector. The findings were illustrated for selected sets of sectored vane modes for five – and six-airfoil low-pressure steam turbine sectored vanes in [1] and for three-airfoil low-pressure turbine sectored vane in [2]. Nevertheless, even though the sectored vanes benefited by the mechanical connection between vanes, flitter was still predicted for certain ranges of inter-sector phase angles.

According to structural analysis of a sectored vane displacement the blades in the sector might have different amplitudes, mode shapes and vibration fre­quencies which obviously affect the aerodynamic stability of the sectored vane. An important contribution of the blade mode shape into the aerodynamic sta­bility of the cascade has been already demonstrated in [4] for a freestanding low-pressure turbine blade with a real rigid-body mode shape. During the aeroelastic design phase, it was recommended to also study mode shape rather than only the reduced frequency of a blade. Further investigation, conducted in

[5] for a wide range of physical and aerodynamic blade parameters confirmed the findings and made it more general.

The approach presented in [3] employed, similarly to [1], the superposition assumption and, unlike [1], allowed a complex rigid-body mode shape with non-uniform amplitude distribution between the blades in a sector. The effect of real rigid-body sector mode shape variation on the aerodynamic stability of a low-pressure six-airfoil sectored vane was shown when all blades in sector were vibrating with identical amplitude. Although it was confirmed that tying blades together in a sector drastically improved the stability of the cascade, for some mode shapes sectored vane still remained unstable at relevant reduced frequencies.