FLUTTER DESIGN OF LOW PRESSURE TURBINE BLADES WITH CYCLIC SYMMETRIC MODES

Robert Kielb

Duke University rkielb@duke. edu

John Barter

GE Aircraft Engines

Olga Chernysheva and Torsten Fransson

Swedish Royal Institute of Technology

Abstract This paper describes a new preliminary design method to conduct flitter

screening of LPT blades with cyclic symmetry mode shapes. As in the method for real mode shapes, baseline unsteady aerodynamic analyses must be per­formed for the 3 fundamental motions, two translations and a rotation. Unlike the current method work matrices must be saved for a range of reduced fre­quencies and interblade phase angles. These work matrices are used to generate the total work for the complex mode shape. Since it only requires knowledge of the reduced frequency and mode shape (complex), this new method is still very quick and easy to use. Theory and example applications are presented and compared with the results of full three-dimensional viscous CFD analyses. Rea­sonable agreement is found. The interaction effects of the cosine and sine modes and the work associated with the steady pressure are shown to generally be sig­nificant.

Flutter, Cyclic Symmetry, Preliminary Design, Low Pressure Turbines

41

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

Unsteady Aerodynamics, Aeroacoustics and Aeroelasticity of Turbomachines, 41-52. © 2006 Springer. Printed in the Netherlands.

1. Introduction

Panovsky and Kielb (1998) presented a method to conduct preliminary flit­ter design analysis for LPT blades. The study identified the blade mode shape as the most important contributor determining blade stability. Each mode shape is represented by three rigid body motions (two translations and one rotation) at the spanwise location of maximum displacement. These three motions can be described by a ‘pitching axis”. The critical value of reduced frequency is determined solely by this pitching axis location. By comparing this critical value with the actual reduced frequency, the stability is determined. Further in­vestigation using the same approach (Chernycheva et al, 2001) has shown that the overall stability behavior, as well as identification of the most stable and the most unstable regions as a function of blade mode shape remain remarkably similar for a rather wide range of physical and aerodynamic parameters of LPT blades with pure subsonic fbw. This method has been shown to be valuable in screening preliminary designs and identifying a minimal set of unsteady CFD analysis for final designs.

Figure 1. Local Blade Surface Velocity and Normal Vector

Many low pressure turbine (LPT) blade designs include a tip shroud (as shown in Fig. 1), that mechanically connects the blades together in a structure exhibiting cyclic symmetry. Since this arrangement is cyclically symmetric, each eigenvalue has a complex mode shape that can be represented by two real mode shapes that are commonly called the cosine and sine modes. The Panovsky-Kielb method results in two pitching axis locations for each eigen­value. Although this can easily be done, experience has shown that it is ultra­conservative. That is, virtually all designs are judged to be unstable. This is shown in Kielb et al. (2003). This paper also describes an approach to ex­tend the Panovsky-Kielb method to consider these complex mode shapes. As

in the Panovsky-Kielb method, baseline unsteady aerodynamic analyses must be performed for the 3 fundamental motions, two translations and a rotation. Unlike the current method work matrices must be saved for a range of reduced frequencies and interblade phase angles. These work matrices are used to gen­erate the total work for the complex mode shape. Since it only requires knowl­edge of the reduced frequency and mode shape (complex), this new method is still very quick and easy to use. This paper describes the complete theory for extension of the Panovsky-Kielb method, gives example results, discusses the importance of the interaction effects of the cosine and sine modes, and discusses the contribution to work associated with the steady pressure.