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Journal ArticleDOI

Effects of Geometric and Structural Parameters on Coupled Bending Torsion Flutter in Turbo Machinery Blades

01 Jan 2008-International Journal of Turbo & Jet-engines (Walter de Gruyter GmbH)-Vol. 25, Iss: 4, pp 269-282

AbstractThe development o f propulsion system technology over the last few decades has encountered and overcome several technological barriers. A large number o f problems were resolved resulting in considerably higher component efficiencies and reduced fuel consumption. These advances led to lighter overall designs and higher power densities compared to earlier designs. The accomplishment of lighter designs for the turbomachinery components also led to some drawbacks due to the reduced margins on the design factor-of-safety. Consequently, aeroelastic stability has become a major concern, and is often the limiting design constraint. So a careful and systematic study of coupled bending-torsion flutter o f a cascade in incompressible flow was carried out which requires estimation of unsteady aerodynamic loads, and a structural model o f the cascade. Unsteady aerodynamic loads were evaluated using Whitehead's solution for incompressible flow through a cascade of arbitrary geometry and interblade phase angle. The lift and moment coefficients calculated were found to match within the four decimal place accuracy with the results given by Whitehead and other literature. The blades were modeled as an equivalent 2-D section at 75% of span, and structural and inertial couplings were lumped into an effective CG-EA offset. Structural damping was included in the equations of motion. The resulting complex eigenvalue problem was solved recognizing the fact that there are two parameters in the eigenvalue problem, namely the reduced frequency k and the interblade phase angle β. The critical flutter speed was determined by minimizing it with respect to β, keeping the constraint on β as suggested by Lane. The solution provided the critical flutter speed with respect to both the torsion and the bending modes as a function of the interblade phase angle as well as dominant vibration frequencif s at flutter. Various structural and aerodynamic parameters of the cascade were varied and the effect of the variations on the coupled bending torsion flutter was studied. A jump was observed in the flutter boundary near frequency ratio of I, which was explained by the change in the mode shape of the vibration, which is represented by interblade phase angle. The developed technique can be used as a preliminary design tool for the aeroelastic flutter analysis of turbo-machinery blades.

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Citations
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Journal ArticleDOI
Abstract: In this paper, optimization of the first blade of a new test rig is pursued using a hybrid model comprising the genetic algorithm, artificial neural networks and design of experiments. Blade tuning...

28 citations


Cites background from "Effects of Geometric and Structural..."

  • ...The advantages of the forward swept blade are highlighted, so that it has direct effects on aerodynamic parameters involving leading edge loading, incidence angle effects and leakage (Pathak et al., 2008)....

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Journal ArticleDOI
Abstract: Torsional aeroelastic analysis of a turbomachinery cascade comprised of three-layered sandwich blades embedded with Magnetorheological Elastomer (MRE) core layer is carried out in this paper. The MRE material is used as a constrained damping layer between two elastic skins in order to investigate its effects on the aeroelastic stability of a blade cascade. To formulate the structural dynamic of the blades, torsional theory of rectangular laminated plates is used and the unsteady Whitehead's aerodynamic theory is employed to model the aerodynamic loadings. Assumed modes method and the Lagrange's equations are used to derive the governing equations of motion of the coupled aeroelastic system. Then, the effects of different parameters on flutter stability of the blades cascade are studied in details. It is found that the magnetic field and MRE layer thickness have significant influences on the flutter boundary of the system and the mistuning of the magnetic field intensity has beneficial effect on the flutter stability. Additionally, the results confirm that the concept of sandwich blades provided with MRE core has capability to utilize as a passive treatment in turbomachinery applications for improving the flutter characteristics of the blades.

7 citations

Journal ArticleDOI
Abstract: A method is presented in this paper to predict cascade flutter under subsonic stalled flow condition in a quasi-steady manner. The ability to predict the occurrence of aeroelastic flutter is highly important from the compressor design point of view. In the present work, the well known Moore–Greitzer compression system model is used to evaluate the flow under rotating stall and the linearized aerodynamic theory of Whitehead is used to estimate the blade loading. The cascade stability is then predicted by solving the structural model, which is posed as a complex eigenvalue problem. The possibility of occurrence of flutter in both bending and torsional modes is considered and the latter is found to be the dominant one, under subsonic stalled flow, for a large range of frequency ratios examined. It is also shown that the design of compressor blades at frequency ratios close to unity may result in rapid initiation of torsional flutter in the presence of stalled flow. A frequency ratio of 0.9 is primarily emphasized for most part of the study as many interesting features are revealed and the results are physically interpreted. Roughly a pitchfork pattern of energy distribution appears to occur between bending mode and torsional mode which ensures that only one flutter mode is possible at any instant in time. A bifurcation from bending flutter to torsional flutter is shown to occur during which the frequency of the two vibrating modes appear to coalesce for a very short period of time.

5 citations

Journal ArticleDOI
Abstract: 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.

5 citations

Journal ArticleDOI
Abstract: The aim of this paper is to report the results of the fluid–structure interaction study of a lightly cambered blade in a cascade under the influence of various inflow conditions and structural parameters, in a cost–effective manner. This work could be viewed as a preliminary design tool that provides the behavioral trend of the blade motion which will be useful when a detailed analysis has to be performed. The methodology employed to formulate the aerodynamic model for lightly cambered airfoils follows the Whitehead's aerodynamic theory for a cascade of flat plates. The aerodynamic loads acting on a blade in a cascade of airfoils are computed to provide the required conditions for the structural model. The aeroelastic model thus formulated is employed to predict the structural response of a blade in a cascade subjected to both steady and unsteady flows. The possibilities of a blade undergoing pure bending or torsion, or coupled bending–torsion flutter are investigated in the present study. The utility of the already developed aerodynamic model is demonstrated by investigating the structural behavior of three different blade curvature profiles – Double Circular Arc (DCA), NACA 65, and NACA a = 1.0 mean lines. The effects of various blade structural parameters such as mechanical damping, center of gravity and elastic axis offset, and cascade geometric parameters such as stagger angle and blade spacing on the blade aeroelastic response are analyzed. The flutter boundary for a range of frequency ratios is then examined. It has been found that compressor blades with frequency ratios close to unity are vulnerable to coupled bending–torsion flutter under the influence of an incoming steady flow. The growing torsional vibrations are in general registered for higher values of air velocity compared to the range of velocities favoring bending flutter. The influence of different compressor unsteady flows – rotating stall and surge, on the aeroelastic behavior of a lightly cambered blade is also examined in the present study.

1 citations


References
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Journal ArticleDOI
Frank Lane1
Abstract: The problems associated with the prohibitive number of possible system modes for a fluttering compressor or turbine blade row are eliminated by the development that comprises the present report. The existence and uniqueness of extremely simple system flutter modes are proved for blade rows consisting of identical blades equally spaced about a common rotor. These simple system modes, if properly interpreted, have the effect of reducing by a factor of n the number of degrees of freedom necessary to analyze an w-bladed configuration. Stated differently, the system of n blades may be considered, with no loss of generality whatsoever, in terms of a single "equivalent blade." The proof holds under any type of flow and any and all types of interblade coupling, so long as a linear analysis is permissible. Moreover, since it is the flutter-inception point that is of interest in predicting critical velocity or rotational speed, it may well be that the conclusions developed apply even to the onset of stall flutter. Practical application of the method to stall-flutter calculations would, of course, require the availability of aerodynamic stallflutter coefficients. The development is carried out first under the assumption of infinite rotor inertia or, in other words, constant rotor velocity. This restriction is then relaxed, and the treatment is expanded to permit torsional oscillations of the rotor itself. I t is proved that under certain conditions the assumption of infinite rotor inertia introduces no error whatsoever.

171 citations

Journal ArticleDOI
Abstract: This paper presents an investigation of the effects of blade mistiming on the aeroelastic stability and response of a cascade in incompressible flow. The aerodynamic, inertial, and structural coupling between the bending and torsional motions of each blade and the aerodynamic coupling between the blades are included in the formulation. A digital computer program was developed to conduct parametric studies. Results indicate that the mistuning has a beneficial effect on the coupled bending-torsion and uncoupled torsion flutter. The effect of mistuning on forced response, however, may be either beneficial or adverse, depending on the engine order of the forcing function. Additionally, the results illustrate that it may be feasible to utilize mistuning as a passive control to increase flutter speed while maintaining forced response at an acceptable level. [A ] [Ar] {AD } { ADr } a b c [D], [Ds [E] E(s,r) [G],[G S

130 citations

Journal ArticleDOI

32 citations


"Effects of Geometric and Structural..." refers methods in this paper

  • ...Then the eigenvalue problem given by equation (4) was solved and damping in torsional and bending modes was obtained....

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Journal ArticleDOI
TL;DR: An overview of the research effort, coordinated between industry, government, and universities, directed toward the development of phenomcnologically founded approaches to induced vibrations in turbomachines.
Abstract: The continuing demand for increased performance in turbine engine turbomachinery has aggravated dynamic problems in the various components, particularly the blading. These problems are generally classified into the categories of either flutter or forced response. Historically, the complexity of the flowfield necessitated the development of empirical flutter and forced-response design techniques. However, such empirical correlations have proven to be inadequate when extrapolated beyond past experience levels. Hence, current research effort, coordinated between industry, government, and universities, is directed toward the development of phenomcnologically founded approaches to these problems. Presented herein is an overview of this ajtack on aerodynamical!}' induced vibrations in turbomachines.

22 citations