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## Unsteady Aerodynamics, Aeroacoustics and Aeroelasticity of Turbomachines

Google Scholar. Francois X. Hillion Francois X. Torsten H. Fransson Torsten H. Author and Article Information. Jul , 3 : 10 pages. Published Online: July 10, Article history Received:. Views Icon Views. Issue Section:. Holmes, D. Silkowski, P. These models are representative of cantilever, interlock and welded-pair designs of rotating parts.

The differences in terms of frequency and mode-shape of the three models are sketched. Finally their relative merits from a flutter point of view are discussed using the 2D aerodynamic damping characteristics. Flutter, Low Pressure Turbine, Stability Map Introduction Flutter has been a problem traditionally associated to compressor and fan blades. However the steady trend during the last decades to design high-lift, highly-loaded low pressure turbines LPTs , with the final aim of reducing their cost and weight, while keeping the same efficiency, has lead to a reduction of the blade and disk thickness and an increase of the blade aspect ratio.

Both factors tend to lower the stiffness of the bladed-disk assembly and therefore its natural frequencies. As a result of the afore mentioned evolution vanes and rotor blades of the latter stages of modern LPTs of large commercial turbofan engines, which may K. Hall et al. Description of the blade motion as a rigid body idea is to assume that the main contribution to the aerodynamic damping is due to the actual blade and the two neighbouring blades.

In this case the aerodynamic damping varies sinusoidally with the inter-blade phase angle and it may be computed with as few as three linear computations. The validity of such approach has been shown both experimentally Nowinski and Panovski, and numerically Panovski and Kielb, Following the approach of Panovski and Kielb just the unsteady pressure field associated to the bending in the x and y direction and the torsion about a given point, P, for a reference displacement are computed.

The unsteady pressure associated to the motion of the airfoil as a rigid body about an arbitrary torsion axis, O, is computed as a linear combination of three reference solutions. Damping as a function of IBPA for the three fundamental modes. Top: single blade configuration. The deviations from the sinusoidal from of the torsion mode are larger, but in all the cases the critical interblade phase angle is still well predicted.

Flutter Stability Maps Panovski and Kielb showed, using flutter stability maps, how the modeshape and the reduced frequency were the basic parameters that controlled the stability of a two-dimensional LPT section.

In practice only the mode-shape is relevant from a design perspective since the possible range of variation of the reduced frequency is very limited. We have extended such analysis to pairs of airfoils moving as a rigid body. The aim is to mimic the mode shapes obtained when pairs of blades are welded to increase the aerodynamic damping of the bladed-disk assembly. The edgewise and flap modes are defined as bending modes along and perpendicular to the line that joins the leading and trailing edges, respectively. The center of torsion of the third fundamental mode is located at the l.

The airfoil used in all the simulations. Flutter stability maps for the single blade configuration. Figure 3 displays the damping coefficient as a function of the IBFA for the different fundamental modes previously described. For both configurations it may be seen the stabilizing effect of the reduced frequency although for the single blade configuration there always exists a region of unstable IBPA for the computed range of reduced frequencies. The stabilizing effect of the weldedpair configuration may be clearly seen at the bottom of the same figure.

The damping curves of the fundamental modes have been fitted to a sine curve and the methodology described in the previous section used to construct the stability maps for both configurations to conduct a complete study of mode shape in a practical and systematic manner.

Figure 4 shows the flutter stability maps for the single blade configuration, the middle section represents the reference section and the shadow regions the locus of the stable torsion centres. It may be appreciated firstly how the airfoil is intrinsically unstable in torsion and secondly how increasing the reduced. Flutter stability maps for the welded-pair configuration. The shadow regions repre- sent the locus of the stable torsion centres frequency the stable region is enlarged. It is worth noting as well that while the axial mode bending in the x direction is stable the flex mode bending in the y direction is unstable, this may inferred by realizing that a torsion axis at infinity y for instance, which is a stable region generates a pure axial bending stable mode.

Figure 5 shows the equivalent map for a pair of airfoils moving as a rigid body. The upper airfoil of the pair corresponds to the upper section of the figure. Global view of the the bladed-disk assembly configurations.

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Although there exists a big leap in moving from pure 2D to fully 3D mode shapes the simplicity of the approach makes the exercise still attractive. The bladed-disk assembly considered in this study is representative of the first stages of modern LPTs. A global view of the whole assembly may be seen in figure 6.

The vibration characteristics of the cantilever, interlock and welded-pair configurations has been obtained with the same grid. The boundary condition in the contact nodes between sliding parts, namely, between the disk and the blade in the attachment, and between the shroud contacts in the interlock configuration enforces that the displacements of these in both sides are identical. This simplifying hypothesis is made to avoid the generation of non-linear models where the concepts of natural frequency and mode-shape need to be re-interpreted.

Since only the first two families are usually relevant for flutter studies we have restricted ourselves to the lowest range of the frequency - nodal-diameter diagram. Two analysis were carried out, firstly at rest and ambient temperature and secondly at the operating sped with the associated temperatures. Only slight differences were seen in this particular case because the increase in stiffening due to the centrifugal force was compensated by the decrease in the Young s module due to the increase in the inlet temperature of the turbine at the operating conditions.

Since both results were very similar and to avoid further complications, the results presented correspond to the ones obtained at rest. The figure 7 shows the frequency characteristics of the first families for the cantilever top , welded-pair middle and interlock bottom configurations. Several conclusions may be drawn upon inspection of this figure and the mode-shapes, not shown here for the sake of brevity, 1 The disk is very stiff compared to the blades. This may be seen in the mode-shapes, that show very small displacements of the disk, and in the frequency nodal diameter diagram that displays a high number of modes with nearly the same frequency within the same family.

The lower nodal diameters of the first family correspond to shroud dominated modes.

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Modal characteristics of the bladed-disk assembly. Left: cantilever. Middle: Welded-pair. Right: Interlock The baseline cantilever configuration is likely to be unstable since the reduced frequency of the first flap mode is too low, the first torsion mode is probably unstable a well. The welded-pair configuration is better from a flutter point of view than the cantilever one, the torsion mode will be stable in spite of having a lower reduced frequency, however, although the frequency of the 1 st flap mode is slightly higher than before, according with with the 2D inviscid results the mode is still unstable although the damping coefficient for the most unstable inter-blade phase angle has been reduced to one third of the original baseline configuration.

This means that to predict absolute flutter boundaries three-dimensional and mistuning effects need to be retained. The interlock configuration raises significantly the natural frequencies of the bladed-disk and hence is an effective mechanism as well to prevent flutter. A very similar interlock configuration was analyzed by Sayma et al.

## Acoustics, Aerodynamics and Aeroelasticity

A plausible explanation may be found by noting that the modes corresponding to the low diameter nodes of the interlock configuration are edgewise modes, which are stable, while the modes corresponding to the high diameter nodes are torsion modes, whose stability depends on the reduced frequency but that figure 3 right shows that is stable. The instability is concentrated in the region where the edgewise modes become torsion modes and the reduced frequency is not high enough to ensure their stability. Concluding Remarks LPT blades are sometimes welded in pairs to increase their flutter characteristics.

It has been shown by means of two-dimensional simulations that the aerodynamic damping welded-pairs is larger than the one of single blades. This specially true for torsion modes and bending modes whose flapping direction is aligned with the tangential direction of the cascade. A more in depth dis-. The frequency characteristics of three bladed-disk configurations have been presented.

The three assemblies differ just in the boundary conditions of the tip-shroud. It has been observed that the frequency characteristics of the weldedpair configuration are essentially the same that the cantilever configuration while the interlock changes dramatically the overall behaviour of the assembly. The prediction of the stability or not of the welded-pair configuration requires to account for three-dimensional and mistuning effects.

The stability of the interlock is compromised by the transition between edgewise and torsion modes with the nodal diameter of the first family. It is believed that the torsion modes with low reduced frequency, that the 2D simulations show are unstable, are responsible of the instability, this is consistent with the results of other researchers.

### Bibliographic Information

Acknowledgments The authors wish to thank ITP for the permission to publish this paper and for its support during the project. References Corral, R. Nowinski, M. Chernysheva, 1 Torsten H.

## TURBOMACHINES: AEROELASTICITY, AEROACOUSTICS, UNSTEADY AERODYNAMICS

Fransson, 1 Robert E. 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, critical reduced frequency. 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. Objectives The present paper aims to investigate further the sensitivity of the critical flutter reduced frequency versus mode shape maps for the sectored vane, namely towards an non-uniform distribution in the amplitudes between the blades in the sector.

The influence of the number of the airfoils in the sectored vane will be demonstrated. Method of attack The method for investigation of flutter appearance in a cascade, where blades are connected together in a number of identical sectors is presented in [3] and can be shortly described as follows: The aerodynamic response of a sectored vane is calculated based on the aerodynamic work influence coefficient representation of a freestanding bladed cascade.

There is a possibility to consider different vibration amplitudes and any inter-blade phase angles for the blades in the sector, while the intersector phase angles follow the Lane s criteria [6] and all blades have the same vibration frequency. Assuming a rigid-body motion allows to define the blade mode shape entirely by its pitching axis position.

Thus, at a selected reduced frequency and given pitching axis positions for the blades in sector the aerodynamic work for the sector is calculated as a function of the inter-sector phase angle as well as amplitude and phase angle distributions between the airfoils in the sector. The absolute maximum of the work is then calculated and the algorithm is continued for another pitching axis position until the whole range of the mode shapes is covered.

This textbook is a collection of technical papers that were presented at the 10 th International Symposium on Unsteady Aerodynamics, Aeroacoustics, and Aeroelasticity of Turbomachines held September , at Duke University in Durham, North Carolina. The papers represent the latest in state of the art research in the areas of aeroacoustics, aerothermodynamics, computational methods, experimental testing related to flow instabilities, flutter, forced response, multistage, and rotor-stator effects for turbomachinery.

Over the past 30 years, leading experts in turbomachinery unsteady aerodynamics, aer- coustics, and aeroelasticity from around the world have gathered to present and discuss recent advancements in the? This volume contains an archival record of the papers presented at that meeting. The ISUAAAT, held roughly every three years, is the premier meeting of specialists in turbomachinery aeroelasticity and unsteady aerodynamics.

The Tenth ISUAAAT, like its predecessors, provided a forum for the presentation of leading-edge work in turbomachinery aeromechanics and aeroacoustics of turbomachinery. Not surprisingly, with the continued development of both computer algorithms and computer hardware, the meeting featured a number of papers detailing computational methods for predicting unsteady?