aeroelasticity at reversed flow conditions—part iii: reduction of surge loads by means of...

Harald Schoenenborne-mail: [email protected]

Mirja de Vries

MTU Aero Engines GmbH,

D-80995 Munich,

Germany

Aeroelasticity at Reversed FlowConditions—Part III: Reductionof Surge Loads by Meansof Intentional MistuningCompressor surge consists of four phases: (i) pressure rise, (ii) flow breakdown, (iii)blow-down, and (iv) flow recovery. During the blow-down phase reversed flow conditionsexist, where a blade may accumulate hundreds of vibration cycles, depending on thesurge volume and the vibration frequency. High vibration amplitudes and blade damageswere observed in the past. In Part I (GT2011-45034) a compressor cascade was analyzedexperimentally and analytically at steady reversed flow conditions. It has been shownthat (i) the steady flow field can be predicted well by CFD analysis, (ii) the overall damp-ing coefficient calculated by unsteady CFD compares reasonably well with measure-ments, and (iii) a blade may become unstable at certain reversed flow conditions. In PartII (GT2011-45035) the analytical procedures used in Part I were applied to the front partof a multistage HPC for reversed flow conditions. It was found that surge loads consist inreality of two physically different phenomena (i) the pressure wave during the flow break-down leading to rather low blade stresses and (ii) flutter during the blow-down phasewhich may lead to very high blade stresses and damages during surge for some stages.As it is well known that intentional mistuning is a way to mitigate flutter, intentional mis-tuning is investigated in Part III of the paper at reversed flow conditions. At first, a CFDstudy of a single airfoil is presented showing the dependency of aerodynamic dampingupon flow angle and pressure ratio over the airfoil at reversed flow conditions, includingintentional mistuning studies. Secondly, an investigation is presented which shows exper-imentally and analytically that surge stresses can be reduced significantly by the use ofintentional mistuning. In a multistage compressor test rig, one rotor stage, which experi-enced very high stresses during surge, was subjected to a cutback on every second blade,leading to significantly reduced surge stresses. Analytically, an aeroelastic eigenvalueanalysis showed the same behavior. [DOI: 10.1115/1.4007683]

1 Introduction

This paper is the third part of a study of aeroelastic effects atreversed flow conditions as they may occur during the blow-downphase of compressor surge. It is motivated by the observation ofblade damages during surge events, which could not be explainedby the hitherto common assumption that the surge loads consistonly of the pressure wave when the flow breaks down. Therefore,the blow-down phase is investigated in more detail with respect toaeroelastic effects.

In Part I [1] a compressor airfoil was studied at steady reversedflow conditions in a nonrotating test facility at the Ecole Polytech-nique Federale de Lausanne (EPFL). The tests were performed atdifferent inlet angles and Mach number levels. Extensive steadyand unsteady flow measurements were performed on the bladesurface at mid span and at the casing. In addition, the cascade wasinvestigated numerically. It was shown that

(i) The steady flow field can be predicted well by CFDanalysis,

(ii) The overall damping coefficient calculated by unsteadyCFD compares reasonably well with measurements, evenwith a linearized Euler code and

(iii) A blade may become unstable at certain reversed flowconditions.

In Part II [2], the blow-down phase during compressor surgewas investigated numerically with quasi-steady flow assumptions.

It was found that blade loads during a surge cycle may consist oftwo physically different phenomena in certain cases:

(i) the pressure wave which goes through the compressorwhen the flow breaks down.

(ii) during the blow-down phase flow conditions can existwhich are aerodynamically unstable and thus lead to flutterfor some rotor stages. The analytical predicted flutterbehavior compared quite well with the experimental datawith respect to excited nodal diameter, excitation level andobserved blade damages.

In addition to the known flutter regions in the compressor map,a new flutter region was detected experimentally and analytically.This flutter region at reversed flow conditions may occur at certaincircumstances. An example for a blade loading during a surgeevent without flutter can be found in Ref. [3].

As it is well known that intentional mistuning is a remedy forflutter problems, intentional mistuning is investigated analyticallyand experimentally in a multistage compressor rig. The presentpaper describes the results from this study.

After a literature survey, a brief summary of the numerical toolsemployed in the present study is given. Then the results from aCFD study of a single airfoil cascade are presented, followed bythe analytical and experimental investigations of surge stress ofone stage of the multistage compressor rig without and with inten-tional mistuning.

1.1 Literature Survey. In [1] and [2] an up-to-date summaryon the literature of blade loading during compressor surge can befound. Thus, the present literature survey concentrates on theinfluence of intentional mistuning on flutter.

Contributed by the International Gas Turbine Institute (IGTI) of ASME forpublication in the JOURNAL OF TURBOMACHINERY. Manuscript received June 29, 2012;final manuscript received September 14, 2012; published online June 5, 2013. Assoc.Editor: David Wisler.

Journal of Turbomachinery JULY 2013, Vol. 135 / 041009-1Copyright VC 2013 by ASME

Downloaded From: http://turbomachinery.asmedigitalcollection.asme.org/ on 08/30/2013 Terms of Use: http://asme.org/terms

Kaza and Kielb were one of the first to investigate the effect ofintentional blade mistuning on flutter [4–6]. They discovered thata “moderate amount of mistuning has enough potential to alleviateflutter problems in unshrouded turbofans.” Alternate frequencymistuning of approximately 7% and 10% was used in theirinvestigations.

In the survey of Ewins [7] many papers on the effect of mistun-ing on flutter are listed, also with the uniform conclusion that mis-tuning always raises the flutter threshold.

The first investigations were done using simple models. Later,methods based on CFD and FEM became more common. Gott-fried and Fleeter [8] used a fluid-structure interaction model tostudy the effect of an 8% frequency difference of the first torsionalmode and found that they became more stable.

Martel et al. [9] used an asymptotic mistuning model (AMM)to analyze the effect of intentional mistuning on the stability prop-erties of aerodynamically unstable rotors during normal forwardflow. An optimization was performed to achieve maximum rotorstability.

In Bleeg et al. [10] a new reduced order aeroelastic model usingprincipal shapes (AMPS) is used to study the aeroelastic effect ofalternate blade mistuning. This new method is important whenmodes belong to more than an isolated mode family or when thereis a geometric difference between the two blade types.

Chan [11] gives a further overview of the actual status of mis-tuning research, including intentional mistuning. Intentional mis-tuning can improve the robustness of blisk design with respect toforced response, but further work has to be conducted in order tofind the optimal intentional mistuning pattern.

Recently, Hohl et al. [12] performed analytical investigationsof the influence of intentional mistuning with additional statisticalmistuning on the forced response of bladed disks with a newlydeveloped cyclic CMS-based substructure model. They found thatan A-B blade pattern reduces the effect of stochastical mistuningfor their unshrouded turbine test case.

Schoenenborn et al. [13] performed an analysis of the free andforced response characteristics of an intentionally mistuned blisk,including aerodynamic effects.

A current overview over the whole mistuning literature can befound in the excellent survey paper by Castanier and Pierre [14],where also intentional mistuning is covered.

2 Numerical Tools

The numerical investigations are performed using the MTUstandard procedure for flutter calculations. As the codes are alreadydescribed in [1] and [2], here only a short overview is given.

2.1 Steady Flow Solver. For the steady aerodynamic flowsolution the MTU and DLR common CFD code TRACE [15–17]is used.

The 3D Reynolds-averaged Navier-Stokes equations are solvedfor compressible flow together with the two equation k-x turbu-lence model with some additional enhancements.

The convective fluxes are discretized using the Roe’s TVDupwind scheme which is combined with the van Leer’s MUSCLextrapolation to obtain second- or third-order accuracy in spacedepending on the used limiter. The derivatives of the viscousfluxes are approximated by central differences.

For a steady multistage calculation, the nonreflecting formula-tion according to Giles is applied at inlet and outlet boundaries,whereas the coupling of different stages is realized by a mixing-plane approach. For more details it is referred to the above men-tioned references.

2.2 Unsteady Flow Solver. The unsteady flow is computedwith a time-linearized Euler method. Therefore, the flow is splitinto a mean, steady flow and a small, harmonic perturbation.Thus, the steady flow problem is decoupled from the unsteady

problem. The steady flow, which is computed with the codedescribed above, is interpolated on a single H-grid for each pas-sage. The time-linear unsteady flow equations are solved on amoving grid, which conforms to the motion of the airfoils. The so-lution algorithm uses a cell-vertex formulation. Nonreflectingboundary conditions are employed to accurately model isolatedcascades. More details of the linearized method and its extensivevalidation can be found in Kahl [18].

2.3 Reduced Order Code. The aeroelastic eigenvalues arecalculated with the reduced order code Turbo-Reduce, which isdescribed in detail in Ref. [19]. This code is based on a cyclic-symmetry FEM sector model of a blisk and a set of cantileverblade modes. The aeroelastic coupling coefficients are determinedwith the unsteady flow solver and fed into the reduced order code,which returns the aeroelastic eigenvalues.

3 CFD Study

In Ref. [1] a study with two inflow angles and Mach numbers atreversed flow conditions for a single airfoil cascade was pre-sented, showing the dependence of the aerodynamic damping onthese two variables. Here, the results of a much more extensivestudy of the same airfoil geometry with five inflow angles (a), fivepressure ratios (PR), and three different torsional mode shapes(TA) are presented. As the cascade has 20 blades, each fluttercurve consists of 20 different interblade phase angles, resulting in5� 5� 3� 20¼ 1500 flutter computations.

3.1 Investigation Setup. Figure 1 shows the computationalsetup of the CFD study. At the inlet, total pressure, total tempera-ture, and the flow angle are prescribed, whereas at the exit thestatic pressure is fixed. The inflow comes from the left andimpinges first onto the trailing edge (TE) of the airfoil pressureside (PS). This results in a complex flow field with a broad stagna-tion pressure region at the pressure side trailing edge and a largerecirculation region on the suction side (SS), close to the trailingedge. The entire flow has to pass through the remaining section ofthe blade passage. In Fig. 2, an example of such a flow field fora¼ 75 deg and a ratio of the total inlet pressure over the static exitpressure PR¼ 1.7 is shown. Overall, 5� 5¼ 25 different steady-state flow calculations have been performed.

Based on the steady-state flow calculations, unsteady calcula-tions are performed with the linearized code. Three different tor-sional mode shapes are investigated. These mode shapes aredisplayed in Fig. 3. The first one has its torsional axis at 25%

Fig. 1 Computational setup CFD study

041009-2 / Vol. 135, JULY 2013 Transactions of the ASME


chord length from the trailing edge (TA_25), the second one at50% chord (TA_50), and the third one at 75% chord (TA_75).The flow direction is indicated by the arrow, which impinges ontothe trailing edge.

For the case a¼ 75 deg, and the pressure ratios PR¼ 1.1 and1.7 the flutter curves for all three torsional modes are presented inFigs. 4(a) and 4(b). Table 1 shows the corresponding inlet Machnumbers and reduced frequencies. Unfortunately, not all calcula-tions did converge, but the minimum damping range is captured.It should be noted that the damping shown in the plots is a normal-ized damping. It can be seen that, as expected, the mode shapeTA_75 is the least stable, followed by the TA_50 mode shape.These two mode shapes have the minimum damping at an IBPAof �90 deg and �108 deg, whereas the mode shape TA_25 has itsminimum damping at þ154 deg and is much more stable. ForPR¼ 1.1, all modes are stable, but for PR¼ 1.7 the modes TA_50and TA_75 become unstable.

Figure 5 shows the aerodynamic excitation for the interbladephase angle of �90 deg, where the torsional mode TA_50 has itsminimum damping (or maximum excitation). On the left-handside, the local excitation on the suction side is displayed, and onthe right-hand side the local excitation on the pressure side isshown. The solid lines indicate the position of the torsional axisfor the respective mode shape.

The mode shape TA_25 has a high excitation on the pressureside close to the leading edge, but also a high damping on the suc-tion side, so that overall the damping prevails. The mode shapeTA_50 shows an excited region on the pressure side as well,

Fig. 2 Flow field for the case a 5 75 deg, PR 5 1.7

Fig. 3 Torsional mode shapes

Fig. 4 (a), (b) Stability curves for the case a 5 75 deg, PR 5 1.1,and PR 5 1.7

Table 1 Mach number and reduced frequency

Mach Number Reduced frequency

PR¼ 1.1 0.26 0.69PR¼ 1.7 0.58 0.32

Fig. 5 Local aerodynamic excitation for the case a 5 75 deg,PR 5 1.7, IBPA 5 290 deg

Journal of Turbomachinery JULY 2013, Vol. 135 / 041009-3


located close to the leading edge and a damped region on the suc-tion side. In this case a region with excitation can be seen on thesuction side close to the trailing edge. Overall, this mode has anegative damping.

The third mode shape TA_75 shows a small region of dampingon the pressure side close to the trailing edge, but most of theremaining blade surface is excited, resulting in a high overallexcitation.

In Fig. 6, the minimum normalized damping of each fluttercurve is plotted over the investigation range of all five angles andfive pressure ratios for the three mode shapes. In the upper graph

(a), the results for the TA_25 mode shape are presented. Thismode shape is stable over the complete range of inflow angles andpressure ratios.

The mode shape TA_50 becomes unstable at a pressure ratioaround 1.3 and angles between 45 deg and 60 deg and at higherpressure ratios at 75 deg. The TA_75 mode shape is unstable atmost of the parameters in the investigated range, except at a com-bination of high pressure ratios and low angles or low pressureratios and high angles.

In Fig. 7, the minimum normalized damping is plotted over thetorsional axis position and inflow angle for the pressure ratio ofPR¼ 1.7. This graph shows the same tendency as Fig. 6. A tor-sional axis close to the trailing edge gives a stable behavior atreversed flow conditions. Moving the torsion axis to the leadingedge leads to an unstable behavior. For this case an angle of 75deg gives the most unstable conditions.

4 Analytical Investigation of Intentional Mistuning

4.1 CFD Study. For a first study of the influence of inten-tional mistuning on the flutter behavior at reversed flow condi-tions, the case a¼ 75 deg and PR¼ 1.7 of the CFD study ischosen. An alternating mistuning pattern of 63% in frequency isstudied.

Figure 8 shows the resulting aeroelastic eigenvalues. In this fig-ure, the normalized frequency is plotted versus the aerodynamicexcitation. A positive value stands for unstable behavior, and anegative value represents stability.

Fig. 6 (a), (b), (c) Normalized aerodynamic damping versusflow angle and pressure ratio

Fig. 7 Normalized aerodynamic damping versus flow angleand torsional axis

Fig. 8 Aeroelastic eigenvalues for the case a 5 75 deg, PR 5 1.7



The mode shape TA_25 (diamonds), which is already stable,does not show any improvement in stability due to the intentionalmistuning. The TA_50 mode shape (triangles), which is slightlyunstable, becomes stable due to the intentional mistuning. Themode shape TA_75 (squares), which is highly unstable, is stabi-lized. It is remarkable that in this case this mode shape showsalmost the same stable eigenvalues as the TA_50 mode shape,which means that for the TA_75 mode shape intentional mistun-ing has a higher stabilizing effect than for the TA_50 mode shape.

4.2 Compressor Case. The next study is performed on a realcompressor case. Figure 9 shows the front block of the compressoras it is used in the CFD calculations. The inlet of the computa-tional domain was set at the exit of the forth stator vane, with aflow angle in negative axial direction. In addition, total pressureand temperature were prescribed. The outlet static pressure wasset at the inlet of the inlet guide vane (IGV).

Aeroelastic calculations based on quasi-steady CFD calcula-tions as described in Ref. [2] are performed for the third rotor forvarious pressure ratios during the blow-down phase. The quasi-steady approach is justified by the fact that, even if the absolutereversed flow time is short, a vibrating blade may accumulateabout hundreds of vibration periods during that time, as also notedin di Mare [20].

For each pressure ratio on the 85% speed line, a stability curveas presented in Fig. 10 is obtained. The damping values are nor-malized with a reference damping due to proprietary reasons. Itshows that the first torsional mode is unstable at interblade phaseangles in the range of 150 deg–180 deg with a normalized aerody-namic damping of �3.2.

In addition to the aerodynamic damping, the correspondingcoupling coefficients are obtained for this case. The behavior ofthe aerodynamic damping during the blow-down phase withdecreasing pressure levels is shown in Figs. 5 and 13 of Ref. [2].

Then, for several levels of intentional mistuning (61%, 62%,66%) the new aeroelastic eigenvalues are calculated. The resultsare presented in Fig. 11, where the normalized frequency is plot-ted versus negative aerodynamic damping. Positive values corre-spond to unstable conditions whereas negative values meanstability. The 61% intentional mistuning leads already to a signif-icant improvement, but the system is still unstable. A mistuninglevel of 62% is more stable, but a further increase in mistuninglevel to 66% does not improve the situation any more.

Figure 12 shows the result of a study of the influence of mistun-ing levels, where the minimum aerodynamic damping versus fre-quency difference is plotted. Up to 64% there is an improvementin stability, but a higher level of intentional mistuning does notimprove the stability further. Overall, the system remains slightlyunstable. This cannot be allowed for normal flow conditionswhere the compressor operates at the operating point for a longertime. But as we are looking at a surge event with a very short du-ration, the question arises how this effects the blade vibration dur-ing a surge cycle. As the vibration amplitude (and thus the bladestress) can be approximated by the equation,

A ¼ A0 � e�d�f �t (1)

Fig. 9 Investigation setup of a compressor front block

Fig. 10 Normal aerodynamic damping versus IBPA

Fig. 11 Influence of intentional mistuning on aeroelasticeigenvalues

Fig. 12 Minimum aerodynamic damping versus mistuninglevel



with the vibration frequency f, the logarithmic decrement of theaerodynamic damping d, and the time from the start of thereversed flow t, the evolution of the vibration amplitude with dif-ferent intentional mistuning levels can be determined.

Figure 13 shows the normalized vibration amplitude versus nor-malized time (t_ref¼ vibration period of first torsional mode)using Eq. (1). If the vibration amplitude of the tuned system is di-vided by that of the mistuned system, the reduction in surge stresscan be calculated directly. The result is shown in the graph inFig. 14. After 70 vibration periods a mistuning level of 61% al-ready yields a reduction of 2.7, whereas a mistuning level of 62%gives a reduction of 4. A higher intentional mistuning levelimproves the situation only slightly.

In order to see if these theoretical considerations are true inpractice, the third rotor stage which showed large vibration ampli-tudes during a surge in the tuned configuration is subjected to acutback of the trailing edge for every second blade. The resultsare presented in the next section.

5 Rig Surge Test With Intentional Mistuning

The compressor used for the investigation consists of eightstages and is representative of a state-of-the-art compressor interms of Mach number and blade loading. All rotors are built as

integrally bladed disks (blisks), providing only very little struc-tural damping. The inlet guide vane as well as the first three statorrows are variable to adapt to flow conditions and stage matchingto optimize performance throughout the speed range. The down-stream volume between compressor exit guide vane and throttlehas been adapted to a volume in order to simulate realistic flowconditions during a surge cycle.

The rotor blade vibrations are measured by tip-timing probes inthe casing with the MTU tip-timing system [21, 22]. Surgeinduced blade vibrations of the type described in the introductorysection have been encountered in the upper speed regime of thecompressor. Data collected during these events formed the basisfor subsequent investigations to uncover the mechanism drivingblade vibrations.

Figure 15 shows the cutback at the trailing edge, as employedto every second blade, on the left-hand side. The mode-shapes ofthe first torsional mode for the tuned and cutback airfoil are shownon the right-hand side. At the trailing edge, the mode-shapechanges slightly, otherwise it remains the same. The achieved fre-quency difference is close to 4%.

In Fig. 16 the normalized surge deflections of the third rotorblade during a surge cycle as already presented in [2] are shown.The bright curve represents the overall, instantaneous deflectionsand the dark curve the averaged deflections. Filtering the fre-quency of the first torsional mode out of the data results in a curvewhich is slightly below the averaged curve. This shows that mostof the vibration content is due to the first torsional mode.

A strong increase in surge amplitudes can be observed betweent / t_ref¼ 100 and 170, which is mostly due to the first torsional

Fig. 13 Normalized vibration amplitude versus time

Fig. 14 Reduction in surge amplitude versus time

Fig. 15 Airfoil cutback and 1T-mode-shapes

Fig. 16 Surge deflections without cutback



mode. After the airfoil cutback, several surges at the same operat-ing conditions were repeated. In Fig. 17 the normalized deflec-tions of one surge are displayed, showing very low deflections ofthe first torsional mode compared to Fig. 16. A slight increase innormalized deflections of the first torsional mode of a factor of 1.4can still be observed starting around t/t_ref¼ 125, which may bedue to a remaining instability. The increase in amplitude predictedby the analytical analysis for this intentional mistuning level isabout 1.7. But overall, the surge stresses are reduced significantly.

At this point it should be noted that the analytical work doesnot claim to yield an exact quantitative prediction of surge stress,but rather reasonable prediction of the physics. For the appliedintentional mistuning of 62% the prediction is a reduction of fac-tor 4 after 70 vibration periods, which compares quite well withthe observations in the rig.

Figure 18 finally gives a summary of the resulting dimension-less blade surge stress. The different bars represent different surgeevents at the same conditions (speed, pressure), showing the scat-ter of blade stress, which may be quite significant. The surgestress is reduced by approximately factor 5. Thus, the intentionalmistuning is very successful in reducing the vibration amplitudesduring the surge blow-down phase.

6 Conclusions

The work is summarized below and appropriate conclusions aredrawn from the investigations:

• A CFD study at reversed flow conditions was performed fordifferent flow angles, pressure ratios, and torsional axes. Theaerodynamic damping for all flow cases was calculated.

• The CFD study shows that a torsional axis close to the trail-ing edge gives stability, whereas moving the torsional axistowards the leading edge leads to instability of the airfoil.

• Maps with the combination of inflow angles and pressureratios over the airfoil were calculated, which indicate the sta-ble and unstable regions of torsional modes at reversed flowconditions.

• Intentional mistuning was investigated analytically for a realcompressor blade during surge based on the aeroelastic calcu-lations in Part II of the paper, showing a large potential inreducing vibration amplitudes during surge.

• Intentional mistuning was applied to one stage of a researchcompressor by a cutback of the trailing edge of every secondairfoil. Compressor surge cycles at the same operating condi-tions without and with cutback demonstrated successfully thereduction in surge stresses.

• The fact that intentional mistuning reduces the surge stresses sig-nificantly is a further indication that the second type of bladeloading during compressor surge is indeed a flutter phenomenon.

Nomenclature

A ¼ amplitudef ¼ vibration frequency

IBPA ¼ interblade phase anglePR ¼ pressure ratioref ¼ reference

t ¼ timeT ¼ torsional mode

TA ¼ torsional axisa ¼ flow angled ¼ aerodynamic damping

References[1] Schoenenborn, H., Chenaux, V., and Ott, P., 2011, “Aeroelasticity at Reversed

Flow Conditions—Part 1: Numerical and Experimental Investigations of aCompressor Cascade With Controlled Vibration,” ASME Paper No. GT2011-45034.

[2] Schoenenborn, H., and Breuer, T., 2011, “Aeroelasticity at Reversed Flow Con-ditions—Part 2: Application to Compressor Surge,” 134(6), p. 061031.

[3] Schoenenborn, H., and Breuer, T., 2004, “Aerodynamic and Mechanical Vibra-tion Analysis of a Compressor Blisk at Surge,” ASME Paper No. GT2004-53579.

[4] Kaza, K. R., and Kielb, R. E., 1983, “Aeroelastic Characteristics of a Cascadeof Mistuned Blades in Subsonic and Supersonic Flows,” ASME J. Vib.,Acoust., Stress, Reliab. Design, 105, pp. 425–433.

[5] Kaza, K. R., and Kielb, R. E., 1983, “Effects of Structural Coupling on Mis-tuned Cascade Flutter and Response,” ASME Paper No. 83-GT-117.

[6] Kaza, K. R., and Kielb, R. E., 1984, “Flutter of Turbofan Rotors With MistunedBlades,” AIAA J., 22(11), pp 1618–1625.

[7] Ewins, D., 1991, “The Effect of Blade Mistuning on Vibration Response – ASurvey,” IFToMM Conference on Theory of Machines and Mechanisms, Prague.

[8] Gottfried, D. A., and Fleeter, S., 2002, “Fluid-Structure Interaction Simulationof Flutter Suppression Via Structural Mistuning,” 7th National Turbine EngineHCF Conference May 14–17, Session 6, Paper 6.

[9] Martel, C., Corral, R., and Llorens, J. M., 2006, “Stability Increase of Aerody-namically Unstable Rotors Using Intentional Mistuning,” Proceedings ofASME Turbo Expo, Barcelona, Spain, Paper No. GT2006-90407.

[10] Bleeg, J. M., Yang, M., and Eley, J. A., 2007, “Aeroelastic Analysis of RotorsWith Flexible Disks and Alternate Blade Mistuning,” ASME Paper No.GT2007-27227.

[11] Chan, Y. J., 2009, “Variability of Blade Vibration in Mistuned Bladed Discs,”Ph.D. thesis, Imperial College, London, UK.

[12] Hohl, A., Panning, L., and Wallaschek, J., 2010, “Analysis of the Influence ofBlade Pattern Characteristics on the Forced Response of Mistuned Blisks Witha Cyclic CMS-Based Substructure Model,” Proceedings of ASME 2010 10thBiennial Conference on Engineering Systems Design and Analysis ESDA, July12–14, Istanbul, Turkey.

Fig. 17 Surge deflections with cutback

Fig. 18 Dimensionless surge stress without and with cutback



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[13] Schoenenborn, H., Junge, M., and Retze, U., 2012, “Contribution to Free andForced Vibration Analysis of an Intentionally Mistuned Blisk,” ASME PaperNo. GT2012-68683.

[14] Castanier, M., and Pierre, C., 2006, “Modeling and Analysis of MistunedBladed Disk Vibration: Status and Emerging Directions,” J. Propul. Power,22(2), pp. 384–396.

[15] Eulitz, F., Engel, K., Nuernberger, D., Schmitt, S., and Yamamoto, K., 1998,“On Recent Advances of a Parallel Time-Accurate Navier-Stokes Solverfor Unsteady Turbomachinery Flow,” Proceedings of the 4th ECCOMAS, K. D.Papailiou, D. Tsahalis, J. Periaux, C. Hirsch, and M. Pandolfi, eds., John Wiley& Sons, New York, pp. 252–258.

[16] Nuernberger, D., Eulitz, F., Schmitt, S., and Zachcial, A., 2001, “Recent Pro-gress in the Numerical Simulation of Unsteady Viscous Multistage Turboma-chinery Flow,” ISABE-2001-1081.

[17] Engel, K., Zscherp, C., Wolfrum, N., Nuernberger, D., and Kuegeler, E., 2009,“CFD Simulations of the TP400 IPC in Off-Design Operating Conditions,”ASME Paper No. GT2009-60324.

[18] Kahl, G., 2002, “Aeroelastic Effects of Mistuning and Coupling in Turbomachi-nery Bladings,” Ph.D. thesis, EPFL No. 2629, Lausanne, Switzerland.

[19] Lim, S., Bladh, R., Castanier, M. P., and Pierre, C., 2007, “A Compact, Gener-alized Component Mode Mistuning Representation for Modeling Bladed DiskVibration,” AIAA J., 45(9), pp. 2285–2298.

[20] di Mare, L., Krishnababu, S. K., Mueck, B., and Imregun, M., 2009,“Aerodynamics and Aeroelasticity of a HP Compressor During Surge andReversed Flow,” Proceedings of the 12th ISUAAAT, Sept. 1–4, London, UK.

[21] Zielinski, M., and Ziller, G., 2005, “Noncontact Blade Vibration Measure-ment System for Aero Engine Application,” ISABE, 17th International Sym-posium on Air Breathing Engines, Munich, Germany, September 4–9, PaperNo. 1220.

[22] Zielinski, M., and Ziller, G., 2005, “Noncontact Crack Detection onCompressor Rotor Blades to Prevent Further Damage After HCF-Failure,”NATO RTO-AVT-121 Symposium on the Evaluation, Control and Preven-tion of HCF in Gas Turbine Engines, Granada, Spain, October 3–6,Paper No. 19.



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