Proceedings of ASME Turbo Expo 2004Power for Land, Sea, and Air

measurements.The unsteady aerodynamic excitation of a compressor rotor

bladwhicomsimbothcomadjathrosystsystforfromrow

areanalresuexpmeaadd

LE leading edge

Proceedings of ASME Turbo Expo 2004 e during surge is determined with a numerical procedurech allows calculating the unsteady flow field in apression system. Blade rows of the compressor areulated by appropriate loss/deviation characteristics covering

the normal and the unstable operating regime of thepressor, including reversed flow conditions. Elementscent to the compressor such as inlet pipes, exit volumes andttles are modeled as required to include their impact on theems dynamic behavior. The unsteady flow field within theem is determined by solving the unsteady conservation lawscompressible, inviscid flow. Blade forces are determined

the change of aerodynamic momentum across a blade.

The resulting forces in axial and circumferential directionused as an input for a direct transient Finite-Element stressysis. The resulting forces are applied to the blades. Thelts of the Finite-Element analysis are compared witherimental results from a compressor test rig. Stress issured by strain-gauges in various positions on the blades. Inition, transient pressure is recorded. Measurements are

n rotational speed [rpm]O surface vectorP pressureR gas constantR source termt timeT temperatureTE trailing edgeU state vectorVm,r, meridional, radial, circumferential velocityV volume deviation ration of specific heat eigenvalue matrix density time constant rotor shaft speed lossAERODYNAMIC AND MECHANOF A COMPRESSOR

Harald SchnenbornMTU Aero Engines GmbH

Dachauer Strasse 665D-80995 Muenchen, Germany

+49 89 1489 8326, +49 89 1489 99414Harald.Schoenenborn@muc.mtu.de

ABSTRACTTypically surge events in compressors are investigated

only from the aerodynamic point of view (aerodynamicinstability or lack of surge margin). For this assessment variousmethods exist during the design phase. For the analysis of thestructural impact of surge in this phase the situation is morechallenging, because an analytical prediction of the bladeloading during surge is difficult to obtain. In this paper acombined analysis of aerodynamic and structural aspects ofsurge in compressor rotor blades of advanced axial flowcompressors with state-of-the-art numerical procedures ispresented and compared to extensive strain-gaugeJune 14-17, 2004, Vienna, Austria

ICAL VIBRATION ANALYSISBLISK AT SURGE

Thomas BreuerMTU Aero Engines GmbH

Dachauer Strasse 665D-80995 Muenchen, Germany

+49 89 1489 2637, +49 89 1489 97643Thomas.Breuer@muc.mtu.de

taken during normal operation of the compressor as well asduring surge. It is shown that the procedure is able to predictthe vibration stress level of the blades satisfactorily.

NOMENCLATURE

A Jacobian matrixa speed of soundE flux vectoret total energyH flux vector matrixht total enthalpyI unity matrix

Power for Land, Sea, and Air June 14-17, 2004, Vienna, Austria

GT2004-535791 Copyright 2004 by ASME

INTRODUCTIONOn the one hand, many investigations have been performed

requires thorough engineering judgement whether thesecorrelations still can be applied.

In contrary, a numerical method which allows calculating

on the pure aerodynamic aspects of surge. One of the firstcomprehensive references on this topic are two publicationsfrom Greitzer [1,2], where in the first part a non-linear modelfor the transient performance of a compressor was developed.The occurence of surge or rotating-stall can be determined witha single parameter. The second paper compares the calculatedresults with experimental data. It is beyond the scope of thispaper to list further publications on the aerodynamic aspects.

On the other hand, few investigations have been performedon the combined aerodynamic and mechanical effects of surge.One of the most detailed papers is that of Mazzawy [3], wherethe impact of the surge on blades and rotors is described. Birchet al. [4] describe a model for predicting the large impulsiveloads that occur during surge in an axial flow compressor.Pressure from a 2-D Navier-Stokes calculation were taken as aninput to an Finite-Element Code. Results were compared with ashock-tube experiment.

References [5-7] describe experimental investigations ofblade vibration during surge in a centrifugal compressor withvarious configurations (with/without vaned diffusor;with/without backsweep impeller). Dynamic pressuremeasurements at the casing along the flow path and strain-gauge measurements were performed.

Fleeter [8] performed a series of experiments in a threestage axial flow research compressor to investigate fundamentalaerodynamics of compressor flow instabilities, includingrotating stall, surge and unstable modified surge flow regimesbetween these two modes.

The aerodynamic and structural aspects of surge of a singleblade was investigated by Rudy [9]. A Finite-Element code wasused for the prediction of the dynamic response. Different loaddistributions and damping cases were studied. No comparisonof numerical results with experimental data was presented.

Quite a lot of publications exist for flutter and forcedresponse analysis, also with coupled fluid/structure approaches.General overviews over these topics are presented by Marshall[10], Slater [11] and Srinivasan [12]. As an example of one ofthe newest publications in this area the work of Doi is cited[13]. But an application of one of these many procedures tosurge or rotating stall is not known to the authors.

Compressors are matched to their environment such thatthey have sufficient stability margin for conditions, which arepossible to occur during operation. However, for extremeconditions in terms of boundary conditions (inlet distortion,), engine condition (deterioration, build tolerances, ) andoperating demands (handling, ), compressor stability cannotbe assured for all possible combinations of these factors.Therefore, mechanical blade design has to take into accountthat compressor instability can occur and that the blades have towithstand the unsteady loads associated with engine instabilityforms surge and rotating stall. A common approach toaccount for the loads associated with either surge or rotatingstall is to use empirical correlations based on experimental data.However, this type of approach is strictly valid only as long asthe compressor design is within the parameter space implicitlydefined by the experimental set-up from which the correlationshave been derived. Any deviation from this parameter space2 Copyright 2004 by ASME

the aerodynamic loads associated with surge and/or rotatingstall offers the advantage of being independent from anyexperimentally derived correlations, because it relies only onthe laws of physics which describe the behaviour of a fluid.

Both terms surge and rotating stall describe a highlyunsteady state of flow, where flow field properties undergorapid changes within very short periods of time. Therefore, afundamental requirement for instability loads prediction is to beable to calculate the flow field accurately in time. Furthermore,both types of compressor instability are strongly influenced notonly by local blade properties, but also by the environmentwithin which the compressor is installed, thereby requiringsimulating the environment and its interaction with thecompressor as well.

The present paper combines the results of an unsteadyaerodynamic analysis of surge events with an FEM analysis.Figure 1 shows the general procedure followed in thisinvestigation. Details of the aerodynamic code and the FEManalysis are presented later.

Figure 1: General procedure

AERODYNAMIC CALCULATIONSNumerical methods, which are widely used for

aerodynamic design of blades and are commonly known asNavier-Stokes solvers are not appropriate to serve the task ofpredicting surge/rotating stall loads. Although they give thebest available representation of the flow around a blade, theyare much too complex and computationally heavy to be usedwithin the frame of surge/rotating stall load prediction. Thisprevents the use of complex Navier-Stokes solvers, because atime-accurate calculation of the flow for systems, which consistnot only of compressor blades but also of its surroundingenvironment cannot be achieved within a reasonable timeframe. Therefore, simplifications have to be introduced, inorder to achieve a reasonable balance between a detailedrepresentation of the flow around the blades and the capabilityto handle potentially complex system configurations withacceptable amount of time. Typical representations of suchmodels are described by Longley [14] and Demargne et al [15].

The most prominent simplification which has beenintroduced for the method described in this paper is to representthe flow around the blades by using blade row characteristics to

UnsteadyAerodynamics FEM Analysis

Test RigExperiments

Resulting BladeForce F=f(t)

NASTRANTransient Response

Measured Strainat S/G Position

Calculated Strainat S/G Position

CalculatedPressure at

Kulite PositionMeasured Pressure

at Kulite Position

describe flow losses and turning behaviour. This removes therequirement to perform a detailed calculation of the flow withinblade passages, the savings in time due to this simplification are

00

rather used to allow for modelling of all components adjacentto the compressor which influence the flow field both in itsinitial stages as well as during the fully developed state ofcompressor instability.

The following passages shortly describe the flow fieldmodel, its numerical representation as well as the modelling offundamental elements of which compression systems areconstituted.

NUMERICAL APPROACH

Conservation laws of flowThe numerical method is based on the conservation laws of

mass, momentum and energy for an unsteady, compressibleflow. The conservation laws are formulated in finite-volumerepresentation for cylindrical coordinate system, representingthe meridional and circumferential direction. Currently, themethod is not capable of resolving the flow in radial directionas well, therefore, all calculations are performed for an averagestream tube.

ElementVol RROdHdVtU

+=+

(1)

Vector RElement represents the influence of arbitraryelements used to build a compression system. For instance, incase of a blade row, pressure losses and turning behaviour arerepresented by appropriate source terms for the conservationlaws of momentum. Further details for blade row modelling aregiven in the chapter Blade row modelling. Other types ofelements, such as ducts with bleed ports, unbladed ducts withloss generation, etc. are modelled in the same way byintroducing their specific behaviour into the correspondingsource terms.

The remaining elements of the conservation laws are asfollows:

vectorstate=

=

t

m

e

VV

U

(2)

rsflux vectoofmatrix22

=

+

+=

ttm

m

mm

m

hVhVpVVV

VVpVVV

H

(3)

vectorsurface=

=

OO

O m

(4)3 Copyright 2004 by ASME

=

0

V

rVol dVr

VVR (5)

= source terms due to representation in cylindricalcoordinates

In order to close the system of equations, the state equationfor a perfect gas is employed.

gasperfectaforequationstate== TRp

(6)

Functional relationships for inner energy and total enthalpyare as follows:

energylinner tota2

p1

1 22=

++

=

VV

em

t (7)

enthalpytotalp2

p1

22

=+=+

+

=

tm

t eVV

h

(8)

These equations are used to represent the unsteady,compressible flow field in a two-dimensional cylindricalcoordinate system.

Time discretisationThe calculation of unsteady flow requires a time-accurate

numerical representation of the flow field, therefore, local timestepping to reduce computation time is not allowed. Theadvantage of using an implicit time integration in order todecouple the integration time step from limitations resultingfrom numerical stability requirements has been discarded,because a high resolution in time (resulting in small time steps)was one of the requirements for the procedure, and theadditional computational overhead for an implicit procedurehad to be balanced against the small benefit of not being able tomake full use of possibly larger time steps. Therefore, anexplicit time stepping procedure has been employed. Thelargest possible time step size is dictated from numericalstability requirements which are calculated from local flowconditions as well as the cell size of individual elements, it isdefined as follows:

( )19.0;*min

,,

,

,

max =

+

+= k

aV

OOVol

ktjiji

jim

ji

(9)

Spatial discretisationFor the numerical discretisation flux vector E is

decomposed into both upstream and downstream weighted

The spatial discretisation of the flux balance across a

control volume follows a procedure developed by Vinckier[16]. In his approach, the spatial flux balance is split into anupstream and downstream component. This assures numericalstability without being forced to introduce artificial dampingterms. The approach is outlined for the one-dimensionalconservation laws, and can be transferred to higher dimensionsas required.

One-dimensional conservation laws of fluids:

=+ RSdOEdV

t

U

(10)

The flux vector E is represented as follows (making use ofits homogeneous property):

UAUUEE

=

= (11)

E(U)ofmatrix-JacobiA =Using the eigenvalues of A, it follows:

1= XXA (12)

1= XXA (13)

+ += AAA (14):, 1XX eigenvector matrix and its inverse

:, eigenvalues matrix, eigenvalue matrix withonly positive resp. only negative eigenvalues

Using these relationships, flux vector E can be transformedas follows:

( ) ( )EAAEAA

EAAAUAAE

+=

+=+=+

++

11

1

(15)

11 = XIXAA (16)

negativenotresp.positivenotiseigenvalueingcorrespondtheif

diagonalmainon"0"matrix,unit=I

EeEeE

+= + (17)

matrix-filter-fluxnegativeresp.positive;1 = XIXe (18)

Introducing these relationships finally yields:

( ) RSdOEeEedVt

U=++

+

(19)4 Copyright 2004 by ASME

components, thereby replacing the spatial integral as follows:

( )( ) RSOEOEe

OEOEedVt

U

ixiixi

ixiixi

=+

+

++

+

,1,1

1,1,

(20)

The corresponding equation for the two-dimensional flowfield is:

( )( ) RSdOFfFf

dOEeEedVt

Um

=++

++

+

+

(21)

This approach yields the decomposition of flux vectors intoupstream and downstream components. The advantage of usingflux-filter-matrices is that a spatial weighting of fluxdifferences is achieved which results in a numerically stablediscretisation without being forced to introduce artificialdamping terms.

Boundary conditionsBoundary conditions at inlet and exit of the computational

domain are derived from the theory of characteristics, whichdemand that a physically meaningful treatment of the flow atinlet resp. exit of the domain requires a split of the flow intowaves which propagate in upstream and downstream direction.This split is already achieved with the spatial discretisationapproach as described before, the difference now being, thatwaves entering the computational domain from infinitycannot be derived from properties in the interior of thecomputational domain. Therefore, that part of the spatialdiscretisation scheme can be used which represents fluxpropagation from the interior of the domain to the domainboundaries. The missing part, representing incoming wavesacross both inlet and exit domain boundaries, has to be derivedfrom conditions at infinity. Typically, total pressure and totaltemperature are used at the inlet, whereas static pressure formsthe boundary condition at the exit of the domain. Details of theimplementation can be found in [17].

Within the scope of the procedure described here, it has tobe considered, that during engine surge, the flow direction isusually reverted during part of the surge cycle. Therefore,geometric inlet and exit boundaries may not necessarilycoincide with physical inlet and exit boundaries. Rather, flowmay leave the domain via the inlet and may enter the domainfrom the back end of the modelled system.

Blade row modellingAs outlined before, the selected approach does not model

the detailed flow field within blade row passages, but ratherreplaces the blade row behaviour by using correspondingcharacteristics for flow turning and losses.

Usually, blade row characteristics are available for thestable operating regime of a blade row, representing steady-state flow conditions. Therefore, both modelling of operation

beyond the stability limit as well as transient adaptation to newconditions require additional modelling efforts.

ssdtd

t

=+)( (23)

Steady-state blade row characteristic

In order to cope with conditions during compressorinstability, including periods where flow reversal may occur,blade row characteristics need to be provided which cover thewhole of possible blade row operating conditions.

Usually, blade row characteristics cover that part of theoperating regime which is associated with stable compressoroperation. They are not capable to represent blade rowbehaviour over the range which is required for prediction ofcompressor instability, therefore, a procedure is needed toextend available blade row characteristics into the regime ofunstable compressor operation.

In order to achieve the required extension of blade rowcharacteristics, the behaviour of compressor stages has beenanalysed first. The advantage of starting with stagecharacteristics is that established procedures exist to extendthem beyond the stability limit. Sugiyama [18] presents amethod to extend stage characteristics into the regime ofunstable and reverse flow of a compressor. As sketched infigure 2, stage characteristics are usually provided up to thestability limit, denoted with letter A. Extension to points B,C, D is achieved using first-order resp. second-orderpolynoms, where levels of pressure ratio and efficiency at thesepoints are derived from data at point A.

As soon as stage characteristics are available for the fulloperating regime of the compressor during compressorinstability, extension of the blade row characteristics can beperformed. To this end, stage losses are split between rotor andstator of the stage at a given flow, using a simple loadingparameter to achieve a reasonable balance of losses betweenrotor and stator. Flow turning across the rotor is deduced fromenergy input across the stage which is only facilitated by therotor, stator turning follows a simple rule to deduce exit flowangle deviation from inlet incidence.

Unsteady blade row behaviourThe modelling of loss and turning behaviour of blade rows

for steady-state operation is described in the precedingparagraph. However, any transient change of operatingconditions require to simulate the corresponding transition ofblade rows to the new state as well.

In reality, blade rows do not adapt instantaneously to newinlet conditions, but rather need some time for the adaptation.The time needed for adaptation is proportional to the time theflow needs to travel through the blade row. Usually, time lagsduring transition from one state to another is described by afirst-order lag function. Its general form is

ssfdtdf

tf =+)( (22)f(t) = time-dependent functionfss = steady-state final condition

This time lag is to be applied to both blade row losses and turning, leading to the following equations for the time-dependent loss and deviation of a stator.5 Copyright 2004 by ASME

ssdtd

t =+)( (24)

In case of a rotor, loss and deviation characteristics are tobe applied in the relative frame of reference. In this case, theabsolute time derivative has to be split into partial derivates oftime and space to perform the translation into the rotating frameof reference, yielding the following equations.

sstt

=

+

+)( (25)

sstt

=

+

+)( (26)

Steady-state values of both losses and deviation areobtained from the blade row characteristics, and are used toderive their time-dependent values.

Figure 2: Extension of stage characteristics

Obviously, this approach depends on the availability ofsuitable time constants. Usually, time constants are provided innon-dimensional form, relative to the transport time of animaginary particle through the cascade. Typical values of timeconstants are provided in [18], [19]. These publications alsoindicate that it is necessary to discern between attached andfully separated flow conditions. Within the scope of theaddressed method, this distinction is performed on the basis offlow conditions obtained from the stage characteristics atselected points (Fig. 2). Attached flow is assumed to occur upto point A of the stage characteristics, whereas flow betweenpoints B and D is assumed to be fully separated. Betweenpoints A and B, the time constant varies linearly.

Representation of blade rowsThe interaction between blade rows and flow is

mathematically represented by provision of correspondingsource terms in the conservation equations of momentum andenergy. These source terms are derived from a momentum resp.energy balance across the blade row, assuming known inletconditions and loss resp. turning characteristics. This yields theexit condition of the blade row (for steady-state flow), from

pressure ratio

mass flow

stable

unstable

- +

A

B

C

D

efficiency

mass flow

stable

unstable

- +

A

CD

which the momentum resp. energy difference between inlet andexit can be derived.

Validation of the model

occasionally used in empirical correlations as well to deducesurge loads.In order to validate the model, extensive comparisons havebeen performed between measured and calculated data,basically pressures. In the following, some of the results arepresented for a 3-stage transonic compressor. The compressorhas been equipped with 8 fast-response pressure transducers infront of each rotor. Fig. 3 presents measured traces of staticpressure for a surge cycle. For each stage, traces are orderedvertically in accordance with their circumferential position.Data show that compressor surge develops out of a rotatingperturbation.

Figure 3: Measured data for a 3-stagetransonic compressor

Fig. 4 shows corresponding traces obtained from acalculation. In agreement with measurement data, calculateddata also show that compressor surge is preceded by a rotatingdisturbance with a speed of approx. 50% of rotor shaft speed.The calculation captures both the development history and therotational speed of the initial disturbance with high accuracy.

Fig. 5 presents a comparison of measured and predictedsurge overpressures in front of each stage for the samecompressor. Again, the agreement between measurement andnumerical simulation is good, not only for the surgeoverpressure, but also for the time history of pressure betweensurge initiation and recovery.

Especially the good agreement with respect to surgeoverpressure is of importance, because this parameter is6 Copyright 2004 by ASME

Figure 4: Calculated data for a 3-stagetransonic compressor

Time consumptionBecause of the selected approach to represent the blade

row passage flow field by its loss and turning characteristics,the computational demands of the model are moderate.Calculations for the presented 3-stage compression system(including its modelled environment to capture all influentialfactors which are of relevance for compressor stability) tookonly a few hours on a conventional single-processorworkstation.

Determination of unsteady blade loadsAlthough the model has not been intentionally developed

to assist in the mechanical design of blades, it turned out that itis quite helpful in predicting surge loads. Forces on the bladesin meridional and circumferential direction are simply derivedfrom the difference between inlet and exit momentum for eachinstant in time, thereby providing the input to FEM models.The model can be run with a time step size compatible withrequirements for unsteady FEM calculations (requiring timestep sizes in the order of a millisecond or even less).

RTa = (27)Figure 5: Comparison of measured and predictedsurge overpressure (3-stage transonic compressor)

FEM STRUCTURAL ANALYSISFor the calculation of the structural response to the

resulting aerodynamic forces the commercial FEM-codeMSC/NASTRAN was used. The transient response option withthe resulting force onto the blade as an input was used. Thecentrifugal forces were applied first as a subcase calculationbefore the direct transient response calculations wereperformed. Thus, the deformation of the structure undercentrifugal load was taken into account.

The application of the forces onto the blades is a difficultquestion. For the period of the reversed flow severe separationoccurs and even a simulation with unsteady Navier-Stokescodes does not lead to any realistic point of application for theresulting forces. Neither are measurements known to theauthors. Thus, engineering judgement has to be used forpractical applications.

Here, two different approaches for the application of theunsteady aerodynamic forces are proposed. The first one(Method 1) assumes that the disturbance moves with the speedof sound through the engine and thus also from the trailing edgeto the leading edge of the blade (Fig. 6). As the resulting spanposition of the steady-state forces is at about 60% span, theunsteady force is applied at all nodes along the pressure side at60% span. This results in a time delay for each single node oft=x/a against the trailing edge node, where7 Copyright 2004 by ASME

is the speed of sound calculated with the average bladetemperature T. The time delay between trailing edge andleading edge can be see in the difference between the black andgreen curve (or red and blue curve) in Fig. 6. The forces arenormalized with the steady-state forces so that at zero time theforce is unity. The time scale is normalized with the rotor speed(t*f = t*n/60 [s*rpm/60]).

Figure 6: Method 1 for force application

Figure 7: Method 2 for force application

The second approach (Method 2, Fig. 7) assumes thatduring the normal flow the force is acting at about 50% of thechord length (red curve) and during reversed flow the point ofapplication is on the trailing edge (blue curve). The black curvein the graph indicates the axial velocity which becomesnegative at a certain point. From simple velocity trianglesduring reversed flow it is found that the flow comes nearlyperpendicular onto the blade surface at the trailing edge andthat this might be a realistic assumption. In order to avoid asingle point of contact the force is distributed radial with thesame distribution as the normal gas bending force.

EXPERIMENTAL INVESTIGATIONSThe LPC rotor and the first stage disk used in the test rig is

presented in Fig. 8 and 9. Figure 10 shows the instrumentationof the first rotor blade of the compressor test rig. Three rotorblades of rotor 1 are equipped with two strain gauges each. Oneis located close to the leading edge on the pressure side and theother is positioned at the middle of the suction side. Twopressure transducers are located at the casing in front of therotor blade at two different circumferential positions and onepressure transducer is located at the casing downstream of therotor blade for the recording of dynamic pressure.

TE LE

60% span

Excitation Forces

0.0

0.5

1.0

1.5

2.0

2.5

6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0t*f [-]

F/F

(t=0)

Fax - TEFum - TE

Fax - LEFum - LE

Excitation Forces (axial only)

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0t*f [-]

F/F

(t=0)

&c

ax

/ca

x(t=

0)

cax

Fax N50

Fax N99

N50N99

TE LE

The results of the measurements are presented in the nextsection along with the calculations.

DISCUSSION OF RESULTSFigure 8: LPC rotor

Figure 9: 1st stage blisk

Figure 10: Rig instrumentation

R1 S1 R2 S2 R3 S3

Pos. X (mid SS on 3 blades)

Pos Y (LE PS on 3 blades)

3 Kulites for dynamic pressureat different circumfer. positions

P1, P2

P38 Copyright 2004 by ASME

Figure 11 shows the aerodynamic model of the compressorrig. In Figure 12 the casing pressure in front of the first rotorand the axial velocity in the first rotor as they are predictedfrom the aerodynamic code are presented. Both values arenormalized with the steady-state values. The pressure overshootis 106%. The magnitude of the velocity during the reversedflow phase goes up to about 80% compared with the normalflow conditions, but into the opposite direction. The duration ofthe total surge event is predicted to be about 40.

Figure 11: Aerodynamic model compressor rig

Figure 12: Calculated pressure and axial velocityin front of rotor 1

Figure 13 shows the corresponding experimental pressure.The data are filtered with 50Hz in order to suppress noise. Thepressure was normalized with the same value as the calculatedgraph. The pressure overshoot is 101%, which agrees very wellwith the calculation. The duration of the event is about 50,which is slightly longer than the predicted duration. The overallagreement between experiment and numerical analysis is quitegood.

intake duct

compressor

exit duct

exit throttle

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

0.0 10.0 20.0 30.0 40.0 50.0 60.0

t*f [-]

p/p

(t=0)

&ca

x/c

ax(t=

0)

normalized axialvelocitynormalizedpressure

p/p(t=0) ~ 1.06

and 0.63 can be found for the positions X and Y. Method 2results in higher amplitudes. Here, the values are 0.86 and 0.93,Figure 13: Measured pressure in front of rotor 1

In Figure 14 the axial and circumferential blade forces asthey come from the unsteady aerodynamics are displayed. Asthe highest stress amplitude is to be expected to occur after thevery sharp axial force reduction at t*f~10.7, the force input intoNASTRAN was kept constant after t*f=15. Due to the highcomputational time the FEM calculation was only carried outup to t*f=27. A quite small time step had to be chosen in orderto capture the dynamics of the blade. A time step of less than1% of the first bending mode cycle period was chosen. Thecalculation was performed without damping because it wasfound that the low damping associated with blisks has anegligible influence on the maximum vibration stress, which isof interest to the engineer (see also Ref. [9]).

Figure 14: Calculated axial and circumferentialunsteady blade force

Figure 15 presents the results of the stress history at thetwo strain gauge positions X (black line) and Y (red line) forthe two methods. The stress was normalized with the average ofthe three strain-gauge readings at the corresponding position.For the method 1 vibration stress amplitudes (0-peak) of 0.7

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

0.0 10.0 20.0 30.0 40.0 50.0 60.0f*f [-]

No

rmal

ized

Forc

eF/

F(t=0

)[-] Normalized axial force

Normalized circum. force

p/p(t=0) ~ 1.01

0 20 40 60 80 100t*f [-]

1.00

1.27

1.54

1.81

p/p(t

=0,

calc

)

0.739 Copyright 2004 by ASME

respectively.

Figure 15: Calculated stress at S/G positions

Figure 16: Measured stress at S/G position X

Figure 16 shows the corresponding experimentalmeasurement of the strain gauge at position X. The measuredstrain was converted to normalized stress so that the y-axis candirectly be compared to the calculations. The time axis wasshifted so that the beginning of the surge coincides with thenumerical simulation. The qualitative agreement between themeasured and calculated stress response is quite good, keepingin mind that the calculation was performed without damping.

A quantitative comparison is presented in Figure 17. Here,for both positions X and Y the maximum vibration stressamplitude for all three strain gauge signals and the twocalculated values are compared. It can be observed that there issome scatter in the experimental data. While method 1underestimates the average value of the experimental data byabout 30%, method 2 comes much closer to the mean values.However, the authors had other test cases where the tendencywas vice-versa. Thus, more test cases have to be analyzedbefore a clear indication for one of the two methods is obtained.

Stress Response Strain Gauge Position / Method 2

-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2

0 5 10 15 20 25 30t*f [-]

Rel.

Stre

ssAm

plitu

de

S/G X

S/G Y

Stress Response Strain Gauge Position / Method 1

-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2

0 5 10 15 20 25 30t*f [-]

Rel.

Stre

ssAm

plitu

de

S/G X

S/G Y

-10 10 30 50 70 90t*f [-]

0

0.36

0.72

0.54

0.90

0.18

- 0.18

- 0.36

- 0.54

- 0.72

- 0.90

Rel.

Stre

ss

Am

plitu

de[-]

0 20 40 60 80

[3] Mazzawy, R. S., 1979, Surge-Induced StructuralLoads in Gas Turbines, ASME-paper 79-GT-91

[4] Birch, N. T., Brownell, J. B., Cargill, A. M., Lawson,M. R., Parker, R. J., Tillen, K. G., 1988 Structural loads due tosurge in an axial compressor, ImechE , pp. 117-124

[5] Haupt, U., Rautenberg, M., 1985, Investigation ofblade vibration during surge of a centrifugal compressor,ISABE-paper 85-7085

Summary of Results / Total Stress Signal

0.6

0.8

1

1.2

1.4

ress

Ampl

itude

0-pe

ak

Calculation Method 1Calculation Method 2Measurement S/G No 1Measurement S/G No 2Figure 17: Comparison of Measurementand Calculation

The calculation procedure presented here is very helpful inunderstanding the dynamic response of blades during surge.The quantitative comparison with experimental results issatisfactorily, but some effort remains to be done to get evenbetter agreements.

CONCLUSIONSA numerical procedure was presented which allows time-

accurate modeling of a compression system during compressorinstability. The procedure has been used to calculate unsteadyblade forces during surge, and its output has been used as inputto an unsteady FEM calculation. The comparison betweencalculated and measured transient pressures shows goodagreement.

The application of the unsteady blade forces onto theblades during surge was done with two different approaches.Both methods give quite good agreements with experimentaldata from strain-gauge measurements in a compressor test rig,underestimating the vibration stress response by some amount.Nevertheless, the calculation procedure presented here is veryhelpful in understanding the dynamic response of blades duringsurge not only in the design phase.

Future work will be aimed at a more realistic distributionof the forces on the whole blade surface. More comparisonswith experimental strain-gauge data during surge are necessaryin order to show which of the two methods for the forceapplication yields the better results for a higher number of testcases. The two-dimensional fluid flow code will be extended tothree dimensions.

REFERENCES[1] Greitzer, E. M., 1975, Surge and rotating stall in axial

flow compressors Part 1: Theoretical compression systemmodel, ASME-paper 75-GT-9

[2] Greitzer, E. M., 1975, Surge and rotating stall in axialflow compressors Part 2: Experimental results andcomparison with theory, ASME-paper 75-GT-10

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St Measurement S/G No 310 Copyright 2004 by ASME

[6] Jin, D., Haupt, U., Seidel, U., Rautenberg, M., 1987,On the mechanism of blade excitation due to surge oncentrifugal compressors, Proc. Intern. Gas Turbine Congress.Tokyo 1987, III, pp. 341-348

[7] Jin, D., Haupt, U., Hasemann, H., Rautenberg, M.,1992, Excitation of blade vibration due to surge of centrifugalcompressors, ASME-paper 92-GT-149

[8] Kim, K. H., Fleeter, S., 1992, Compressor unsteadyaerodynamic response to rotating stall and surge excitations,AIAA-paper 93-2087

[9] Rudy, M. D., 1982, Transient blade response due tosurge induced structural loads, SAE Technical paper 821438

[10] Marshall, J. G., Imregun, M., 1996, A Review ofAeroelasticity Methods with Emphasis on TurbomachineryApplications, Journal of Fluids and Structures , 10, pp. 237-267

[11] Slater, J. C.; Minkiewicz, G. R.; Blair, A. J., 1998,Forced response of bladed disk assemblies - a survey, AIAA-paper 98-3743

[12] Srinivasan, A. V., 1997, Flutter and resonantvibration characteristics of engine blades, The 1997 IGTIscholar paper, Journal of Engineering for Gas Turbines andPower, 119, pp. 742-775

[13] Doi, H.; Alonso, J. J., 2002, Fluid/structure coupledaeroelastic computations for transonic flows inturbomachinery, ASME-paper GT-2002-30313

[14] Longley, J. P., 1997, "Calculating the FlowfieldBehavior of High-Speed Multi-Stage Compressors, ASMEpaper 97-GT-467

[15] Demargne, A. A., Longley, J. P., 1997, "ComparisonsBetween Measured and Calculated Stall Development in FourHigh-Speed Multi-Stage Compressors, ASME paper 97-GT-468

[16] Vinckier, A., 1991 "An Upwind Scheme Using FluxFilters Applied to the Quasi 1D-Euler Equations", Zeitschriftfr Flugwissenschaft und Weltraumforschung, 15, pp. 311 318

[17] Veuillot, J.P., Meauze, G., 1985, "A 3D Euler Methodfor Internal Transonic Flows Computation with a Multi-Domain Approach", AGARD Lecture Series 140

[18] Sugiyama, Y., 1984, "Surge Transient Simulation inTurbo-Jet Engine", Ph.D. Thesis, University of Cincinnati,Department of Aerospace Engineering and Applied Mechanics

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