-
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
[email protected]
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 [email protected]
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
0
0.2
0.4
S/G X S/G YS/G Position
Real
tive
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
[19] Nagano, S. Y., Machida, Y., Takata, H., 1971,"Dynamic
Performance of Stalled Blade Rows", Tokyo JointInternational Gas
Turbine Conference and Product Show
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