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TRANSCRIPT
7 AD-A141 004 T W O4IEWNSI CSAL AND UASI THU E -01 NSI OSAL 1TC N /f
EDPERAS0 ASSIWSAII LSASIENTAL SIAWiARO COW IOU. Sil II COLE POLTOIU
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11U IMICROCOPY RESOLUTION TEST CHART
NAT)ONAL BUREAU OF STANDArDS-1963-A
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ECOLE PO YTECHNIQUE ERALE
DE LAUSANNE
)IlrLaboratoire do Therique Appiqude
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6kITWNsESOALADOAITRE-IESOA
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ECOLE POLYTECHNIQUE FEDERALEWNW= DE LAUSANNE
FL Laboratoire de Thermique Appliqude
TWO-DIMENSIONAL AND QUASI THREE-DIMF NSIONAL
EXPERIMENTAL STANDARD CONFIGURATIO NS FOR
AEROELASTIC INVESTIGATIONS IN
TURBOMACHINE-CASCADE S.
Compiled by T. Fransson and P. Suter
DTICJUN7 I 94
ASeptember 30, 1983
This work is jointly sponsored by the United States Air Force under GRANT
AFOSR 81-0251, AFOSR 83-0063 with Dr. Anthony Amos as program
manager and by the Lausanne Federal Institute of Technology.
Peport
LTA-TM-83-2 ' - t~~ Yc.Ie t
1
Preface
At the 1980 "Symposium on Aeroelasticity in Turbomachines", held in
Lausanne, Switzerland, it became clear that it was Oirtually impossible
to compare different analytical models for flutter and forced \ibration
prediction and to establish their alidity.
The Scientific Committee (*) of this meeting has deiided to initiate a
workshop on "Standard Configurations for Aeroelasticity in Turbomachine-
Cascades". The aim of this project is to establish a data base with a
few well documented experimental data, and to initialize and coordinate
future experimental investigations in existing test facilities. The standard
configurations to be compiled should also ser~e as test cases for present
and future prediction models for aeroelastic phenomena in turbomachine-
cascades.
This report constitutes the first product, a standard set of two-dimensional
and quasi three-dimensional experimental configurations. These configura-
tions will be treated by calculation models from several research groups
during 1983, whereafter a second report with a comparison between the
experimental and the theoretical results will be established and presented
at the Third S.mposium on Aeroelasticity in Turbomachines 1984). It
is the hope of the Scientific Committee that these reports will constitute
a bench-mark for the \alidation of both experimental and theoretical
aeroelastic inmestigations in turbomachines.
September 30, 1983
P. SuterChairman of the Scientific Committeeof the 1980 "Symposium on Aeroelasti-city in Turbomachines"
The members of the Scientific Committee at the 1980 Symposium are:
• H. Forsching, GermanyG. G~armath , Switzerland -cor ForR Leqendre, France A& -I-
A A.A. Mikolajczak, USA ' ,M. Ro\, FranceP. Suter, Switzerland 'chairman). .
Y. Tanida. JapanD.S. Whitehead, United Kingdom
F , 1',,.oI _ I ;tII__ 4
3
Abstract
The aeroelastician needs reliable, efficient methods for the calculation
of unsteady blade forces in turbomachines. The \alidity of such theoretical
or empirical prediction models can only be established if researchers
apply their flutter and forced vibration predictions to a number of well
documented e\perimental test cases.
In the present report, the geometrical and time-a~eraged flow conditions
of nine two-aimensional or quasi three-dimensional experimental standard
configurations fcr aeroelasticity in turbomachine cascades are giken.
For each configuration some aeroelastic test cases are defined, comprising
different incidence angles, Mach numbers, interblade phase angle, reduced
frequencies, etc.
Furthermore a proposal for unified nomenclature and reporting formats
is included, in order to facilitate the comparison between the different
experimental data and theoretical results.
\j*1
i'4
tIn it erits page
Preface I
Abst ract 3
Cont ent s 4
Nomenclat ure 5
1. Introduction 11
2. Recommendations for Urnfied Representation of the Results 13
2.1 Stead\ Two-Dimensional Cascade Nomenclature 14
2.2 Unsteady Two-Dimensional Cascade Nomenclature 17
2.3 Precise Reporting Formats 28
3. Standard Configurations 35
3.1 First Standard Configuration 59
1.2 Second Standard Confiluration 55
3.3 Third Standard Configuration 72
3.4 Forth Standard Configuration 87
3.5 Fifth Standard Configuration 90
3.6 Sixth Standard Configuration 119
,.7 Se'enth Standard Configuration 149
.8 Eighth Standard Configuration 167
,.9 Ninth Standard Configuration 1804. Proposed Calculation of the Standard Configurations 190
4.1 Present List of Participation 191 J4 .2 Participation With a Prediction Model 191
Acknowledgement 195
Re ferences 196
Appendix: To he returned b\ the participants in the theoretical
part of the pro)ect. 199
rIJ
• _..=-,L* "4
5
Nomenclature
Note:
a) Throughout this report, "standard configuration" will designate a cascadegeometry and "aeroelastic case" or "aeroelastic test case" will indicatethe different time dependant (and, in some cases time averaged) conditionswithin a standard configuration.
b) The tables and figures will be numbered as the chapters. For example,Figure 3.7-2 denotes the second figure in chapter 3.7.
Sy mbol Explanation Dimen-sion
Latin Alphabet
A amplitude (A-h for pure sinusoidal heaing)(A= " for pure sinusoidal pitching) rad
A Fourier coefficient
c chord length m
"F t) unsteady perturbation force coefficient vectorper unit amplitude, positive in positive coordi-nate directions:
C'F(O)=CFe t-F 1
" L't) unsteady perturbation lift coefficient per unitU amplitude, positive in oositive y-direction:
CL(t)=CLeIWt -LINote: In the present work, the lift coefficient
is defined as the force component perpen-dicular to the chord.
CMt) unsteady perturbation moment coefficient perunit amplitude, positive in clockwise direction:
cmmt)cme, vt - M1
C ",t) unsteady perturbation blade surface pressure -
Cp coefficient per unit amplitude:
C,,(x,t)-C,(x)e1w - Pcoefficient for aerod-namic work done on the
airfoil during the cycle of oscillation
d maximum blade thickness 'dimensionless
with chord)
,4>
6
f vibration frequency Hz
f function
h x,.',t) dimensionless (with chord) bending vibration,positive in positive coordinate directions
h dimensionless (with chord) bending amplitude
Vi-
i indicence deg
k reduced frequency = CW
k harmonic in Fourier series
M Mach number
n unit vector normal to blade surface, positivenwards
p \,t) pressure N/m 2
,without superscript :time dependant perturbation),with superscript 11 :time averaged)
"l dimensionless vector from mean pikot axisIto an arbitrary point on the mean blade surface
R real part of complex valuei ~Vic
tRe Reynolds number = j
s unity %ector tangent to blade surface, positive
in positive coordinate-directions
Str Strouhal number fet (-k/TT)
T dimensionless time: T = t/T °2 T0
T period of a cycle S0
t time s
V velocity m/s
7i
7
Vre f reference velocity for reduced frequency and m/sStrouhal number:
Vref V for compresor cascadeVref V2 for turbine cascade
w circular frequency = 2rf rad/s
dimensionless (with chord) chord-wise coordinate -
x dimensionless (with chord) chord-wise position -
of torsion axis
dimensionless (with chord) normal-to-chord -
coordinate
dii iensionless (with chord) normal-to-chord po- -
sition of torsion axis
z dimensionless (with chord' span-wise coordinate -
(reek Alphabet
(t) pitching vibration, positive nose-up rad
pitching amplitude rad
13 flow angle deg Jchordal stagger angle deg
heaving vibration direction = tai (h/h x) deg
ac(xjt) unsteady perturbation pressure difference coeffi- -
cient
&C;'(x't)-CV 'SI(x't)_CP (",S)(x,t) 17C(x)e,* -wt 0P)
phase lead of pitching motion towards heaving deg,radmotion of blade (m)
V/ kinematic viscosity rn/s
-' aerodynamic damping coefficient, positive for -
stable motion
+IiS3
bJ
interblade phase angle between blade "m-l" and deg,rad
blade "m". rie for constant interblade phaseangle.
is positive when blade "m" preceeds blade"m-i t.For idealized conditions (constant interbladephase angle between adjacent blades,d , andidentical blade vibration amplitude for all blades)the motion of the (m)th blade, for flexion,is given by:
- (0)h (x,y,t)=h(x'y) e'llwtmcl
1' dimensionless (with chord) blade pitch= gap-to-chord ratio
OF phase lead of perturbation force coefficient deg,radtowards motion
A phase lead of perturbation lift coefficient to- deg,radwards motion
0M phase lead of perturbation moment coefficient deg,radtowards motion
OF' phase lead of perturbation pressure coefficient degradtowards motion
O phase lead of perturbation pressure difference deg,rad
coefficient towards motion
phase angle in the Fourier series deg
i.
-- 4 a,
9
Subscripts:
A A h for heavingafor pitching
G center of gravity
global global (= time dependant + time a~eraged)(see eq. 7)
imaginary part
is isentropic \,alues
LE leading edge
k k-th harmonic in Fourier series
R real part
ref reference \elocity for reduced frequencyVref V1 for compressor cascade
SV2 for turbine cascaderef 2
TE trailing edge
t total head \alue
x component in x-direction
y component in y-direction
z component in z-direction
a position of pitch axis (see Fig. 1)
1 measuring station upstream of cascade
2 measuring station downstream of cascade
- '.alues at "infinity" upstream
,do values at "infinity" downstream
______ _ V !
10
Superscripts:
'B) designates lower or upper surface of profile,B) 'B) = Js' for lower surface of profile
,us) " upper
(is) lower surface of profile
im) blade number m = 0, 1, 2, ... If the amplitude.interblade phase angle, .... are constant for theblader under consideration, this superscript willnot be used
,.us) upper surface of profile
time a\eraged (= steady) \alues. This superscript willonly be used in ambiguous context
amplitude of unsteady complex \alue
I
V9
11
1. Introduction
In axial-flow turbomachines considerable dynamic blade loads max occur
as a result of the unsteadiness of the flow. The trend towards exer greater
mass flows or smaller diameters in the turbomachines leads to higher
flow \elocities and to more slender blades. It is therefore likely that
aeroelastic phenomena, which concerns the motion of a deformable struc-
ture in a fluid stream, will increase exer more in future turboreactors
'fan stage! and industrial turbines last stage' 1101.
The large complications, and high costs, of unsteady flow measurements
in actual turbomachines makes it necessary for the aeioelasticiar, to
rely on cascade experiments and theoretical prediction methods for minimi-
zing blade failures due to aeroelastic phenomena. It is therefore of great
importance to \alidate the accuracy of flutter and forced Oibration predic-
tions as well as experimental cascade data and to compare theoretical
results with cascade tests and trends in actual turbomachines.
Sexeral well documented unsteady experimental cascade data exists through-
out the world, as well as many different promising calculation methods
for sol\ing the problem of unsteady flow in two-dimensiona , and quasi
three-dimensional cascades. However, due to different basic assumptions
in these prediction methods, as well as many different ways of repreqenting
the obtained results, no real effort has been made to compare the difeient
theoretical methods with each other. Furthermore, the \alidity of these1!theoretical prediction analysis can only, since hardly any exat solutions
are known, be \erified by comparison with experiments. This is very seldom
done. partly because of the reasons mentioned abc'e. partly as well docu-
mented experimental data normally are of proprietar\ nature.
It is the purpose of the present project to partly remedy this situation
by selecting a certain number of standard configurations for aeroelastic
in\estigations in turbomachine-cascades and to define an unified reporting
format to facilitate the comparison between different theoretical results
and the experimental standard configurations.
The final objective of a comparatixe work of the present kind is of course
to \alidate theoretical prediction models with experiments performed
under actual conditions in the turbomachine, i.e. under consideration
of unsteady rotor-stator interaction, flow separation, %iscosity, shock-boun-
dar la 'r interaction, three dimensionalit., etc. Such a far-reaching ohjec-
J
12
tie does howe\er not correspond with the present state-of-art of aeroelas-
fie knowledge, neither for predict ion models nor as regards well doumen-
ted experimental data to be used as standard configurations.
The scope of the present report will thus be limited to fully aeroelastic
phenormena under )dealized flow conditions in two-dimensional or quasi
three-dimensional cascades. Such interesting phenomena as rotor-stator
interact ions, stalled flutter and fully three-dimensional effects will thus
be excluded, unless as an extension from the iGealized two-dimenrsional
cascade flow.
In this first report, nine standard configurations, ranging fiJm flat plates
to highly cambered turbine bladings and from incompressible to supersonic
flow conditions, are selected and a certain number of aeroelastic test
cases, mostly based upon existing experimental data, are defirtd for
analysis by existing prediction methods for flutter and forced brations.
It is intended that an extensive number of "blind test" calculations b,
different prediction methods "see chapter 4) should be performed in the
autumn of 1983. The experimental data will thereafter be distributed
,in beginning of 1984) to all researchers ha ing performed the recom-
mended analysis; the comparison of the experimental and theoretical
results will so prepare a base for detailed discussions of the different
e\perimental and theoretical results during the "Third Sfniposium on
-\eroelasticity in Turbomachines" 1984 I1, 121.
In the beginning of 198Lt it will also be possible for the participants to
. e~ entually refine some aspects of their experimental or theoretical proce-
dure and to prepare, if possible, a contribution to the 1984 Symposium
on Aeroelasticit y.
The final comparison of the experimental and theoretical results will
he distributed at the 1984 S\mposium on Aeroelasticit\. Attention will
then also be focused upon still unresoled aeroelastic problems and a
coordination of future experimental and theoretical inkestigations may
be iitiated.
\ ,,
13
2. Recommendations for Unified Representation of the Results
The physical reasons for self excited blep kibitions in turbomachines
are not presently understood in detail. Various representations of experimen-
tal and theoretical results are thus used by different researchers. The
number of different reporting formats used may be \ery large, as \arious
importance is attached to different results, depending upon the scope
of the aeroelastic in,,estigation.
However, as the main objecti\ve for both experimental and theoretical
aeroelastic studies is to provide a tool for the designer of turbomachines
to minimize blade failures, the important results from the different inesti-
gations should be standarized to allow for interpretation of non-specialists
in aeroelasticity.
In order to facilitate the comparison and to establish the mutual \alidity
of both theoretical and experimental results, a certain amount of informa-
tion must be unified. This is also desirable in order to a~oid misinterpreta-
tion of some results.
In the present project, a minimum number of prescriptions ha~e been
defined. Both the nomenclature and the representation formats are based
upon references 131 - 19 1, especially the publication by Carta 131 117 1'.
It has been chosen, furthermore, as similar as possible to the presentation
prep iousl, used for the experiments serving as standard configurations,
this to aoid e\cessike retreatment of the data.
, IQ I'
I- -.
2.1 Steady Two-Dimensional Cascade Nomenclature
The profiles under investigation are arranged, in a two-dimensional section
of the cascade, as in Fig. 2.1-1. In this figure, all the physical lengths
are scaled with the chordlength "c", and the nomenclature in Table 2.1-1
is used.
It is here important to note that the chord is defined as the straight
line between the intersections of the camber line and the profile surface,
and that the x-coordinate is aligned with the chord.
Throughout this report, e\tensi e use will be made of the time a\eraged
blade surface pressure coefficient, which will be defined as
/cascade leading
edge plane
y
profile "0"MI - - -t
.- >+I 0.0 1.0 " " "
/ M2
• d .. . profile "-l"
lower surface
t i(Ire 2.1-1 (1 eady t wo-dimnerisional cascade (jeometry
4'
5 mbol I \planat ion Dimen-s i o n
chord lenght m
d ma\imum blade thickness dimensionless with chord',
Cp time a~eraged pressure coefficient
i incidence d e
M Mach number
n" unity \ector normal to blade surface, positie inwards -
p time a~eraged pressure N/m 2
Rdimensionless vector from mean pi~ot to an arbitrarypoint on the mean blade surface
Re Reynolds number
s4 units \ector tangent to blade surface, positike in posi-tihe coordinate directions
V elocity m/s
Vref reference ,clocity for reduced frequency andStrouhal number: "Vref" "V " for compressor cascade
"V " = "V 2 11 " turbine " m/sref c
dimensionless 'with chord) chord-wise coordinate
y ~ dimensionless 'with chord) normal-to-chord coordinate -
z dimensionless 'with chord) span-wise coordinate
flow angle deg
- chordal stagger angle deg
'V kinematic \iscosity M /s
dimensionless blade pilch - grap-to-chord ratio
Table 2.1-1 contl iii;)n cf) ne\t page,
Np
16
Subscripts
G center of gravity
is isentropic values
t total head value
X component in x-direction
y component in y-direction
z component in z-direction
1 measuring station upstream of cascade
2 measuring station downstream of cascade
- 0 \alues at "infinity" upstream
0 v alues at "infinity" downstream
OL pitch axis '.see Fig. 1)
Superscripts
m) mth blade, m=O, 1, 2,....If the amplitude, interblade phase Vangle,... are constant for the bladesunder consideration, this superscriptwill not be used
Js) lower surface of profile
(us) upper surface of profile
steady ( time a~eraged) values. This superscript will only beused in ambigous context.
Table 2.1-1 Steady two-dimensional cascade nomenclature
h .
17
2.2 tkisteady Two-I)inensional Cascade Nomenclature
Bllade Motion
Fig. 2.2-1 is a -cheiiatic representation of cascaded two-dimensional
airfoils; the form of the profiles is co'isideed to re-1 in rigidly fixed
during heaving and/or pitching oscillations, "} (x,y,t) and -&(t) resp., in
which the components h., h and 1 of the motion vectors h and a arey
noted in complex form to account for phase differences between the
translation and the rotation.
We will therefore define
hm(xyt)-hx~y) le1 wlrntlfor heaving motion
(2)(m)(t)-- ne(m)t +e for pitching motion
where ,m) a(m) are the dimensionless amplitudes, and W m ) the circular
frequency, of the vibration of blade (m).
It is also assumed that the torsional motion, for tie (m)th blade, preceeds
the bending motion by a phase angle- Furthermore, if the amplitude,
circular frequency or phase lead is identical for all blades, the superscript
(m) will be omitted on the corresponding symbol (see Table 2.2-1).
k
1ii
4 Li'
prfle8l
Zupper surface
-profile "-1"'
Fiqiure 2.2-1 Unst eady two-dimensional cascade nomericlat Lire
L -j
11% [bol I \planat ion I)fn n-S i o n
A amplitude A h for pure sinusoidal hea\ing
A- .. .. p. ching r a d
C F t, unstead\ perturbation force coefficient kector perunit amp' Wude, positive in positive coordinatedirections:
C L t, unstead perturbation lift coefficient per unit ampli-tude. positi\e in positike )-direction:
CL(t)= CLe,,t -WI
Note: In the present report, the lift
coefficient is defined as the force componentperpendicular to the chord.
C t unstead\ perturbation moment coefficient per unitamplitude. positike in clockwise direction:
U \.t instead\ perturbation pressure coefficient per UnitI
amplit ude:
C (xt)=C (x)e " I(" v'oefficient for aerodynamic work done on the ssstem
\/ during rice c cle of oscillation
f ibrat on frequency Hz
h -,.\.t dimensionless with chord bending %ibration, positivein positive coordinate directions
h *,.s dimensionless with chord' bending amplitude
k reduced frequency - CW
p time dependant perturbation pressure N/m 2
St r St rouhal number f /C (==k/n)Vref
Table 2.2-1 continuation on next page'
.... ,
20
T dimensionless time T-t/T °
T period of a cycle s0
t time s
w circular frequency = 2n f rad/s
a(t) pitching vibration, positive nose up rad
pitching amplitude rad
heaving vibration direction z tan-l(hY/h,) deg
ACp(X,t) unsteady perturbation blade surface pressure differencecoefficient:ACo ~,t) =CPOls)(x ,t )- c p'us'(x ,t ) ACp(x)e",!wt " - pl
phase lead of pitching motion towards heaving motion deg or
of blade (m) rad
_ aerodynamic damping coefficient, positive for stablemotion
phase lead of perturbation force coefficient towards deg or
motion rad
phase lead of perturbation lift coefficient towards deg or
moti on rad
0,.. phase lead of perturbation moment coefficient towards deg ormotion rad
P(, ) phase lead of perturbation pressure coefficient towards deg ormotion rad
0 (y) phase lead of perturbation blade surface pressure deg or
difference coefficient towards motion rad
Cm) interblade phase angle between blade "m-I" and deg or
blade "m" rad
Table 2.2-1 'continuation on next page"
I I I
21
o"% d for constant interblade phase angle. -1 is
positike when blade "rm" leads blade "m-I".
Under idealized conditions constant interblade phase
angle between adjacent blades.e , and identical
\ibration amplitude for all blades) the motion of
the mth blade is gien, for flexion, by
-- P'0) =?ma0h(x,y,t)=hNx,y) e' t-m~l
and similar for torsion, b%
a' ' (t)__-G(O)e 'wt- to- ea
Subscripts
A A = h for hea% ing
A = a for pitching
global global (- time dependant - time a\eraged ,see eq. 7)
Iimaginar\ part
R real part
Superscript
Is) lower blade surface
'M) blade number m 0, 1. 2.
us) upper blade surface
amplitude of unstead\ complex alue
Table 2.2-1 Unsteady two-dimensional cascade nomenclature
$
_ _ _ _ _ _ _ _
Two-PIm)itosisowal Aerodynamiiic (ne fficiet its
T he unst eadv %comnplex' blade surface pressure coefficient C *as wellp
as the lift C Ll force C F and moment C I coefficients per unit span
are scaled with the amplitude of the corresponding motion amplit ude
-"A", where A- h mor a I Accordinrg to the con\ ent jonal di'fini ti is
of these parameters, we thus ha~e:
p8 (x t)C,: (X,t)o P, I
LA A~ 0 J -00
S~I~3C9XLe
lCFA (t)A F -P 4P(x~t) -n'-dS
-s4n
C 1 R0x IP(X,t)d.sJIi-e 6
"~A A Fropt c~
where
- p is the unist each pFert urbat ion pressure
- "li ft" coe fficient is de fined normal to chord
- force components are positi~e when acting in Pnsiti~e coordinate direc-ions
- is posit i\.e when acting in clockwise direction
-superscript B. denotes the blade lower surface (ls' or blade upper surface
Furtermrethe global &time a~eraged + time dependant) blade surface
pressure coefficient is defined as
P 5-- P5-5 (OP-P-- (7
A further important quantity, for slender blades, is the normalized un-
steadv pressure difference along !he blade chord. ACp(X).
This is defined as the difference of the time dependant nressures on the
blade lower and upper surfaces:
f~s) ((8
Acjx) Co(x~) -C (X~) (
23
All of the abo~e mentioned \ariables can be expressed in either complex
exponential form or in component form as:
Cp(xt)= Cp(x)e'lwt 0p(x) 1 - {CpR(x)+4iCp(x)}ewt (9)
Here, the subscripts "R" and "I" denotes the real and imaginary parts
of the pressure coefficient C p(x,t). Physically, these two parts can be
interpreted as the components of the pressure coefficient which are in-pha-
se real part) and out-of-phase (imaginary part) with the blade motion.
Furthermore, the phase angles 0 p(x), OAp(N), OL' OF' OM are all defined
positive when the pressure pressure difference, lift, force or moment,
resp. leads the motion.
The amplitude and phase relationships in eq. '9) are defined in the usual
mariner, that is:
{ o(X VCpR(X+C2 2 (X)
SCP(x))//CP C (x) i 0a)
{ q~)C xlcs¢(x),,b)C,,Wx = (p(x)-sin(¢ ()IO
It should here be noted that, in computing the blade surface pressure
distribution, only components, and not amplitudes or phase angles may
be differentiated (/3/). Therefore(is)t (us)
ACVR(X)=CpR (x)Cp(X)- ts(us) J 1 a)
aC,(X)=Cp,(x) I-C (X
A,(X)*Cp ()- eps x) Jib)
(Is) (us)
Two-Dimensional Aerodynamic Work
The two-dimensional differential work, per unit span, done on a rigid
system by the aerodynamic forces and moments is conventionally expressed
by the product of the real parts 'in phase with motion components) of
force and differential translation, as well as mo.rient and differential
__'i 't
24
torsion. Thus, the total aerod\ narnw work coe'fficieot per period of oscill a-
tion, done on t~systemn is obtained b c'o;-mputmri
CW-CWh+ CWO± CWrCO±CWan ( 12,
Expressed in this wa\, the aerod~nanm work coilfficiprit. c, c c
C wahW c wh- are all in nondimensionalized form, with the product of the
pressure di f ference ,W ) and chordl as normalizing factor.
From the definition eq. 12 and 1 5 it is se-n that these cooificio nts
become neqati, e for a stable motion.
As the force and momnrt coefficients each ha\ c timne d-pendart parts
from both the h-a\ ing and pit chinig wail Ia t ions.; c wh 's defined Rs the
work done on the profile duririg a pore hea\ rig i- cle rio torsion . 5li ml r-
k . c is the work done On the blade' duingM A pore pitihing c~ c rio
bending ;c w hanid - h6is the wi! done t) the pitching force due
to hea\ ing arid b tte hea~ij mn tliinr'r dute to pit ching. respect i\ cl
Thus, the work coeffi cts maij he e ~ sdin cor entional form as
Cwh-f Rejh-C",t) Re~dhft~cycle 01
cycl if
osc ' 0
CW0o- #RejdCcot)[Rejcttlt)ICyc e 0 f
Intecase of pore sinusoid(al rra ta-i r bending or pure sinusoidal
to-sional '%ibration, as well as SirisoidAl lft arid nioment responses,, respF-c-
tively, the expressions .15, rna\ be initeri;ited to qi\,Ce the following simple
formulas -2 -2
Cwh=nh -CLI =~h -CL'Sifl(L)
CwG,,Tra'CM n'Cm-sin(0Mj)
CWhaO-
VVOP = 0It is thus seen that the aerodyriarmc work onl-, depen"dS upon the \alute
of the out of phase component of the lift and moment ca)efficrents, and
that the airfoil damps the motion when thr, imaqinar part of the lift
25
and moment coefficient, resp. is negatie.
The aerod\namic work can be e\pressed in normalized form as the aerod -
namic damping parameter _ /3/. With the same assumptions as in eq.
,14), this parameter is defined as{ - -Ch 21=C1
The normalized parameter = is thus positive for a stable motion.
Non-Harmonic Pressure Response
All theoretical prediction methods for flutter and forced \ibrations aaila-
ble today, make a few basic assumptions.
Most of the methods are submitted to restrictions regarding
o sinusoidal blade %ibrations
o sinusoidal pressure response
o identical ibration frequencies for all blades
o identical \ibration amplitudes for all blades
o constant interblade phase angles
In experiments, howe~er, these assumption can ne\er be e\actl fullfilled.
The large energ input needed to drive a cascade with prescribed frequen-
cies. amplitudes and phase angles makes it impossible to satisf the three
ittter Issumptions, apart from in tests with low frequencies and/or small
anplitudes. Een in this case though. the pressure response on the profiles
will, in general, not be sinusoidal.
For the detailed comparison between the experimental data and the predic-
tion model, it is thus important to realize how well the theoretical assump-
tiors approximate the experiment.
The non-sinusoidal pressure response on the \ibrating blades does not
hinder the computation of the aerodynamic work and damping coefficients,
as only the frequency of the pressure response spectra corresponding
to the blade \ bration frequency contributes to the aerodynamic work.
The \alidit of this statement ran be demonstrated if we suppose that
Ihe blade motion is sinusoidal with angular frequency w, and as any perio-
dic signal F'wt), of which fwt) is the unsteady part, can be represen-
ted as a Fourier series
00
FRwt)=A + fw )A+ I Ae '' wk~l
', J
2 I
As exernple of proof of the statement, let us cionsider a pure sinusoidal
pitchingi mode (oG real)
ai(t)aelw
with a moment signaldcma(O OO I C .' ! lk
w l ' 0 M kj}aCMa(t)={ Z cMk
k=1The aerodynamic work coefficient cwa becomes thus
2n 0Cx
cw = RejdCM,(t)Rejdc(') }f(1 Red I CMk eClkwl.MkI 'Rejide'wt d(wt)Oscl lation
2,n oo
=16'1 I CM0,k COS(kwt±-M k)} {-asin(wt)}d(wt)=0 k=l
co 2v=-a2 I CMak{JCOS(kt+OMk) sin(wt)d(wt)}=
k=l 0
2-CuakSin(kom) if k=l CW0 &C (17)
0 if k1 Ca
Thus, in the computation of the work coefficients only the first harnonic
of the force or moment response appears (compare eq. 14).
This simplification of a non sinusoidal pressure response is however only
possible due to the existence of a pure sinusoidal motion and the integra-
tion over a cycle of vibration. A verification of the actual time histories
of the experiments is thus needed.
This is even more important in experiments with non-identical blade vibra-
tion amplitudes and interblade phase angIles, as these differences largely
ma\ contribt to discrepaerles between the experimental and theoretical
Cleatli/eJ, results.
(On the bse; ()f (Itet l11.(11 tilne ruordin s, a statistical evaluation or a
di ,'relte I o)Jrlr lNir,'li l; ea\ be used to appreciate how well the different
i~leall/ lItm !i in itli, F710(11 l(011 ilih(11'15 a)prOxXiit mhe real cascade flowh' lli}l t It) v;
II I',J; r ,- ... ... ,'',t t' f If ' Wam Iflit IA P ,)t all lhr"' physic-al quLant it ies
1. r I, . . l' l w rl;
II m I t i ;impllhll id , C ) l ti(e first hair iii(, it a I (utirier analysis is used
27
o as the root-mean-square \alue ,RMS' times a factor V"'. if a statisti-
cal e aluation is used (example: h -t/ TJh(t) d(t) :,*). The factor0
is here introduced in order to equalize the statistical amplitude with
the full amplitude for a purely sinusoidal fluctuation.
In both cases, an indication of the quality of the signal should, if possible,
be given. This criteria can, for example be established as
o higher harmonics for Fourier analysis
o fluctuation of result with different averaging times for a narrow-band
filter
o shape of spectral peak at a distance of, e.g., 20 dB relative to peak
for spectrum analysis
In order to e\aluate e entual discrepancies between the experimental
data and theoretical results, it is of importance that an analysis of the
abo\e mentioned kind accompan, the data.
i
! 1
T) This RMS-\alue may occur e.g. as the output of a narrow-band filter
applied to the unsteady pressure signal, centered at the blade oscillation
frequency.
_ _ iI
aN
2. !" I iii(2i a I oein 111 I urinals
Cj f tlie riwi;l Voblirrc; fur Ima cnini,)ii loon of experinierit a iol id r' I
cat ar.reli~ ii! iri\ c s: ioA Ian- ; 11 1 ti 19 8f0 "S, rnm i Limrn Avroetzust icit
in -1uLrbacn achire_;' wa s t hf hick< of cofl lr (.1 cy i n I hu I epuI in(1 f orrIfolat! i
t: e rei Iarcl i I ;P'! I IL pa t i i i(Ii i t he p,, it p10oc 1 are t he re fnre in,, it ed
to f oftI !w I W, lide-I ifnes for a st ,viod~ri /zed report rfig forrmat, giv~en iri
this, chap er.
Two rn in qvfo :p of rr-sei ita;t ion' %v'. 11 be used:
1: IT-hic i~ !A ucur icr s t hec de't Oil Ped cornpariSOr IOf the [TMSUred and
cakl lat ed hi ac pressri ir di st ri bUtions.
11. I he SeCoi it re'preseit'at ion is direct ed towa rd- the physi en I mechanism,
of t Ibe Ifott t er pher iomnena, its import anft pzirameters and t) owa r d
Itie est ahl i sfirmrnt of thfe flut teri boundaries for t he di ffereicit cascades.
It is evi tier it that alt part ici rant S are DFncouraged to uise any I'fI f crrpr
irig format s in order to0 est ablish ot her compari so[ s or to 1 emphasi ze
any special poit it of iot crest in thei r in\ est igat ions.
I: Detaniled comparison of experimentnil iosuls m id theoretical approaches
The coe biihilr of the \ati (lit y of ttreoret ical result s (:ari oily be dorne
by a rout tal agreement '1.t ween thte Mea.51ui-ed soid cluat1 UriSt eaitx
pressuce dist r ibut ionis on hot h blade( Su~t aces3. T!his (let a iIe d cor-opar isori
will hec performed on the basis of Figure 2.-5-1 \vhich is to be presentedi
for- di ffererit comibinat ions of
0 interhlacle phase anqlo,
0 rfCIL~edfrequency
0 inlet Condtitions
o CaSCOCle g, Oiii(!t[Vdeperidiri upon thte e \isting cetiwri.-iwi t Odatita for, trie con firourat ion tinder-
invest igat ion.
Quit C. a few pT ecdit ion0 models fOr' ftJ I tCi or forC-ed vi brat, ions are based
Upon S'1all pert urhabit ion theorlies, Vtirf-ii the St eail jPressure( dist ribut err
on ttcm blade is arfi input dat a. The expar imeritally drt ermiried I irn amcra-
gad h IA(tf Sulr f ace'( p~re'ssuLre (list ritbat iris is t herefore speci fiert for soti
SItric'"S.as iii I ig. 2.3-2.
F r tihcinior e I h- comnpariion btwrihtte st ead 'J ig 2.3-2) aird inst eady'
() W2 -1bade' pressLre (fi~tritLitit ! Mrsra\ in some~f cases give a qiiarit i-
29
ti'e notion about the aeroelastic phenomena under in~est gation instabili-
ties due to stall, choke, shockwa\es, coupling effects between the stead'
and unstead> flow fields...).
The distribution of the blade surface pressure difference coefficient along
the blade, A C X,, indicates the presence of stable and unstable zones.P
This information is thus also of interest, and will be plotted as in Figure
2.3-3.
II. Flutter boundaries
The second form of representation concerns the \.alues of the resultant
aerod'namic blade forces and moments, as well as the aerodynamic work
and damping coefficients.
Two different representations see Figures 2.3-4 and 2.3-5' will be used
to elaborate the influence of se.eral important parameters on the flutter
boundaries
o reduced frequency
o interblade phase angle
o inlet flow \elocity
o inlet flow angle
o outlet flQw \elocity
o cascade geometry
First. the unsteady blade pressure coefficients will be integrated to 'ield
the aerod.namic force, or lift, and moment coefficients as in Figure
2.1-4. The phase angles 0 , ariOcM resp., gi\e in this repr-;2titation imme-
diate information about the aeroelastic stability of the s\stem see chapter
2.2
Secondl>, the aerodynamic work and damping coefficients per ccle ofoscillation may be calculated if the mode-shape of the motion is wellknown. Most of the problems treated in the present work will concern
motion of nondeformed profiles "at least for the theoretical predictions,
wherefore the aerodniamic damping coefficient can be easil computed
and plotted. This information is useful for the turbomach~ne designer
for the judgement of the aeroelast ic beha,.iour of a specific cascade
Figure 2.5-5.
I
-I
/
2 Y,,
x I
flr,.i Z .' ' I r tL: r:~.;.i ,' . ., r3 S
20. 2
I P2x
c 10. W
k
0. d:
+360 + +-- _ _ -360
STABLE
+180 -180
UNSTABLE
-380 ++-360
.0 .5 1.x
FIG. 2.3-I: MAGNITUDE AND PHASE LEAD OF UNSTEAoY BLADESURFACE PRESSURE DISTRIBUTION. f
r P:]N pIT'H " ' ;T' \, V I. 1 LF'3 1 i I. IF r. 1*lit
C
7 -
,
X
x
x 1m
P2
AEROELRSrICITY IN IURBOMRCHINE-CRSCAOE5.STNOARD CONFIGURPTION NUMBER
M2 ,
hx
hY
k
P -
-1o. -- 4 - -
c
0.
Ix
b$
FIG. 2.3-2: TIME AVERAGED BLADE SURFACEPRESSURE COEFFICIENT.
:
Jc
_,_,_,,_-----.---- -----.
/- - '17' ' x/x
,c
p 3 i
3 i N- i T, N' " r SLo
2.
C .
+360
STABLE
i +180
UNSTABLE
0 O.z P S T A B L E
hI
'" -180
. UNSTBLE
-3 6 0 , - -- --- .. . .I -0. .5I.I
X
FIG. 2.3-3: MAqGNITUDE AIND PiiASLE LEAD OF I,STEPiDT BLADOE.SURFACE PRESSURE [3IFFER-NICE COEFFICIENT,
10", ,1 If .,
C
xx
Pi m 2Ya
REROELRSTICETI IN 7UPBOMACHrNE 'p DES.5TPNDARO CONFIGURPTION NUMBER
2.
L C :
k
F 8
c a:M
0. 'd a :)
~+360
STABLE
+180
UNSTABLE
O0.L
STABLE
F-180
M UNSTABLEM
-360 - ' I
-180 0 180
FIG. 2.3-4: AERODYNAMIC FORCE, LIFT AND MOMENT COEFFICIENTSTOGETHER WITH THE CORRESPONDING PHASE LEADS IN DE-
PENDRNCE OF CASCADE GEOMETRY AND FLOW QUANTITIES.
I ,, i
/h x 1
-____ _____ _____ __ p
CI(~U \k
Sb ~f~L'CT
di91 -1.ARL
;TBL0.x
JO h
-30 0 30
F16.2.3-: RRODYPMI WOP (;N DR1PIN COFFICE (3
IN D~cfDRNE OF CRCPO GCOETR AN
FLO _ CNTTES
35
3. Standard Confiqurations
On the basis of existing test facilities of the participating laboratories,
and in relationship with the state-of-art of theoretical methods, nine
standard configurations(*) for establishing the mutual validity of two-dimen-
sional and quasi three-dimensional aeroelastic cascade experiments and
prediction models have been selected. The configurations should approxima-
te idealized flows, wherefore stall effects have been excluded, except
as extensions of unstalled experiments.
In order to guarantee a correct validation of the theoretical models,
the quality of the experimental results must also be verified. If possible,
two rather similar experimental cascade geometries have therefore been
identified as standard configurations for each of the following flow regimes:
o low subsonic (- incompressible)
o subsonic
o transonic
o supersonic
Out of the nine standard configurations, which are summarized in tables
3.0-1, seven are based upon experimental cascade results; the eighth
is directed towards the establishment of validity for prediction models
in the limiting case of flat plates and for comparison of the large number
of existing flat plate theories. The final configuration (ninth) is defined
as to investigate blade thickness effects upon the aeroelastic behaviour
of the cascade, and upon the theoretical results, especially at high subsonic
flow velocities.
Each of the standard configurations selected allow for a systematic varia-
tion of one or several aerodynamic and/or aeroelastic parameters. How-
ever, a too large number of aeroelastic cases in each standard configura-
tion would limit the usefulness in this report in providing comparisons
for experimentalists and analysts working independently of each other.
For this reason, a restricted number of aeroelastic configurations for
each test case, based upon available experimental data, has been chosen
(*) Throughout this report, "standard configuration" will designate a
cascade geometry and "aeroelastic case" or "aeroelastic test case" will
indicate the different time dependant (and, in some cases, time averaged)
conditions within a standard configuration.
'~i
I
- - - -------
I x x x
>' Y) X( X
____- x I <xI
___ I X x
--- -- x - . x x
X x x< x
- n _ _ x _ _
X X
___ x x __
________I ______ _____ ____MM ____
57
0
"o - 0. -......
,4.-. . --
,4 0.. .4 4. 7.4 0 4). 0. 07 - . . . . ..
O o 0. O C. C * CO 00 C .. . - C- . o C o C .
0o U, o U U U U U C UrU 4. 4- -
0 0 _. -. C-I
ii(i
\'F: Ft' ' U[+' if I((l ltd l .'t; 11:51 i ' l ''0 !t '3 V t ( ' itt] F \t'l F ! F ( :.' '
I) tt1 ! ,f :
I'Ii ii FJ'; ' JI ' ' i. i i, '' " '' ' 'jtJ t ' '''''V . ' ' ' ' 1I 0 1 V. I
C, I ;t I I :' F ': I FiF
i , F Iii, ' ' ii I l t . " i t I i F I it (t I t I if s It
I L F 1i ' 1~ F3' II''i F' fi Fw t I t t t t/'U 3 'Fl f fl it' .3 i tS 'lt I it I w f I tt It . I i I
f t7 t ntt F I , '> ' r i t' ' ! ', t . t ' ' , i t It I t 'II 1,
Iit' : l I FIt f it I 11 3) (f ( 3(Y 111(3
lit0 13 I I l C II c i 3 f I F i ti t 3 i( It fro F( o3(
Il + it t + w ,or i , + I o .I t , h :. 1 1 I f' I r, f' t1 , 1 ,I I'
lIl i'I f 1 , i] [;O ll, t):tl Al I{Jl ' :; ' , ( C:i ! t ( l'+ ; l~ I , , lf t Lji, t . J, F!)O -
tlr if{ Iiil dt r tl I' I P 'I It O"f f !f F,
(-'(;[] !' ; l }(][ ++ ('( [IL £'I' I ] \'. t t ['f~ l]: l } :[ [+(: l'. ' l~ l' Jiql ' I t (> t~ J 5; ".. { i[ [1[
,,viii,~ ~~~~ ~~~ ~ r1 LI{ I, r, Ifi+ Ii(.' ,.il IP t ,, , h ,j, . I ,' i~ t ,; ]t [i
5.1 f irst Standard Confiquration
This configuration is compiled from two-dimensional cascade experiments
in the low subsonic flow region. It is therefore mainly directed towards
the validation of incompressible predictions.
The experiments have been performed, in air, in the linear low subsonic
oscillating cascade wind tunnel at the United Technologies Research Center
andi are included in the present work by courtesy of F .0. Carta.
The cascade configuration consists of eleven vibrating NACA 65-series
blades, each having a chord c 0.1524 m and a span of 01.254 m, with a
10 degree circular arc camber arid a thickness-to-chord ratio of 0.06.
The gap-to-chord ratio is 0.750 and the stagger angle for the experiments
here presented is 351 .
The cascade geometry and profile coordinates are given in Figure and
lable 3.1-1.
The airfoils oscillates in pitching mode around a pivot axis at (0.5, 0.0115).
Experiments have been performed with oscillation frequencies between
6 and 26 Hz and with two pitching amplitudes (0.50 and 20). Both the
time averaged and time dependant instrumentation on this cascade is
very complete, and a large number of well documented data have been
obtained during the tests. The instrumentation allows for determination
of both local and global unsteady forces on the blades (i.e. several high
response pressure transducers arid integration of these signals for global
effects), and th'- "esults are presented in several ways.
F r o m these tests, 15 aeroelastic cases have been retained as recomrnmenda-
lions for off-design calculations. The cases are contained in Table 3.1-2,
together with the proposal for representation of the results. They corres-
pond to two different mean settings of the cascade (see Table 3.1-2),
for each of which the steady blade surface pressure distribution is given
in F igures 5.)-2 and Table 3.1-3.
According to the recommended representation, the test data concerning
the, unsteady blade surface pressures as well as the mornent coefficient
i rnd 'rd,,r VmiW dtintpl[ 1 shall he gliffri ii dependanice of the redonce d
tl''(I I II(-, ;Ind l' I (' r h I; angeIf . Anii e(xaTple of t he rep fe wler Iti if I
ii fh, ;t ;arndiid r i/ed i, )oirt iiiij format to hi used II N, l ne rj) 1 it l it) I
of I h ' ' ifi,'1w 'r la;11 ;tll th 'oret il-;)1 da t a' o t t thfile depoor ;it r ' ;ill
ti lti ha-a di' r' ;htow I ci igores I. ;rid I abli' 1. -,.
u C,
0 . + . . 0 . " 1
y_ _ 35. -0 --
f i l l !
c '0 15 1 5 0 7
c 01%' IC T= 0.75(
cho2.d
'4
c 15.24 cm (0 in.)
SUCTION SURFICE PRIESSURE SURFACE
x Y x Y
0.0008 0.0020 0.0012 -0.0019
0.0046 0.0053 0.0054 -0.0042
0.0070 0.0064 0.0080 -0.0050
0.0120 0.0083 0.0130 -0.0061
0.0244 0.0116 0.0256 -0.0077
0.0494 0.0164 0.0507 -0.0098
0.0743 0.0204 0.0757 -0.0115
0.0993 0.0237 0.1007 -0.0129
0.1494 0.0290 0.1506 -0.0150
0.1994 0.0331 0.2006 -0.0165
0.2495 0.0364 0 .2505 -0.0177
0.2996 0.0387 0.3004 -0.0185
0.3998 0.0411 0.4002 -0.0188
0.5000 0.0406 0.5000 -0.0176
0.6002 0.0370 0.5998 -0.0146
0.7003 0.0306 0.6997 -0.0104
0.8003 0.0223 0.7997 -0.0069
0.8503 0.0176 0.8497 -0.0053
0.9003 0.0127 0.8997 -0.0040
0.9502 0.0078 0.9497 -0.00320.9975 0.0030 0.99,3 -0.0025
RADIUS CENTOR ODORDINATES
J' L.E. RADIUS/c = 0.0024 X = 0.0024, Y = 0.0002
T.F. RAI)IUS/c = 0.0028 X = 0.9972, Y = 0.0003
l tble 5.1-1 1 ir,;t 'ir;m rd.r[ C {{}rnfi(j-rat un: I)lm nsionless Airfoil ('oor{ir ales
-u - -. -r
XI -),).i~uV" - .7.
O )Sr.:)
.J~w 'A
I 2l )!I m lf Ii V . 'I
P2 1
REROELR5TIC1TY IN TURBOMRCH]NE-CRSCROES. jSTANOARO CONFi:2JFRATIDN NUMBER I
P2
hx
h
k
XX x xd
0. 5
FIG. 3.1-2A: FIRST STANDARD CONFIGURATION.
TIME AVERAGED BLADE SURFACE PRESSURE i,COEFFICIENT FOR INCIOENCE 2. DEGREES.
//
, C
/ T ;
*,' ..
!FL. L T
- / Yu.
• " ,_ _ 2... .. .. ... .. ..".........
//
M
h :x
XX t
O. .5 1.X
F;G 3. I-2B: FIRST STPNDRRD CoNFIGURPTUIc.
TIME AVERRGED BLi cES!3 E. ,-- PES SRE
COEFFICIENT FOR INCIDENCE . DEGREES,
Aeroelasticity in Turbomachine-CascadesFirst Standard ConfigurationTime Averaged Blade Surface Pressure Distributions
l-) 0.18 0.17
0) 2 6
p2/PtI ( 0.9818 0.9852
(o) 28 17.5
Upper Lower Upper Lowersurface surface surface surface
x Cp Cp Cp Cpp p p p
.012 -.2341 .2618 -.7874 .6278
.062 -.2587 .0904 -.3910 .3139
.148 -.1992 .0441 -.2390 .2148
.261 -.1561 .0503 -.1465 .2015
.392 -.1078 .0688 -.0485 .2115
.530 -.0565 .0955 .0385 .2269
.661 -.0S8S .1345 .0782 .2599
.774 .0236 .1817 .1531 .2896
.860 .0739 .1961 .2037 .3128
.910 .0934 .2094 .2247 .3106
la I)I( 5.1 -5 1 11- ;t 0) ;1 1(h ~f (d I f q)) f I t f~lr: 1 1(m ' ,\ (,[.a (jc d M a d l~ ; ( ' m l fa ('f
i tm d
( ( :~ t tS Na~ .0
(1 1 -- 0
L c I" i) 'n" ',) 11 c= F, u = o . i c [ c 1 t,
S ) (s0 ()
' 2 i r 2 :p ) ' F p
'.l ...... . 1: ____ o: '-
b] Loc: T. o V l . dn iJ ~ Sturf <cc Peossure t~oefectnit (12 I c
b ___ 1KI __ __ I_ _
IL
1{ f______ , i
'i _ _- _ _ _
_!t I_ _
__________-___i_;i <,, ,': '< t i ;,,,I ___________'I I. l ',.f t i(i _________
IIl l' 'fi:,:fl :c<l ,Ul l I'!,! I1 :._ __ _ _ __-,_ ___ _ ___ __ _
_____ B I__
_ "_ _"_-_ _ _ _
y
2 xa
x 1 : 4
I 1:
AEROELRSTICITT IN TURBOMRCHINE-CRSCROES. 1 ,STANOARD CONFIGURnTION NUMBER I J
40.
P2h
x
hy
a:
p Ca :
k
5 :
a:
d
+360 -360
STABLE
+180 -180
UNSTABLE0.S~ f{LS ___
STABLE
-180 +180
UNSTABLE
-360 ' - 1 -I--1- +360.0 .5 1.
xFIG. 3.1-3A: FIRST STANDARD CONFIGURATION.
MAGNITUDE AND PHASE LEAD OF UNSTEADY BLADE
SURFACE PRESSURE COEFFICIENT.I": IN PITCH M11J .NflIfIt ,H N VAI ID IJP TflI[H PM ['1 I LI ,ix I'll\.~
m /
h M
-10..
0..I I
4 6 313 : FIS5T RDC0N URAT1MnGN TUD nio PH SE fi-Ll F U11c-T[-*AD
540.EPHSSR Dl:E.-NI-ECIF E
f i T(,
X :
Z0 2
x l :
REROELRSTICITr IN TURBaMRCHINE-CRSCADES. I i.STANDARD CONFIGURATION NUMBER I I
P2
hx
hY
L
k
- __8 .:
a.
+360
STABLE
+180
0. UNSTABLE
o..L
STABLE
-180
.1 UNSTABLE
-360 - ' I-180 0 180
FIG. 3.1-3C: FIRST STANDARD CONFIGURATION.
AERODTNRMIC LIFT COEFFICIENT AND PHASE LEADIN DEPENOANCE OF INTERBLADE PHASE ANGLE.
V P. / / C
i / / / " '"
/
r7 ,
k k
.. I
0F.L
-10INS A* c
-450 0 4LI G :, R___1_
A STFiLE
-180 .. . ... . . .. .
__ I UNSTRUBLE
I! I I
-. JVU -- - II. .-- Jr-- i-, - -- T" ,
- L 5 0 15
F I C ., 3 . 1 - 3 : F I E K T S 5Lr ,f lFI[ : O '.] ! r ] F__ , IR ? ! Z_ , ., ,
f E C 9ll T ~ i 1 q ' C L I F T fC , _F F j E E ND Fr, P H R $S E r aFI
I .4 fFI F '~f" N C F O F r '. , U E F- ..I ~
y )1
xx
m P2
REROELRSTICITI IN TURBOMACH[NE-CR CROES. 1STANDRRD CONFIGURRTION NUMBER I _
P2
hx
hy
k
. a
I I I I :
+360 -
STABLE
+180
UNSTABLE
M 0.
STABLE
-180 =
UNSTABLE
-360 -
-180 0 180
FIG. 3.1-3E: FIRST STANDARD CONFIGURATION.AERODYNAMIC MOMENT COEFFICIENT AND PHASE LEAD
IN DEPENOANCE OF INTERBLADE PHASE ANGLE.
7 c
xx
m 2P 2
xx
h
mx
k
cr
d
UNSTRE F
UST RBL E
0..51k
3V 2 -F: F R 5T 5 T A!-4'DJIMD CFGIJRRTI ON.H 1100'rNO~MIC HOMENT COE~FFICIENT flND PHR BE LEROTM tJ[P[NEDPNCIE OF F73fjlUCFO FIF-OK N CY
c
7 7:
I
AEROELRST[CITT IN TURBOMRCHINE-CPSCABES.STRNOPRO CONFIGURATION NUMBER 1
P 2 :
-1".
hxh
(X)
-5 k
C:
w 0.
C • USTABLE
-180 0 180
FIG. 3.1-3G: FIRST STANDARD CONFIGURATION.
AERODYNAMIC WORK AND DAMPING COEFFICIENTSIN DEPENDANCE OF INTERBLADE PHASE ANGLE
U
/' /
/ / ,
i3 ,/L~ / '- : 3 '
f / " / 2
+ .
I T C
I... . . ... . . . .... .I F:.TS
... .... . . . . . " N
I _ _
"° ... ... . .. . ...... . . .. .. .. . . .
" - 1I- - - -. .--.- .- !*
. .. . . .4 . ... . .... .. ...
0. 5 1.
~Ic
\ i .1 H F 2 I IfT 11Thil I I . .
3.2 Second Standard Configuration
This incompressible two-dimensional cascade configuration has been mea-
sured in a water cascade tunnel at the University of Tokyo. The results
have been submitted by courtesy of H. Tanaka.
The cascade consists of eleven vibrating and six stationary double circular
arc profiles. Lach of the blades have a chord of c 0.0)%) m and a span
of 0.100 m, with a camber angle of 16' and a gap-to-chord ratio of 1.00.
The water velocity during the tests was V 1=2 m/s, with the R~eynolds
urnber situated at Pe 1.2 . 10 The eleven vibrating blades oscillate
in pitch, with an amplitude of 0.06 rad (3.4' ) and a frequenc\ between
1.i and 1 5Hz. Thus, the reduced frequency lies in the domain 0.1 tol.0.
The cascade geometry is given in Figure 3.2-1 and the profile (coordinates
in Table 5.2-1.
Lxperiments nave been performed with incidence ranging from attached
to partly separated and fully separated flow. Further, the stagger angle
as well as the interblade phase angle and pivot axis have been varied
systematically.
Tne experimental data indicates the unsteady lift and moment coefficients
(arnplitudes together with the corresponding phase lead angles). These
coefficients are computed from strain gage measurements; no time depen-
dant pressures are measured on the blade surfaces.
From the experiments, 22 aeroelastic cases are selected for "prediction".
These aeroelastic test cases are summarized in Table 3.2-2, toqether
with the proposal for representation of the results.
The 22 aeroelastic cases correspond to 5 cascade geometiles see Table
5.2-2). The recommended representation of the results of the second
standard configuration includes therefore trends of lift and momrent (oeffi-
ci onts for aeroelastic pararmeters, such as interhlatl, pha;v ang(l, anid
reduced frequency. bul also for cascade pararm't'!; Ih' w,
and1 stagqer angle.
The tirne-averaqed ba de irifi, e ;t di l r i it i l nil' w;e i. i n ' f lrw , 1 t l irl(
tiew experimeits.
It i l re(oni n wrr h d t i lf ith , r ,- Jl , t i 11 f I ) I I I ''. ' I
i- an I IIlf Z I
d /
t];it C:.<--0 0'"g'l !'h i
//it 1\/
/i
2 / LC ' J_0H-5 l "i;. e
S . S 2------.
5y/l I Mi
/ : ) iil .O
c/0 ____ __'__
- c Ti-l d -11 O. O 2)
! illi'l J. -!(;' ;~i h or li <fiL ( 16ii 1trl!ll V 6. Q,,, Th.2, ,
1)7
)ouble (ircular Arc Bladec- 0.150 m (1.968 in.)
Suction surface Pressure surface(upper surface) (lower surface)
\ ( iy / % ) 0 "0%
0 0 0
5 1.644 -0.404
10 2.657 -0.127
15 3.509 0.115
20 4.262 0.326
25 4.897 0.505
30 5.416 0.650
35 5.818 0.764
40 6.105 0.845
45 6.272 0.893
50 6.334 0.910
55 6.272 0.893
60 6.105 0.845
65 5.818 0.764
70 5.416 0.650
75 4.897 0.505
80 4.262 0.326
85 3.509 0.115
90 2.637 -0.127
95 1.644 -0.404
100 0 0
L.L. and T.E. R ADIUS RADIUS CENT[ R COORDINATES
L.JA. RADIUS/c 0.666 (%) x 0.666 (0if), 0 0 (0)
[a e .R I ( i/t 0. 6( 6 0A.99 5 % 1oin o
Table 5.2-1 !wcornd 'Aamliard (C ai tura~ tio: Dimnsioiiloss Airtoil C Wordi-
) I
__ ~ 441 2
I I
ii I I
'1 ~ 1' I
.....-..........I.................- I I
I
Necroc last ic itN in Turbomachline-Cascakcs.
;ci t aridard Configuration.
Aeroelastic test' case No:.
0 .0V 1=2 rn/s. y __= . 1
-(-2)= (-l)= -(O) = -(+1)= -(+2) = ___ (a
0(-2)= * 1(-1>= 0 0)% 0(+1)= (+2) = __ 0 (0)
a) Global Aeroelastic Coefficients
b) Local Time Dependant Blade Surface Pressure Coefficients
p p p p PA
_______________________i iy j~a f o~ i Ta______________ f____________ __________ __________
_ _ _ _w _ _ _ _' _ _IMf~~ _ _[0 h ; I( t (w
Ic
/
I /6 . / / r ,
Si
1.
Y
+18:
UNSTABLE
0. ---- -- -- -_-___
m/
I STAlBLE
-150
-180 0 180
F 16. 3.2- r'; : S [C 0N' 0 -rfn o P.,, Ui ctF JGu ii n io :nFR6D~fYNflNIC IOFC I CEFIF IFNT FINO FHqSE LEAD
N 0p[IND il C GF f F; ' )E F..GLE
C
x
P2 2________x__ xm
m 77 2
x x I
AEROELAST]CITY IN TURBOMACHINE-CASCADE7. ISTANDARD CONFIGURATION NUMBER 2I
hx
h :Y
c 2.- (J)H :
k
0 . I , , 'd :
+360
STABLE
+1801UNSTABLE
UNSTABLE
" 1 USTABLE
. UNSTABLE
-360 - - -O.0. 2.
k
FIG. 3.2-2B: SECOND STANDARD CONFIGURATION:RERODTNAMIC MOMENT COEFFICIENT AND PHASE LEAD
IN OEPENDRNCE OF REDUCED FREQUENCY.
l II
/
Y /c
-L // // ,.:.
/ /.
X/
S " 2 . -- --- -
CM 2.
0.*
, I ,.. ___. ...__ . . . .....
I £ A /oa
-- - STAlBLE
-- 180NSTABLE
36 t /_____
-I-. . 0
F I. 3 2-C:SFjCC1N S)TPUJD CVCf0jr' t ;MJrf- I C fOiE~i E11V H I T r;:.1 PIP.SE LERO
Di c P~ r .N D I u P N C E E t :L E
/ c
7 Ex 7 ,
x m IM M1
AEROELASTICITY IN TURBOMCHINE-CRSCROES. 1..STANDARO CONFIGURATION NUMBER ! 2
P2
hxhy
c
M 2. :a
k
+360
STABLE
+ 180 UNSTABL
UNSTABLEO0.
M. STABLE
-180-- _ _ _
UNSTABLE
-360 - ---10. 0. 10.
i
FIG. 3.2-2D: SECOND STANDARD CONFIGURATION:RERODTNAMIC MOMENT COEFFICIENT AND PHRSE LEADIN DEPENDANCE OF INCIDENCE ANGLE.
/P
2
F~ 14 .
,k
5 T_
STBLK0.
USTRBLE_13
I U_[I_1__t
7j( Y fl : F ' CC[iF f F I JE IT _E H2A flJ> iF9 [I P;.' 9.- F GD F L.
/ c
7x
01 OJ ~ 2 aO
REROELAST[CITT IN TURBOMACHINE-CASCROES. 1 1.:
STANDARO CONFIGURATION NUMBER 2 jP 2
8.
h
h
cF 4.)
k
82:
0. - -d
+360
STABLE
+180
UNSTABLE
0F 0. - _ _:
STABLE
-180
UNSTABLE
-360 - -
0. 1. 2.k
FIG. 3.2-2F: SECOND STANDARD CONFIGURATION:AERODYNAMIC FORCE COEFFICIENT AND PHASE LEADIN DEPENOANCE OF REDUCED FREQUENCY.
/ i..
- •... . . . . . . . . . ..... .o ,
,I .. .-.
II
7:h
.L
".....~... _ _6
I d
IF.: . >T
f l ... .... . .. ..(
V ,
/ ,C
//XX
YY
x ml
1, 7 -1,y SCoc
m2
8.
h
c .
F 4 W
k
0. - - - - d
+360 "
STABLE
+180.8 -UNSTABLE
0. O __ _--_- _ _
FSTABLE
-180 -
UNSTABLE
-360 - --60. 0. 60.
FIG. 3.2-2H: SECOND STANDARD CONFIGURATION:
AERODTNAMIC FORCE COEFFICIENT AND PHASE LEAD
IN DEPENDRNCE OF STAGGER ANGLE.
Moi-
xx
hY
k
0*
dC _ UNSTRBLE
sl RFOLE
-180 0 180
F IG. 3. 2- t'I: SEMOKJ STPNL1PRO CON I GURPT ION:AERODYNnRMIC HORK DRU0f~1ING COEFFICIENTSIN LJFPENODiNCE OF INTERBLRAjE PHR,3E INGLE .
y c
x
x l :
AEfROELRSTICITT IN rURBOMACHINE-CASCROES. ISTANDARD CONFIGURATION NUMBER :2I
P 2
h
h:T
k :
d :
c 0. U N S T A B L E
W!• STABLE
[ . . 2.
FIG. 3.2-2K: SECOND STANDARD CONFIGURATION
L AERODYNAMIC WORK AND DAMPING COEFFICIENTS
IN DEPENDANCE OF REDUCED FREQUENCY.
.- .. ... , I I
[ij~
. IP
I I
I f-. 1
I-
I I . jhA
. 2 .
I I II I
* j t
I U
I.: cI* j..- I ..- *1 t ~3II;:j:A I
-I.. I p
T
I.
TI I
-. ~ I * p * pI ' I
Q
I~i.~v C.
Cy 71
RERBELRSTICITT IN TURBMRLHINE-CRSCROEz. 2.:STRNOPRO CONFIGUBRTION NUMBER 2
xx
P2
Pi ~Y
k
d :
P,
W IN I I -H- +- E n USTABLE I
-60. 0. 60.
IFIG. 3.2-2M: SECOND STANDARD CONFIGURATOON:N U 2
AERODTNAMIC WORK AND DAMPING COEFFICIENTS
~IN DEPENDANCE OF STAGGER ANGLE.
------ I I2
.i.
I!
it / V
I.
I F.tFF I,.
1. (r .F~[;
F I Ft'FIiFI'ii..!
V F 'lW1 1
:v I
V. FYI ii ';1
V . 5 p, 5 it F: F I i.i~n~> . H
F ~~ F 'F ,', '<F'' Fr'!.' 'FF2 F
F. ''Fl F'!'
'I F
IF i '''I F ' : F '.~ F''
F ' F'' F ~,. '' I F',,'FF F F
[F .1.
73
configuration allows detailed comparison of the local time dependant
blade surface pressures and trends of global effects (moment and aerody-
namic damping coefficients) in dependance of expansion ratio (P 2/Pt),
blade vibration frequency and interblade phase angle (see Table 3.3-4
and Figure 5.3-3).
it
- S
/
-' I ~---- ---
'1 - - - ~---- ------- - -
C C ~7 r. y C>
C ~:: *'j ) ((1 1 1, 4
I.
.- ~ '-.' I - -
I
7"
0.072 m
SUJCT ION qWX:ALE PRESqRE S.JRFACE
(Lower surface) (Upper surface)
x Y x ys Ip
0.0 0.0 0.0 0.0
-0.073 -0.0096 0.0247 +-0.0108
-0.0115 -0.0290 0.0439 +0.0066
-0.0051 -0.0487 0.0718 -0.0073
0.0102 -0.0698 0.0932 -0.0144
0.0296 -0.0918 0.1213 -0.0265
0.04o2 -0.1080 0.1478 -0.0356
0.0668 -0.1240 0.1742 -0.0434
0.0887 -0.1384 0.2014 -0.0502
0.1117 -0.1508 0.2289 -0.0538
0.1358 -0.1610 0.ZS63 -0.0601
0.1606 -0.1693 0.2840 -0.0637
0.184 -0.1749 0.3119 -0.0660
0.2122 -0.1781 0.3395 -0.0674
0.2354 -0.1797 0.3676 -0.0676
0.2584 -0.1800 0.3891 -0.0669
0.2814 -0.1793 0.4113 -0.0662
0.3046 -0.1772 0.4329 -0.0657
0.3274 -0.1745 0.447 -0.0646
0.3432 -0.1719 0.4765 -0.0639
0.3591 -0.1692 0.4982 -0.0623
0.3748 -0.1657 0.5201 -0.0613
0.3904 -0.1621 0.5419 -0.0596
0.4058 -0.1580 0.5633 -0.0579
0.4806 -0.1396 0.5850 -0.0562
0.5552 -0.1208 0.6069 -0.0540
0.6291 -0.1018 0.6285 -.0.0519
0.7038 -0.0829 0.6502 .0.0497
0.7780 -0.0640 0.6721 -0.0470
0.8525 -0.0452 0.6939 .0.0446
0.9270 -0.0264 0.7152 .0.0419
1.0 -0.0075 0.7368 -0.0388
0.7583 -0.0.359
It. 7986 -0.0295
o.8387 -0.0237
0.8792 -0.0170
0.9195 -0.0118
0I.9597 - 0.00t6t
1.0 0.0
|I ab le 1. 5- 1 1 d ,I ;Irl(l;)[ (I I ( m t tl l I(pi) ;ilf ).l. ' \If hl~ l] mI () firJ;ft,,
I ( 'ril l(';Il ( 'r I l ' ti - V ifl f,)I( ) );irl ,,
I -
I ..
1 I
I -. ~.
-. - - . I
- - . , - -~ I ~ ~
I..
M -~ I.. -~ .----- ~.-.. I 1(1~.. -. 1 -.
-I
I. . *. . .
pp
hx
f A,
IL L
Y
- I
I..
K
h
h
2
P {L x : 'K >< i:-... x K-6. I' m dLi
m _ m
~ I I I ~ L
0. V 1.
'I
TII;I ~~':§?;~.'i ~ 7 rr
/ "L
-,-'--7 --.
f2P.,
cJ-
I IL × × ,, x *x
IC - + ' r
-114.i ' I I
0. .51.
i .P i . i *II
I,
- I! ,-.'
I ,-' I~ I- -- I----
K r '-
* II 1~--*-~~ - I
I I
- - .- - - - - - ~ ~-~:'
- - - __ __ -C,.'; --.- '
I,'.!-
Acroe last i city in Turbomach inC-CascadesThird Standard Configuration.
Aeroelastic test case N 0°:
X1 1=P2 /Ptl I NI2= - 0 B1= o a B2 0 k=-(-2)= -(-1)= -(0)= -(+1)= (+2)= 9 (fads)
go 'A 0 0 CLras
(-2) • (-1) = o(0) • (+1) = (+2 = ___ ()
a) Global Aeroelastic Coefficients
____=__ =______ ____ •_7_ _ = 0 (-)
______ _____- Cw-__ (0)
b) Local Time Dependant Blade Surface Pressure Coefficients
SCp(lS I) lS) (0) C (us) (pus) (0) ACp (-) Vp ()
I aiuLe S. 5 5-4. Thi11d Ht ;IrOtIn r(1t a o ari ti i Irt. k atle tot tI-,ett it im oi ot
t he 1 1 i ,t ( '(-o rI 1 d ed \ r'v wtfc t ivI;t 1 ( ; I ,; , ,.
C,
N , - - . I
'N .
I I
h
(K)
:1 2;1~~, I A I F, ci
I I
I I S{r~7.: 7
I .. -300I Ii>0[iAL H
I F IF'
I , ST&;LL~j F
I (' , I (~
At"
I I UI<7>'JAI
- , 1,~,*, - - I~ *:-- -
I' I,x
C
x7 7 :
o PM2
m 1 I
AEROELASTICITY IN TURBOMRCHINE-CASCAOES.STANOARD CONFIGURATION NUMBER : 3
M2
h
h
M
k- 8 :
d
+360
STABLE
+180
UNSTABLE
M 0.
STABLE
-180
UNSTABLE
-360 - - I-180 0 180
FIG. 3.3-3B: THIRD STANDARD CONFIGURATION.AEROOTNAMIC MOMENT COEFFICIENT AND PHASE LEADIN DEPENDANCE OF INTERBLADE PHASE ANGLE.
/ I
/. 7
h' \
c/
" //
/ /
/k
/d
, --~ /
II I.._,
-9 T h
CC..
I iST fB L.E
+180 -I .. . ... .
u o. - ....._
-STPBLE
I UNST P OLE
C
7 ',
xxml xc :
N1 :
m
AER ELRSTICITY [N TURBOMACH[NE-CASCROES. I.:
STRNOARO CONFIGU RTION NUMBER 3
N2
P2hx
h
k
d:
W 0. STABLE
-180 0 180a
FIG. 3.3-3D: THIRD STANDARD CONFIGURATION.
REROOTNRMIC WORK AND DAMPING COEFFICIENTS IN
DEPENDANCE OF INTERBLADE PHASE RNGLE. .1
y
86 'r
P! 7
N1 N2Y,
{m IM1
REPOELA5T1CITY IN TURBOMRCHINE-CPSCROES. 1~TANDARD CONFIGURATION NUMBER !3J
hx
hcc
a)
k
8:•
a:
d
0 . UNSTRBLI
w STRBLE
0.5 1. 1.5M 2
FIG. 3.3-3E: THIRD STANDARD CONFIGURATION.
AERODYNAMIC WORK AND DAMPING COEFFICIENTS INDEPENDANCE OF OUTLET FREON MACH NUMBER.
urbinir ro t or sect. ns are, perfol rried in I few u uJlflari u'adl taluiIt '~at
thIe I W aann I s t e II.IIPOf I echruog o b M. I)igeri.
h IS fourtfh st andard cofig urat Ion i; o f mnt erest rmiuly hecaww fe ut le
relative high blade thickness and camnber, the ighjl Subsonic- flow (Mirdition:i;
and for Its resemblance with the third standard con figuration.
I etailed test results will be ivailable at. the end of 19[35. so that t henreti
cal res;ult s can be validated against the data from this configuration seoul-
aneousk as aglainst other standard configurations.
The cascade con fi gurati0o) consists of twent y vibrating prismatic blades,
each ha\.ing a chord of c 0).0744 mn and a span of t0.04t) m, witht 4110
towMig and a maX imum ticknes--t n-chord ratio of 01.17 7
The st agger angle is 15.4'. with) the gap-I n-chord rat io of the C-ascadle:
0.07 hub)
t0.76 midspan)
0.84 .tip
The hub-tip ratio in the test. facility is 0.8.
The cascade geometry is given in Figure 31.4-1 and the profile coordinates
are tabulated in Table 3.4-1.
Experiments are performed with variable inlet flow angle (MV, i), expansion
ra tio0 (pp M2 ), vibration mode, oscillation freguency and interblade(Pphase angle. All the experiments presently performed have constant span-wise flow condi tions iipst ream. The time dependent instrument at ion ifcl u-
vies pressure rainsduIcers on one blade nidspan) and strain gages.
T he aeroelast ic eases for this Standard con figurat ion are not yet full\
defined. whereforo they will be dist ribut ed together with the corresponding
m1fe a\.eraged bl1ade sur~face' pressure dist ribut ions towards the end of
I90 5.
The recommejfndedj present ation formiat will be Similar to the one used
in~do r ud n1I urot or;six.
cascade leading
edge plane C/C
y 33.35 upper surface
BI lower surface
pressure surface
Nsuction surface0.1 -~. *. ____ ____ ____
0.0 . ... pressure surface . .
-0. 1 -" -__
-0.2 --
0 0.2 0.4 x 0.6 0.8
c = 0.0744 m = 33 350
span = 0.040 m camber = 45
T = 0.67 (hub) thickness 0.170.76 (midspan) chord0.84 (tip) hub/tip = 0.8
Nominal values: MI: 0.31 M2:0.90
a,= 45.90 2 17.60
Figure 3.4-1 F ourth Standard Configuration: Cascade Geometry
C .0744 M
UPPER SURFACE LOIR SURFACE
0.000 0.000 .514 -.053 0.000 0.000 .443 -. 163.003 .010 .524 -.055 .001 -.011 .443 -.160.010 .018 .535 -.055 .003 -.021 .464 -.160.020 .021 .546 -.055 .006 -.031 .464 -.156.031 .022 .556 -.055 .010 -.041 .485 -.154
.042 .022 ,567 -.055 .014 -.051 495 -.151
.052 .021 .578 -.055 .020 -.060 -.149
.063 .020 .588 -.055 .025 -.069 .506 -. 146
.074 .019 .599 -.054 .031 -.078 .526 -. 144
.084 .018 .610 -.054 .038 -.087 .536 -. 141
.095 .016 .620 -.053 .044 -.095 .547 -.139
.105 .014 .631 -.052 .052 -.102 .557 -.136
.116 .012 .642 -.052 .059 -.110 .568 -.134.126 .010 .652 -.051 .067 -.117 .578 -.131
.136 .008 .663 -.050 .076 -.124 .58 -.129
.147 .006 .673 -.049 .084 -.130 .590 -.126
.157 .004 .684 -.048 .093 -.136 .609 -.123
.168 .001 .695 -.047 .102 -.142 .619 -.121
.178 -.001 .705 -.046 .111 -.147 .629 -.11
.188 -.003 .716 -.044 .120 -.153 .640 -.115
.199 -.006 .726 -.043 .130 -.157 .650 -.113
.209 -.008 .737 -.042 .139 -.162 .660 -.110
.220 -.011 .74? -.040 .149 -.166 .671 -.107
.230 -.013 .758 -.039 .159 -.170 .681 -.104
.240 -.015 .768 -.037 .169 -. 173 .691 -.101
.251 -.019 .779 -.036 .179 -. 176 .701 -.099
.261 -.020 .790 -.034 .190 -. 179 .712 -.096
.271 -.022 .800 -.032 .200 -. 181 .722 -.093
.282 -.025 .811 -.030 .211 -. 182 .732 -.090
.292 -.027 .821 -.029 .221 -. 184 .742 -.087
.303 -.029 .832 -.02? .232 -.105 .753 -.084
.313 -.031 .842 -.025 .243 -. 185 .763 -.081.314 -.033 .852 -.023 .253 -.186 .773 -.078
.334 -.035 .863 -.021 .264 -.186 .783 -.075
.345 -.037 .873 -.019 .274 -.186 .794 -.072
.355 -.039 .884 -.017 .285 -.186 .804 -.06
.365 -.041 .894 -.015 .296 -.185 .814 -.066
.376 -.043 .905 -.013 .306 -.184 .824 -.066
.387 -.044 .915 -.010 .317 -.183 .834 -.060
.397 -.046 .926 -.008 .328 -.182 .844 -.057
.408 -.047 .936 -.006 .338 -.181 .855 -.054
.418 -.048 .946 -.004 .349 -.179 .865 -.O50
.429 -.049 .957 -.001 .359 -.178 .875 -.047
.439 -.051 .967 .001 .370 -.176 .885 -.044
.450 -.051 .978 .003 .380 -.175 .895 -.041
.461 -.052 .988 .006 .391 -.173 .905 -.037
.471 -.053 .401 -.171 .926 -.031
.482 -.054 .412 -.169 .936 -.020
.493 -.054 .422 -.167 .946 -.024
.503 -. 055 .433 -.165 .956 -.021
.966 -.017
.976 -.014
.986 -.011
.996 -.007
Ifa lh V, ) I ;m(hil d ( rflyulr'dl I' : I. IIIrisio ol h ;sI \irtoil ( ou di-
11 1| l' t I•i III .' I 1 w|~l ,
5.5 F ifth Standard ['ofi(quration
This two-dimensional subsonic/transonic cascade conficura-tion has been
tested in a ft ctilinear cascade air tLinnel at the Office NI 1t onal d'lt udes
2t de Recherches A6rospaciales ONERA. The configuration arid experi-
mental results are included by courtesy of E. Szechen,,i.
The cascade configuration consists of six fan stage tip sections, each
blade haing a chord of c-0.090 m and a span of MID) m. The maimum
thickness-to-chord ratio is 0.027, with no camber and a gap-to-chord
ratio of 0.95. The present configuration was measured with a stagger
angle of 30.70.
The cascade geometry is gien in Figure 3.5-1 and the profile coordinates
i-i Table 3.5-1.
The two center blades can ,ibrate in pitch about seeral axis, whereafter
the aeroelastic coefficients for different interblade phase anq!es are
cnmputed b'v linearized summation of the unstead\ pressure r ;pnoses
on all six blades.
Experiments have been performed with oscillation frequencies between
75 and 550 Hz, inlet Mach numbers between 0.5 and 1.0 and with iriidernce
angles between attached and fully separatei flow .2' to I')'.
Both the time averaged and time dependant instrumentation on this cas-
cade is very extensive and 3 large number of well documented da; a haye
been obtained during the experiments. The large amount of flush mounted
high response pressure transducers on one blade allows the determination
of resultant time dependant blade forces.
From the results obtainei during these tests, 27 aeroelastic cases are
recommended for off-desiqn calculations. They' are contained in Table
3.5-2, together with a recommendation for representation of the results.
The 27 cases correspond to 11 different settings of the cascade ,see Table
3.5-2.
The steady blade surface pressure distributions of the 11 time-averaged
settings are given as a basis for time-variant calculations by small perturba-
tion prediction models in F iqure 3.5-2 and Table 3.5-3.
Of special interest in this fifth standard configuration is the extensive
,ariation of time-averaqed parameters, such as inlet flow velocity "'v
and incidence (i.
The inlet Mach number is varied from M1 0.5 to M -1.0, and the ranget1
91
of incidence is from fully attached (incidence less thdn 51) up to fully
separated (incidence greater than 10u) flow conditions.
The recommended representation of the results includes detailed compari-
son of unsteady blade surface pressure coefficients as well as aerodynamic
damping arid moment coefficients in dependance of the parameters inci-
dence (i), flow velocity (M 1 ) and reduced freguency (k), as proposed in
Figure 3.5-3 and Table .5-4.
I
- t. .
- ~ -___________.
ascade leadir-.gedge Plane.
C
+y
suction surface (upper surface)
leading -edge
trail ingedge
c O.090 m T = 095span = 0.120 m y 30.7camber =00 thickness
chord- = 0.027
Fi(pire 3.5-1 Fifth Standard Configurat'on: Cascade Geornetr>
9 5
c 0.090 m
Upper surface Lower surface(Suction surface) (Pressure surface)
xy y
0. 0. 0.0.0124 0.0016 -0.00160.0250 0.0018 -0.00180.0500 0.0026 -0.00260.0750 0.0033 -0.00330.1000 0.0041 -0.00410.1500 0.0053 -0.00530.2000 0.0062 -0.00620.2500 0.0079 -0.00790.3000 0.0101 -0.01010.3500 0.0103 -0.01030.4000 0.0111 -0.01110.4500 0.0119 -0.01190.5000 0.0124 -0.01240.5500 0.0128 -0.01280.6000 0.0133 -0.01 530.6500 0.0135 -0.01350.7000 0.0135 -0.01350.7500 0.0128 -0.01280.8000 0.0116 -0.01160.850 0.0098 -0.00980.9000 0.0076 -0.00760.9500 0.0048 -0.00481.00 )0 0. 0.
r;I iIC, II r d I w;tH
l al)lf' 5',- 1 f r ft I iilr~ ( n)rlfi(I 1nnt (H: )ir uir I i tnt ,, /\(1 l "oriliratt ,';
'd Iult !cmillt irI aeterC r h,_ IIM J e RCV C Iot It 10rWit, t r
\ f C LC
t P c1
Ful I e p4
-5 0.1 SAt ce 1 1 4
30 P
125 1 an1 saftn in o
30 (). Ss ()oc 000
Table~ ~ ~ ~~~~~5 5..-1 1 th udr o igm n 2 ~em ne eols
7-A
c
xx
P2
P ~Ya
ROnELASTICITY IN TLJHBOMICHINE-CRSCAOES. jSTflNDARD CONFIGURTION NUJMBER 5
P2
hx
h
cr
~ d
-10. -F- -+---- H
0. .5
FIG. 3.5-2l: FIFTH STRNDPRO CONFIGURlTION4:
TIME RVERPGEO BLRAJE S5URFH(
OIST1 9IBUTION FOR MI-l r-i~
A0D-A141 004 TWO-DIMENSIONAL AND QUASI 1IUEEDIMENSIUMLtEAPERINNIAL STANDAD COSUIO.IUI I COE POLITICHNIOUEFEDERALE DE LAUSANNE IMIIZERLI LAB K..
UNCLASSIFIED T FEANSON E1 At. 30 SEP 03 F/ 204 ML
* .111.lomm""
'Oiiinlllon ME,,a __ /,
-
IlllhI,.o1~ 36 lii.-
II~lI IIN IIII *,
MICROCOPY RESOLUTION TEST CHARTNATIONAL BUREAU OF STANOARDS - 1963 A
.4F
! ; •
96
7 x T7'
xxP2ml/ 4 M 2 x :
Y ,
x m
hX
h :T
+1. - __ __:.
k =
XXXX xx m x~ X' I'__ ____ 8 I
0. U_ d-
0. .5
'-
FIG. 3.5-28: FIFTH STANDARD CONFIGURATION:TIME AVERAGED BLADE SURFACE PRESSUREDISTRIBUTION FOR MI=O.5 AND INCIDENCE=4 DEG.
A
y : 97
x
P2mM 2 X, :
pi
REROELRSTICITY IN TURBOMRCHINE-CRSCROES.STANDARD CONFIGURATION NUMBER 5
M2
h :x
h
. Ca :
k
5 :
X Xxxx d
-0 . - -H
0. .5 1.X
t 2
~ FIG. 3.5-2C: FIFTH STANDARD CONFIGURATION:TIME AVERAGED BLADE SURFACE PRESSURE
SDISTRIBUTION FOR M=0.5 AND INCIDENCE=6 DEG.
C
98
T 19 E 2 xc :
REROELRSTIC[TT IN TUR8IOMRCHINE-CRSCRDES. #5TPNDRR CONFIGUIRTION NUMBER9 2 5
M2
h :x
hy
+1. ' -
k
XXXXXXx x d:
p J
m
0FIG. 3.5-2: FIFTH STANDARD CONFIGURATION:
TIME AVERAGED BLADE SURFACE PRESSURE
DISTRIBUTION FOR M1=0.5 AND INCIDENCE=8 DEG.
c
72 x
x
REROELRSTZCITY IN TURBOMRCHlNE-CRSCROES. :
STRNORRO CONF1GURRTItON NUMBER :5
M2 ,
x
+1. __ __:.
k :
- oc
Nmm--1, I
xx
0. ,5 1.
Xh
1
kk
,0. .5
FIG. 3.5-2E: FIFTH STANDARD CONFIGURATION:
TIME AVERAGED BLADE SURFACE PRESSUREDISTRIBUTION FOR MI=0.5 AND INCIDENCE=lO DEG.
Cy
100 r
xP2
Yx
h
k
M_ _ _ _ _ __ _ _ M:
xxxxxxxxx~xxm
C3 d
L.
0.IN- D r
0. .5 1
FIG. 3.5-2F: FIFTH STANDARD CONFIGURATION:
TIME AVERAGED BLADE SURFACE PRESSUREDISTRIBUTION FOR M1=0.5 AND INCIDENCE=12 DEG.
101
i ;7 ,
xx
REROELRSTICITY IN TURBOMRCHINE-CRSCRDES. 2STANORD CONFIGURATION NUMBER 5
M2
hx
hY
+1. ___ __:a
k
cp 0. m
XX
0. .5 1
tx
!-
FIG. 3.5-2G: FIFTH STANDARD CONFIGURATION:
TIME AVERAGED BLADE SURFACE PRESSUREDISTRIBUTION FOR MI=0.6 AND INCIDENCE=IO DEG.
102 X c ,
102 2XX P2m 2
AEROELASTICITY IN TURBOMACHINE-CASCRDES. p1STANDARD CONFIGURATION NUMBER 5
2
M2
hx
hr
*1. - C :
k8 :
Xxxxxxxxx~mxmm 2'
c m
0. .5 1.xX 4
FIG. 3.5-2H: FIFTH STANDARD CONFIGURATION:TIME AVERAGED BLADE SURFACE PRESSURE
DISTRIBUTION FOR MI=O.7 AND INCIDENCE=1O DEG.
113 __ N
y 103
MI 9 m M2 xcc :IT
77 M
pYc :
P1
REROELASTICITY IN TURBOMRCHINE-CRSCAOES.STANDARD CONFIGURATION NUMBER 5
M2
p2 '
hx
hr
+l. Ca :
kx !" Xxxxxxxx' mm x
In d
0. .5 1.
FIG. 3.5-21: FIFTH STANDARD CONFIGURATION:TIME AVERAGED SLADE SURFACE PRESSUREDISTRIBUTION FOR MI=0.8 AND INCIDENCE=1O DEG.
yC104 2
7 2
_ 19M 2 x = :
X-
PEROELSTICITY IN TURSOMRCHINE-LASCROES. ISTANDARD CONFIGURATION NUMBER 5
M2
hx
h
+1. - ____C.
k
8.
. - D, o I
FIO..-t: IT .TNDR COFGRAIN
TIME AVERAGED BLADE SURFACE PRESSURE
DISTRIBUTION FOR MI=0.9 AND INCIDENCE=10 DEG.
7 x~
ERERCELRSTICITY IN TURBOMCHINE-CRSCROES.STNOPI9O CONFIGUR TI N NUMBER 5 M
P2hx
hr
k
x a
Jo0.
FIG. 3.5-2L: FIFTH STANDARD CONFIGURATION:TIME AVERAGED BLADE SURFACE PRESSURE ~IDISTRIBUTION FOR M1=1.0 AND INCIDENCE=10 DEG.
106
01 . 9 0 000C r-X~~~ a., 7* ~ ~ C Ct.n te O-0NC -rfl,-
C. In W) 0n I 7,70
C CDC0C 0 0CC0QCCCCC C C
C D -
-C ... ....... . . . . .CCOCOO 00000 CC CC C CC C
r- to C1 00000 0000 00 0 OOC1 O ' 00 C CCC w ,Cf C .7 .0 0 0 0 CD 0 C DI
.0 Z-C- C C )C- ~ ~ ~ ~ ~ " m Ln m w n-~.r..7 fr.~.
InC C-C; QC .0 .7 C)C-' C; 0 C, C
C7 C O 0 C 0 C CCCC 0C C C C C
~~~~~C w C, C .4IW~~.7000 4 J I .
IC~~~~ ~~ .7 . ..- . .C. .4 ... '.7 qC7.0a
-~~ ~ -0 a, 'n 100. CIJo7f~f~--.- C0 C7,--r-r-,-.
0 C CDCC CCC0 CD m Q C
r- .7'I-..70I---,.D.
-~I - N,)I 0C C C 4 'otD - - - - - - - -.
CD C C:: a-
~ .CCC CCCC C C C, C 0 0 C C CCCC
0.07 1 I I.0 09 I'9 071 1.1 .- 19 .7 .. 19 .
0 C CD0 00 C C D 0 0 CD 7. CD C> C 1C 0 C C C
C, V, w C1 C, CD w~C0 0 OC O O0 CO13 >.. in Cn"0 CC).** .~ . -C)
- C
'n -tr LnCIQ- 1 I 0 0 m 10 1
C C; C C C; C C C= CD C C CC D C 0 CCC ( CD C, CD1 mI C
ft C 00 D c? 0 0 0 C 4m
0 a00 0 00 0 C
C~~ ~~~ - - .7~f. 9t/0 ... 1) 9.7 140 9c;1 7C; 47 104 ;.- C). IC 0 C 0Im C -C; I
C , 'o0 .D S 7I~ttt.77f14. Z.- M w ( 0, 0 F
.147.C) .. 7 .IOC. 0.7QQ7 z Cm0 0 CD ID CCDCQ J
- -- C~ -'. - -7C a C) C, 8 CD m
"I~~ ~ ~ N IO a m I0 In In %0' v- 0I n "1- O 4
0M 0 m0 oC -0wWC 0C cc w-C tC-.7 C7o7 . CtO 10Im *0.7N 0 m10cIn-~ ~~ ~~~~~~ - .- . .~ttrC 71.tt. .7 .7700000411. .
~0. 0 0 0 0 ; 0 0= 0 0n 0Q 0 0) 0 m 0D 0 0D 00
* U ) 104 In w -W0 0i~ . . .In Q LMttf 0 r- 744.11 m. W)07 Q.0to "no IS.00 )S. 'S 4.00 tn 10 In C 'n
Table 3.5-3 (continuation on next page)
1017
Aeroe!a ,c xty in Turbanachine-Cascades
Fifth Standard Configuration
Time Averaged Blade Surface Pressure Distributions
M j 0.80 0.91 0.90 1.00
1 (o) 10.0 10.0 10.0
Ptl( ill) 140'350 200'110 140'070 199'950 199'900
p (.,/n) 92'040 131'740 82'150 118'250 105760
x P/Ptl Cp P/Ptl Cp P/Ptl Cp P/Ptl Cp P/Ptl Cp
UpperSurface
0.0333 0.4837 -0.5000 0.4911 -0.4895 0.2041 -0.9248 0.3793 -0.5191 0.1979 -0.70320.1000 0.4944 -0.4689 0.4991 -0.4661 0.2719 -0.7608 0.4102 -0.4435 0.239 -0.61400.1667 0.5334 -0.3556 0.5351 -0.3607 0.4750 -0.2696 0.4616 -0.3177 0.2638 -0.56330.2333 0.5725 -0.2420 0.5618 -0.2826 0.5715 -0.0363 0.4882 -0.2526 0.4129 -0.24670.3000 0.6118 -0.1278 0.5920 -0.1942 0.6230 0.0883 0.5210 -0.1723 0.4690 -0.12750.3667 0.6442 -0.0337 0.6208 -0.1099 0.6383 0.1253 0.5532 -0.0935 0.5147 -0.03050.4333 0.6699 0.0410 0.6464 -0.0349 0.6443 0.1398 0.5817 -0.0237 0.5671 0.08080.5000 0.6886 0.0953 0.6667 0.0245 0.6500 0.1536 0.6052 0.0338 0.5979 0.14620.5667 0.7042 0.1406 0.6836 0.0739 0.6565 0.1693 0.6251 0.0825 0.6109 0.17380.6333 0.7163 0.1758 0.6976 0.1149 0.6653 0.1906 0.6415 0.1226 0.6176 0.18800.7000 0.7269 0.2066 0.7091 0.1486 0.6745 0.2128 0.6546 0.1547 0.6216 0.19650.7667 0.7356 0.2319 0.7189 0.1773 0.6820 0.2310 0.6652 0.1806 0.6296 0.21350.8333 0.7434 0.2545 0.7272 0.2016 0.6903 0.251 0.6747 0.2039 0.6339 0.22260.9000 0.7487 0.2699 0.7298 0.2092 0.6998 0.2740 0 6823 0.2225 0.6418 0.23940.9667 0.7078 0.1511 0.6106 -0.1397 0.6982 0.2701 0.6893 0.2396 0.6556 0.2687
LowerSurface
0.0333 0.8398 0.5346 0.8337 0.S133 0.7983 0.S122 0.8014 0.5140 0.7508 0.47080.1000 0.8010 0.4219 0.8002 0.4152 0.7481 0.3908 0.7585 0.4090 0.7024 0.36810.1667 0.7772 0.3527 0.7751 0.3417 0.7201 0.3231 0.7285 0.3355 0.6701 0.29950.2333 0.7665 0.3216 0.7640 0.3093 0.7087 0.2955 0.7150 0.3025 0.6573 0.27230.3000 0.7593 0.3007 0.7568 0.2882 0.7021 0.2796 0.7074 0.2839 0.6506 0.25810.3667 0.7549 0.2879 0.7525 0.2756 0.6963 0.2656 0.7021 0.2709 0.6449 0.24600.4333 0.7500 0.2737 0.7487 0.2645 0.6919 0.2549 0.6977 0.2602 0.6406 0.23680.5000 0.7480 0.2679 0.7469 0.2592 0.6904 0.2513 0.6964 0.2570 0.6394 0.23430.5667 0.7480 0.2679 0.7469 0.2592 0.6907 0.2520 0.7003 0.2665 0.6406 0.23680.6333 0.7475 0.2664 0.7461 0.2569 0.6904 0.2513 0.7003 0.2665 0.6411 0.23790.7000 0.7455 0.2606 0.7439 0.2504 0.6881 0.2457 0.6963 0.2567 0.6389 0.23320.7667 0.7442 0.2569 0.7412 0.2425 0.6872 0.2435 0.6926 0.2477 0.6363 0.22770.8333 0.7440 0.2563 0.7394 0.2373 0.6879 0.2452 0.6897 0.2406 0.6355 0.22600.9000 0.7459 0.2618 0.7382 0.2337 0.6926 0.2566 0.6856 0.2305 0.636-4 0.22790.9667 0.7514 0.2778 0.7394 0.2337 0.7031 0.2820 0.6861 0.2318 0.6434 0.2428
lable $.5- fifth Standard Configuration: Time Averaged Blade Surface
Pressure O)istributions for the 27 Recommended Aeroelastic Cases
10]8
Aeroelasticity in Turbomachine-Cascades.
Fifth Standard Configuration.
Aeroelastic test case N o
= O • p2/Ptl= e .* M 21=- 0 02 . 0 k-
-(-2) = (-1 )= - (0). - (+1). - (+2) .__L_ -0 = a 0 aLC = 0 a = * (rads)
0(-2)= 0 (-1)= 00 a(0)= 0(+1). 9 (+2). _ (o)
a) Global Aeroelastic Coefficients
cI= • =. @ CW= *..()
, ., = o 0 L= 0 (o)
b) Local Time Dependant Blade Surface Pressure Coefficients
X ( - c ( Sp )P(I s ) ( ) C ( u s ) ( _ ( u s ) ( o 0 ' - p ( ) A
Table 3.5-4 1 ifth Standard configuration: Table for Presentation of
the 27 Peconm-fnded Aeroelastic 'ases
109
7 P2
m= Mt :7a:
REROELRST[CITY IN TURBOMRCHINE-CRSCROES. I 2STANDARD CONFIGURATION NUMBER : 5I
20. M2P2
hx
h
cp 10.
k
0.0 d : i
+360 -360
P 0. STABLE
+180 -180. UNSTABLEM
(us)~ O. LS)l
a. P
•STABLE x
-1BO +180
UNSTABLE
-360 '+--' - ' 360
.0 .5 1.x
FIG. 3.5-3R: FIFTH STANDARD CONFIGURATION:MAGNITUDE AND PHASE LEAD OF BLADE SURFACEPRESSURE COEFFICIENT.(w:JN PITCH MODE.NOTRTION VALID UPSTREAM OF PITCH AXIS)
110
P2IY,
x
AEROELPSTICITY IN TURBOMRCHINE-CRSCnOES.STANDARD CONFIGURATION NUMBER 5
20.P2
h-X
hg
Ac P 10.Wp a
k
.
*360 -
STABLE
+180
UNSTABLE
0.
N
STABLE
UNSTABLE
-360 -
0. .5 1.x
FIG. 3.5-3B: FIFTH STANDARD CONFIGURATION:MAGNITUDE AND PHASE LEAD OF BLADE SURFACEPRESSURE DIFFERENCE COEFFICIENT.Iw:IN PITCH MODE.NOTRTICN VALID UPSTREAM OF PITCH RXIS) L
y i
Ix
M1 2J M2 xo :,!~~ P2P2 I
Y,:
REROELFSTICITY IN TURBOMRCHINE-CRSCRDES. I :STRNDARD CONFIGURATION NUMBER 5
2.0
P2
hx
hT
c
--CM 1 .0 C',
k___5 :
or
STABLE
+180 UNSTABLE
Mi
STABLE
ii -180
UNSTABLE
-360 - -L - -i--0. 0.5 1.
k
FIG. 3.5-3C: FIFTH STANDARD CONFIGURATION:AEROOTNAMIC MOMENT COEFFICIENT AND PHASE LEADIN DEPENDANCE OF REDUCED FREOUENCY.
C r
112
xxT / P2T,
l [ P2 x :2J 2 Ya:
Pt7
AEROELASTICITT IN TURBOMACHINE-CRSCROES. jSTANOPRO CONFIGURRTION NUMBER 5
2.P2
h
xh
:S 1
M " ):
k
D. 0
*360 -___
+360 STABLE
*180
UNSTABLE
M 0.
STABLE
-180
UNSTABLE
-360 -
0. 0.75 1
FIG. 3.5-30: FIFTH STANDARD CONFIGURATION:AERODTNRMIC MOMENT COEFFICIENT AND PHASE LEAD
IN DEPENDANCE OF INLET MACH NUMBER.
L -A..
C i113
x
xx
AERCELASTICITY IN TURBOMRCHINE-CASCADES.STANORRO CONFIGURRTION NUMBER ~ 5
20. _____
P2
hy
M 10. Co
k
II
STABLE
+180
UNSTABLE
4) M 0.
M t :
STABLE
-180
UNSTABLE
0. 10. 20.
FIG. 3.5-3E: FIFTH STANDARD CONFIGURATION:AERODYNAMIC MOMENT COEFFICIENT AND PHASE LEADIN DEPENDANCE OF INCIDENCE ANGLE.
h :/
C114
xr7 / 7/
N 1 ~ mP 1
x :
REROELRSTICITY IN TURBOMRCHINE-CRSCnOES.STANDARD CONFIGURATION NUMBER : 5'
20. M2P2
hX
hr
C 10
k8:
360 - --I
STABLE
+180
UNSTABLE
0. 051
M°
ST.BLE
~UNSTABLE
-360
0. 0.5 I
CC
FIG. 3.5-3F: FIFTH STANDARD CONFIGURATION:
AERODTNAMIC MOMENT COEFFICIENT AND PHASE LEAD
IN DEPENDANCE OF PITCHING AXIS POSITION.,) ,
|C
y 115
7 xX7xj P2P2
REROELRSTIcITT IN TURBOMRCHINE-CRSC
OES.
STRNRRO CONFIGURATION NUMBER : 5
""v M
2
x
X
P,
P2
qh
h
Ca)
-2. k
d
C 0. -- +... +... .+.-..+-.B UNSTABLE
W STABLE
+2.
0. 0.5 1.k
FIG. 3.5-3G: FIFTH STANDARD CONFIGURATION:
AERODYNAMIC WORK RND DAMPING COEFFICIENTS '
IN DEPENDANCE OF REDUCED FREQUENCY.
1 16 "
n M2 x c
p~t Yc
REROELASTICIT IN TURB(OMRCHINE-CASCAOES. Ii .STANDARD CONFIGURATION NUMBER 5
M2
-14. P2 :
h
h
-2. kS.
d
c 0. UNSTABLEW OSTABLE
+2.
JO 4
0.5 0.75 1.
FIG. 3.5-3H: FIFTH STANDARD CONFIGURATION:AERODTNAMIC WORK AND DAMPING COEFFICIENTSIN DEPENDANCE OF INLET MACH NUMBER.
' I I I
C!
Y /117
7x 7
2P2
STAND RD CONFIGURTION NUMBER 5
P2
hx
h
-2. k5:
d
c 2 Ij UNSTABLE
+2.
0. 10. 20.
FIG. 3.5-31: FIFTH STANDARD CONFIGURATION:AERODYNAMIC WORK AND DAMPING COEFFICIENTSIN DEPENDANCE OF INCIDENCE ANGLE.
IC
y118 =
x
7 P2
M M2 x-X
xI :
REROELASTICITY IN TURBOMACHINE-CASCROE5. I 1STPNDARD CONFIGURPTION NUMBER I5
M~2,
-4. P2
hx
h
my
-2. k8:
d
.0 -±- - - 1 UNSTABLE
W STRBLE
___________________+2.
SCC
0. 0.5 1.
FIG. 3.5-3K: FIFTH STANDARD CONFIGURATION:AEROOTNAMIC WORK AND DAMPING COEFFICIENTS
IN DEPENDANCE OF PITCHING AXIS POSITION.
-- - - - - - - - --I - -p.
119
3.6 Sixth Standard Configuration
This configuration is directed towards investigations of turbine rotor
blade tip sections in the transonic flow regime.
Experiments have been performed, in air, in the annular cascade test
facility at the Lausanne Institute of Technology by D. Schlifli.
The cascade configuration consists of twenty vibrating low camber prisma-
tic turbine blades. Each blade has a constant spanwise chord of c7-.0528 m
and a span of 0.040 m, with 140 camber and a maximum thickness-to-
chord ratio of 0.0526. The stagger angle for the experiments presented
here is 16.60, and the gap-to-chord ratio is:
0.952 (hub)
1.071 (midspan)
1.190 (tip)
The hub-tip ratio in the annular test facility is 0.80.
The cascade geometry is given in Figure 3.6-1 and the profile coordinates
in Table 3.6-1.
Experiments have been performed with variable inlet flow velocity inci-
dence angle, expansion ratio, vibration mode shape, oscillation frequency
and interblade phase angle.
Both the time averaged and time dependent instrumentation on this cas-
cade is complete, and a large number of well documented data have been
obtained.
However, due to the very thin profiles, only a limited number of pressure
transducers are built into the blades, wherefore no integrations of the
time dependant pressure signals to obtain global unsteady forces are per-
formed. Instead, the self excited flutter limits of the cascade have been
established for several parameters.
From the results obtained during these tests, 26 aeroelastic cases are
recommended for off-design calculations. They are contained in Table
3.6-2 together with the proposal for representation of the results.
The vibration mode for all these cases is bending (G =43.20), and the para-
meters varied are inlet flow angle, expansion ratio and interblade phase
angle.
The 26 aeroelastic cases correspond to 12 different time averaged set-
tings of the cascade (see Table 3.6-2), for each of which the steady blade
* surface pressure distribution is given in Figures 3.6-2 and Table 3.6-3.
\ * _ _ _
.1,
120
A1 eperiments presented here ha, e been performed with const ant span-
wise upst ream flow elocit ies and flow angles.
It is recommended to present the results as In F inUres '.6-S and Tablet 6-4.
I
a , 4I I I I II I I I I - I I- -
12 1
cascade leadi:.gedge plane
0. 1 upper surface
prpressur surfacee)
Y' 0.0 .....
0 0.2 0.4- x 0.6 0.8 1.0
C = 0.0528 m y = 16.6 0
span = 0.040 m camber = a4T = 0.952 (hub) thickness-
1.071 (midspan) chord = 0.05261.190 (tip) hub/tip =0.8
Fiqiire 5.6-1 Sixth Standard Configuration: Cascade Geornetr'.
122
C 0 0.05277 N
UPPER SURFACE LOWER SURFACE
8 y X y y Y x V
0.0000 0.0000 .5033 .0191 0.0000 0.0000 .4930 -.015.0078 .0063 .5135 .0189 .0008 -.0097 .5032 -.0148.0176 .0090 .5236 .0187 .0085 -.0161 .5133 -.0145.0275 .0109 .5338 .0185 .0178 -.0202 .5234 -.0142.0375 .0127 .5439 .0183 .0275 -.0232 .5336 -.0138
.0475 0143 .5540 .0181 .0373 -.0256 .5437 -.0135
.0575 .0157 .5642 .0179 .0473 -.0274 .5538 -.0132
.0676 .0171 .5743 .0177 .0573 -.0288 .5640 -.0130
.0777 .0184 .5845 .0175 .0674 -.0298 .5741 -.0127
.0877 .0195 .5946 .0173 .0775 -.0305 .5843 -.0124
.0978 .0204 .6047 .0171 .0877 -.0309 .5944 -.0121
.1079 .0213 .6149 .0169 .0978 -.0311 .6045 -.0119
.1181 .0221 .6250 .0167 .1080 -.0310 .6147 -.0116
.1282 .0225 .6352 .0165 .1181 -.0307 .6248 -.0113
.1383 .0230 .6453 .0162 .1282 -.0303 .6349 -.0111
.1484 .0235 .6554 .0160 .1384 -.0298 .6451 -.01081586 .0239 .6656 .0158 .1485 -.0294 .6552 -.01061.R7 .0242 .6757 .0156 .1586 -.0289 .654 -.0104
.1/19 .0243 .6859 .0153 .1688 -.0284 .6755 -.0101,1890 .0243 .6960 .0151 .1799 -.0278 .6856 -.0099
.1991 .0243 .7061 .0149 .1890 -.0274 .6958 -.009721183 .0242 .7163 .0147 .1991 -.0269 .7059 -.0095.,'194 .0240 .7264 .0144 .2093 -.0264 .7161 -.00932296 .0239 .7366 .0142 .2194 -.0259 .7262 -.0091.2397 .0237 .7467 .0140 .2295 -.0254 .7363 -.0089
.2498 .0236 .7568 .0137 .2397 -.0250 .7465 -.0087
.2600 .0235 .7670 .0135 .2498 -.0245 .7566 -.0085
.2701 .0235 .7771 .0133 .2599 -.0240 .7668 -.00832803 .0234 .7873 .0130 .2701 -.0236 .7769 -.0082
.2904 .0233 .7974 .0128 .2802 -.0232 .7870 -.0080
.3006 .0232 .8075 .0125 .2903 -.0227 .7972 -.0078.3107 .0231 .8177 .0123 .3005 -.0223 .8073 -.0077.3208 .0229 .8278 .0120 .3106 -.0219 .8175 -.0075.3110 .0227 .8380 .0118 .3207 -.0214 .8276 -.0074
.3411 .0225 .8481 .0115 .3309 -.0210 .8377 -.0072
.3513 .0223 .8582 .0112 .3410 -.0206 .8479 -.0071
.1614 .0220 .8684 .0110 .3511 -.0202 .8580 -.0070
.1?15 .0218 .8785 .0107 .3613 -.0198 .8682 -.0068
.3817 .0215 .8886 .0104 .3714 -.0194 .8783 -.0067
.3918 .0213 .8988 .0102 .3815 ..0190 .8884 -'006
.4019 .0211 .S089 .009 .397 -.0186 .8986 -.0065
.4121 .0210 .9191 .0096 .4018 -.0183 .9087 -.OOb4
.4222 .0208 .9292 .0093 .4119 -.0179 .9189 -.0063
.4324 .0206 .9393 .0090 .4221 -.0175 .9290 -.0062
.4425 .0204 .9495 .0088 .43e2 -.017? .9392 -.0061
.4526 .0202 .9596 .0085 .4423 -.0168 .9493 -.0060
.4628 .0200 .9697 .0082 .4525 -.C164 .9594 -.0060
.4?29 .0198 .9799 .0079 .4626 -.0161 9696 -.0059
.4831 .0195 .9900 .0076 .4727 -.0158 .9797 -.0058
.4932 .0193 1.0002 .0073 .4829 -.0154 1.0000 -.0057
Table 3.6-1 Sixth Standard Configuration: Dimensionless Airfoil Coordina-
tes (identical over the whole span)
123
Aeroelasticity in Turboachine-CascadesSixth Standard Configuration
Time Averaged Parameters Time Dependant Parameters Recomended representat ion@1ia 0a-
o 0
M l'Is 61 P,/pl M2,is h 0 I k a 6 c p ,c p CF(.) (o) (-) (-) H ft ) -- ) . [))
10..0 30 6 0 008 0 43.2 1 2 9
Z :45(9a 1 2
4 -135S -180 1
I -135-- 90 III
8 -459 0 10.0 0.50 1. 0 0.096 -90 1 2 4 1010 [.$. 20.0 0. 0 1.14 0.097
1! 0 2 13. 0.02 1.02 0.1081. U.S2 19.8 0.o, 0.98 0.113 0 1 2 3 6 91 3 :4514 -90
10 013S
,- 180 I -
I-7 1 , -13518 :90 219 -4
20 03 4 0 .2b 1 .60 0.009 90 - 8 1121 0.39 27.4 0.26 1.061 0.06b . 7,8 10,11
U.39 27.2 0.35 1.40 0.079 --
0.39 27.2 0.37 1.37 0.08002.0 0.9s 0.11t
0.37 27.5 0.85 3.85 0.13 4b 0.30 27.9 0.89 0.57 0. 1 93
MOIS: a) Isentropc Mach timbers
1) cp as a function of x 6) as a function of a
2) t p x 7) M ' is3) cy .. 8) C, 8.. . B4) L-12 is 9) a ....
3) l .. .. M6,) s
111 E ... " B
Table 3.6-2 Sixth Standard Configuration: 26 Recommended Aeroelastic
Cases
Y l :
124 T
T P2T,Ei-, M2 x : :
__ _ xM1
AEROELASTICITY IN TURBOMACHINE-CRSCROES. IuSTANDARO CONFIGURATION NUMBER 6
P2hx
hy
k8 :
d :X X x X x N 5 X x x
C_ . _ _ _ _ _
0. .5 1.x
-, i
FIG. 3.6-2A: SIXTH STANDARD CONFIGURATION.TIME AVERAGED BLADE SURFACE PRESSURECOEFFICIENT FOR B1=20 DEG AND M2(15)=1.63
Mt :
At3ELPSTICTr IN TUR8OMRCHINECASCPOES.
STPNOPAO CONFIGUFRTION NUMBEI : 6
M2
hX
hx
Li. _ _ _C :
k_8:
El w Uj L, J L! L! J ] [
X . x x XX X X d
-12.
0. .5 1.
FIG. 3.6-2B: SIXTH STANDARD CONFIGURATION.TIME AVERAGED BLADE SURFACE PRESSURE
COEFFICIENT FOR B1=20 DEG AND M2UIS)=1.20 j.
|C
126
7 x
P1 o 2
FEADELASTICITY IN TURBOMACHINE-CRSCROES.STANOARD CONFIGURATION NUMBER 6
P2
hx
h
4r
k
M~E l M x
-12.
0. .5 1x
FIG. 3.6-2C: SIXTH STANDARD CONFIGURATION.
TIME AVERAGED BLADE SURFACE PRESSURECOEFFICIENT FOR Bl=20 DEG AND M2(IS)=I.1LI
IC
y 127
P2
M 1 xcc :
P i 2 Y a :
REROELRST[C[TY IN TURBOMACHINE-CRSCROES. 1.2STANDARD CONFIGURAT[ON NUMBER 6
m 2 ,
P32 "
xh
I. -
k
o ;< x > x x x ir
- x d
-12. ---0. .5 1.
x
FIG. 3.6-20: SIXTH STANDARD CONFIGURATION.TIME AVERAGED BLADE SURFACE PRESSURECOEFFICIENT FOR 81=20 DEG AND M2115)=1.02
1\-
c128 Y
x
TNOPRO CE NFIS URII TIaN NUM8ER -C6
M2 ,
p2 "
xh'V
k:
0x >
-12. ---- -- - -0. .5
x
FIG. 3.6-2E: SIXTH STANDARD CONFIGURATION.TIME AVERAGED BLADE SURFACE PRESSURECOEFFICIENT FOR 81=20 DEG AND M2(IS)=0.98
</
1 29
9Y
PEROELPSTICITY IN TUReOMACfiINE-C1ASCAoES.STPNOARO CONFI1GURPTION NUMBER 6
L
m 2
P2
hx
hy
-12 " a')
1 •01
k
d
xx AX x
0. .5
FIG. 3.6-2Ft SIXTH STANDARD CONFIGURATION.TIME AVERAGED BLADE SURFACE PRESSURE
COEFFICIENT FOR B1=25 DEG AND M2(IS)=I.60
- .-- I I_ _IIII_
4I I IN I.
7' T
_ _ _ _ x
p 1 o r/M
REOB L RSIIIT IrUR O R H nE.....[ PMESx
M2
c 2
x
-12a I
0. 5
FIG. 3.6-2G: SIXTH STANDARD CONFIGURATICN.TIME AVERAGED BLADE SURFACE PRESSURECOEFFICIENT FO3R BI=27 DEG AND M2(15)=1.61
y C
/ x
: P2
PEROELPSTVCITT IN TURBOMCHINE-C SCROES.STPND AD CONFIGURPTION NUMBER 6
p2
x
h
k
8 :L] J
13:
P x x xX X
xx
-12. ,
0. .5 1.x
FIG. 3.6-2H: SIXTH STANDARD CONFIGURATION.TIME AVERAGED BLADE SURFACE PRESSURE ,
COEFFICIENT FOR B1=27 DEG AND M2(IS):=I.O
132
x
III i2
m P2 i
M- 2 xY :
x // 1 MI
AEROELASTICITT IN TURBOMACHINE-CR5CAOES.STANDARD CONFIGURATION NUMBER 6
M2
hx
hr
cW
k
-j U
0. .5C -
FIG. 3.6-21: SIXTH STANDARD CONFIGURATION.TIME AVERAGED BLADE SURFACE PRESSURECOEFFICIENT FOR Bl=27 DEG AND M2(IS)=1.37T
yCX 1
P1 E1
2
AEROELASTIC T IN TURBOMACHINE-C
ASC POES.
1
STRN0RRQ CONFGURRTION NUMBER 5
P2
m 1 4P2 P2
h
x x
h
k :[]
d :
xx
4
GX
-12. - '
0. .5 1.x
FIG. 3.6-2K: SIXTH STANDARD CONFIGURATION.
TIME AVERAGED BLADE SURFACE PRESSURE
COEFFICIENT FOR B1=28 DEG AND M2([S)=0.95.....
. = ... - ' - -- ; - -.... --... .. . .
C!7
P2 1
M 2 x
REROELASTICITY IN TURBOMRCHINE-CASLRDES. I .5TANDARD CONFIGURATION NUMBER 6
M2
P2
h
hy
Lll
4.
k
a.
C _x x x d
x
-12. - -
0. .5 1.x
FIG. 3.6-2L: SIXTH STANDARD CONFIGURATION.TIME AVERAGED BLADE SURFACE PRESSURE
COEFFICIENT FOR B1=28 DEG AND M2(15)=0.85
P,Yc
I I
m
AEROELP$TLCI Y IN TURBOMACHINE-CRSCROES.
STANDARC CONF15URPTION NUM1BER 6
P2h
x
hY
4.Ci
k
X d
P/
x
0. .5 1
FIG. 3.6-2M: SIXTH STANOAR CONFIGURATION.TIME AVERRGEO BLAOE SURFACE PRESSURECOEFFICIENT FOR B1=28 DEG AND M2(15)=0.57
" V- - .t0 dtC4..r ..,,-r
--: - C_ S - -T T T 2 - , , , ,',- 't
:z __z.. . . . . . -. . . . .
- . . .. . . . . . . . ,' . . . . . .
_ -P, =- -. - - 4"fl ? . . 9 7 5 , .. . . . .. .. , , , , ,
, 7 77 77 77 77
.1 . . . . . . . .
.0~u . .. . .tC . .~u .l~ Z
IllSI
TC C C C .T Cr-.
- -S C ~f-c w.ft ~~i ,~Ji~~lZ - Z
C A fC C.4fq~lJ C- - ~~t-~
C -- ' C CA C ClC7C
-, 7 ~ ~r~lC~r'J. C~ ~ itC J~i l 0
.71 ~ . C '~ ~ ,-,r.r- .-. fl.,rr.,, .1.2
Table~ ~ 3.6- Sixth Sadr Cofqrto:Tm Ir dM d ufc
Pre-,S~rpDitri~tIrl orthe26 ec mme dedAprulsti C-se
MX P 2 xc :
P , M a :
AEROELPSTICITT IN TURBOMRCHINE-CASCROES. l aSTANDARD CONFICURATION NUMBER 6
20. M2P2
h X
hY
C 10.
cp Wa
k
0. -. +-
+360 -360 STABLE
+180 -180
UNSTABLE
$p 'j 0*. $P ISTABLE
-180 "+-180
UNSTABLE
-360 "- - ' +360
.0 .5 1.
FIG. 3.6-3A: SIXTH STANDARD CONFIGURATION.MAGNITUDE AND PHASE LEAD OF UNSTEADY BLADE
SURFACE PRESSURE COEFFICIENT.(x:IN PITCH MOOE.NOTRTION VALIO UPSTREAM OF PITCH AXIS)
2x
m
Z//- P,
AER3ELASTICITY IN TURBOMPCHINE-CASCPOES I5TPN[)qRD CONFIGURATION NUMBER ES. I
20. M2P2
h
0C O.W
k
8 :
0 . - I - - - + - ,I- - - - - H -
+360
STABLE
+180K
UNSTABLE
O0.&P
STABLE
-180
UNSTABLE
-3600. 5 1.
xFIG. 3.6-3B: SIXTH STANDARD CONFIGURATION.
MAGNITUDE AND PHASE LEAD OF UNSTEADT BLADE
SURFACE PRESSURE DIFFERENCE COEFFICIENT. K(-:IN PITCH MOOE,NOTATION VRL]I UPSTREAM OF PITCH RXIS)
y 1 59
II
M 2a
X P1AEROELRSTICITT IN TURBOMRCT 'INE-CASCAES.
STANORRD CONFIGURATION NUMBER 6
P2
xh
cF ca
k
' I , I I I a
360 STABLE
+180
UNSTABLE
F 0.
STABLE
a,, -180
UNSTABLE
-360 "- --- --180 0 180
FIG. 3.6-3C: SIXTH STANDARD CONFIGURATION.
AERODTNAMIC FORCE COEFFICIENT AND PHASE LEADIN DEPENDRNCE OF INTERBLADE PHASE ANGLE.
JC
140 y
xT7P2 T7P
/ 2
PEROELRSTICITT IN TURBOMPCHINE-CRSCOE5. 1,2 :STANDARD CONFIGURATION NUMBER 6
- -P2
h-X
h
F
k
+360 I 4
STABLE
+180I UNSTABLE
DF 0.
STABLE
a, -lO
UNSTABLE
-360 "i
0. l 1 1.6m 2
FIG. 3.6-3D: SIXTH STANDARD CONFIGURATION.AERODTNAMIC FORCE COEFFICIENT AND PHASE LEADIN DEPENDANCE OF OUTLET 1SENTROPIC VELOCITY M2115).,
y 141
x
0(1 M x<X1
2
/ ×
REROELASTICITt IN TURBOMRCHINE-CASCROES.STANOARD CONFIGURTION NUMBER 6
P2
hX
hI:r
k5:
d:
+360
STABLE
+180
UNSTABLE
F 0.
STABLE
-180
UNSTABLE
.. , -360
15. 25. 35.
FIG. 3.6-3E: SIXTH STANDARD CONFIGURATION.AERODYNAMIC FORCE COEFFICIENT AND PHASE LEAD
IN DEPENDANCE OF INLET FLOW ANGLE BETRI.
142
Mi P2 M x= :
_IIx m
RERCELASTICITT IN TURBOMRCHINE-CASCROES. IzSTANOARD CONFIGURRTION NUMBER 6
p 2
h
T
M c
k
+360-
STABLE
+160 UNSTRBLE
M 0.STABLE
-180
UNSTABLE
-360
-180 0 180if
FIG. 3.6-3F: SIXTH STANDARD CONFIGURATION.AERODTNAMIC MOMENT COEFFICIENT AND PHASE LEAD
IN DEPENDRNCE OF INTERBLRDE PHASE ANGLE. .9
C 143
xT~ :
M2 Xa:
P1 El Yc :
Mx m
P1
REROELASTICITY IN TURBOMRCHINE-CPSCROES. 1STANDARD CONFIGURATION NUMBER 6
P2
h
xh
M (J
k
5:
+360
STABLE
+180
0. UNSTABLE
~0. -M
STABLE
-180
UNSTABLE
-360 ' ' - - -0. 1. 1.6
M2
FIG. 3.6-3G: SIXTH STANDARD CONFIGURATION.AERODYNAMIC MOMENT COEFFICIENT AND PHASE LEADIN DEPENDANCE OF OUTLET ISENTROPIC VELOCITY M2(IS).
W Now J
|C
y
x
m P2 Xo:1] --- " 7/ 4 M 2 X,
x m I
AEROELRSTICITT IN TURBOMACHINE-CRSCROES. j5TRNOARD CONFIGURAPTION NUMBER 6
P2
hxh
M Ca :
k
8 :
+360S1 .. ST ABLE
+180 "
UNSTABLE
0.*MSTABLE
-180
UNSTABLE
-360 - I-
15. 25. 35.
FIG. 3.6-3H: SIXTH STANDARD CONFIGURATION.AERODTNAMIC MOMENT COEFFICIENT AND PHASE LEADIN DEPENDANCE OF INLET FLOW ANGLE BETAI.
* S
c
7 x7
PERIOELPST1C1TY IN TURBOMPCHINE-CASCROES. ISTPNDPRD CONFIGURATION NUMBEI9 6 6
_P2'
pip2
xh
k
d
'-H a _ UNSTABLE
-180 0 180
FIG. 3.6-31: SIXTH STANDARD CONFIGURATION.AERODYNAMIC WORK AND DAMPING COEFFICIENTSIN DEPENDANCE OF INTERBLADE PHASE ANGLE.
C
1-46
X MI I
AEROELASTICITY IN TURBOMACHINE-CRSCADES. j 1,.5TANDARD CONFIGURATION NUMBER 6
M2
hxh
ck:
d :
C+ - - , ; UNSTABLEW ' STABLE
I i
0.L 1 1.6M2
FIG. 3.6-3K: SIXTH STANDARD CONFIGURATION.
AERODYNAMIC WORK AND DAMPING COEFFICIENTSIN DEPENDANCE OF OUTLET ISENTROPIC VELOCITY M2(]S)
I I I I I I M
2c
7 7P,
REROELRST[CITY IN TURBOMACHINE-CASCAOES. I 1STANOR90 CONFIGURATION NUMBER 6
P2
hx
h
k
d:
~ 2 UNSTABLE
15. 25. 35.
FIG. 3.6-3L: SIXTH STANDARD CONFIGURATION.AERODTNAMIC WORK AND DAMPING COEFFICIENTSIN DEPENDANCE OF INLET FLOW ANGLE BETRI.
148
\Wroelasticity in Turbomachine-Cascades.
Sixth Standard Configuration.
Aeroelastic test case No:
1 pK/Ptl= _ * 2= •_ 1 2
-(-2)= • ;(-1)= __ _ -* 0) __-_1)= ___ _ S ( = 9 (rads)
(-2) (-1) (0) 0(+1)= 0(*2)= 0)
a) Global eroelastic Coefficients
,.,______ _ _- • (o)
b) Local Time Dependant Blade Surface Pressure Coefficients
(Is) I S) 0 (s( 0p p p p p
,- -
Table 5.6-4 S)ixth St andard Uonfiquration: Table for Present at on of
the 26 fIecommenrded Aeroelast ic Uases
1|-|
3.7 Seventh Standard Confiquration
The seventh standard configuration has been tested in the DL,oit Diesel
Allison rectilinear air test facility, and the results are included herein
by courtesy of the sponsoring agent, D.F. Boldman at NASA Lewis Re-
search Center. The configuration is representative for tip sections of
fan stages of turboreactors (multiple circular arc transonic profiles'.
Each blade has a chord of c-0.0762 m and a span of 0.01762 m, with a
-1. 100 net camber and a maximum thickness-to-chord ratio of 0.054.
The gap-to-chord ratio is 0.855 and the stagger angle 28.450.
The cascade geometry is given in Figure 3.7-1 and the profile coordinates
in Table 3.7-1.
The airfoils oscillates in pitching mode about a pivot axis at (0.50, 0.00),
with a frequency in the range between 710 Hz and 730 Hz. The pitching
amplitude of the reference blade lies between 0.060 and 0.20, depending
upon the test conditions, with some scatter in the motion amplitudes
between neighbouring blades.
Both the time averaged and time dependant instrumentation on this cas-
cade is extensive, and data have been obtained for different interblade
phase an les and axial velocity ratios.
From the tests, 44 aeroelastic cases are selected as recommended test
cases. They are contained in Table 3.7-2, together with a proposal for
representation of the results.
The 4 4 aeroelastic cases correspond to four different time averaged set-
tings of the cascade. The time averaged blade surface pressure distribu-
tions for these nominal settings are qiven in Table 3.7-3 and Figures
3.7-2.
The recommended representations of the results from the seventh standard
configuration allows detailed comparison of the local time dependant
blade surface pressures and trends of global effects, such as moment
coefficient and aerodynamic damping coefficient, in dependance of inter-
blade phase angle and axial velocity ratio. If possible, the results shouldbe represented as in Figures 3.7-3 and Table 3.7-4.
Cascade leadingedge plane
2upper surface
M / Suction surface
B1=26.040 Pressure surface"
/ \Ot ifi
Leading pressure surface Traiingedgeedge
c = ).0762 m T = 0.855span = 0.0762 m (x ,y ) = (0.5,0.)camber = -1.30 thickness : 0.034y = 28.45 o chord
F i(qure 5.7-1 seer!h ')t inrdard Configuration: (iasuade Coeomrtry
\I
= 0.0'62 n (3.00 in)
Upper surface Lower surface
(SJCTION S RFACE) - PRESSURE SURFACE)
x Y X -Y
0 -0.0029 0 0.0029
0.0026 -0.0004 0.0027 0.00S6
0.02'8 0.0015 0.0279 0.0066
0.0655 0.0041 0.0657 0.0019
0.1032 0.0065 0.1035 0.0092
0.1410 0.0087 0.1412 0.0103
0.1788 0.0107 0.1190 0.0113
0.2165 0.0124 0.2168 0.0123
0.2543 0.0139 0.2546 0.0131
0.2921 0.0152 0.2923 0.0138
0.3299 0.0162 0.3301 0.0144
0.3551 0.0168 0.3552 0.0148
0.3929 0.0175 0.3930 0.0152
0.4307 0.0179 0.4308 0.0155
0.468S 0.0181 0.4685 0.0158
0.5063 0.0181 0.5063 0.0159
0.5441 0.0179 0.5440 0.0159
0.5820 0.0174 0.5818 0.0158
0.6198 0.0167 0.6195 0.0156
0.6576 0.0158 0.6573 0.0153
0.6828 0.01SO 0.6824 0.0151
0.720S 0.0137 0.7202 0.0146
0.7583 0.0122 0.7580 0.0140
0.7961 0.0105 0.7958 0.0133
0.8338 0.008" 0.8336 0.0124
0.8716 0.0067 0.8714 0.0112
0.9093 0.0047 0.9092 0.0098
0.9471 0.0026 0,9470 0.0082
0.9848 0.0003 0.9848 0.0063
0.9974 -0.0005 0.9974 0.0057
1.0000 -0.0029 1.0000 0.0029
L.E. RADIUS/C- 0.0027At A T.E. RADIUS/C- 0.0027
Table 5.7-1 Seventh Standard Configuration: Dimensionless Airfoil Coordi-
nates
152
- --- - - - ------
z x *4 z z ------
- -------------- --------
-7-
------- ----- --- ------ ------ --------
-- - - - - - ------------
------- ........... . --------
Table 3.7-2 Seventh Standard Configuration: 44 Recommended Aeroe-
lastic Test Cases
Aeroelasticity in Turbomachine - Cascades
Seventh Standard Configuration
Time Averaged Blade Surface Pressure Distributions
M(-) 1.315 1.315 1.315 1.315
1 (0) 26.0 26.0 26.0 26.0
(-) 1.04 1.20 1.35 1.45
?t2/ tl - 0.958 0.9S6 0.956 0.957
M, (-1 1.25 1.14 1.05 0.99
08, ( 27.2 26.6 26.7 26.4
lInper surface -
0.0SOO 0.365 0.016 0.373 0.028 0.362 0.011 0.0482 0.374 0.0290.1SO0 0.377 0.034 0.380 0.039 0.364 0.014 0.1481 0.40, 0.0 S0.2500 0.382 0.042 0.378 0.036 0.362 0.011 0.2486 0.330 0.C300.3250 0.37S 0.031 0.381 0.040 0.366 0.017 0.3242 0.377 0.034n.490n 0.354 -n.002 0.352 -0.005 0.336 -0.029 0.3995 0.34- -0.01-O.52n 0.31? -n.056 0.317 - 009 0.302 -0.082 0.5201 0.310 -0.0-o0.600 0. 301 -0.084 0.292 -0.098 0.277 -0.121 0.5099 0.303 -o.081n. 7590 0.315 -0.06' 0.31" -0.059 0.327 -0.043 0.7503 0.339 -0.02S0.9553 0.353 -0.003 0.330 -0.039 0.345 -0.016 0.850 0.454 0.1530.9615 0.367 0.010 0.382 0.042 0.457 0.1S 0 .9604 0.531 0.23
Lower surface
r.90 0.412 0.088 0.407 0.081 0.408 0.082 1.0414 0.530 (.271n.1500 ).345 -0.016 0.338 -0.026 0.338 -0.026 0.1404 0.548 0.20 )0.200 0.320 -0.054 0.315 -0.062 0.313 -0.065 0.1963 0.518 0.2S30.250n 0.301 -0.084 0.298 --0.088 0.279 -0.118 0.2465 0.490 0.2090.3250 0.364 0.014 0.371 0.025 0.381 0.040 0.3221 o.519 0.2540.40n 9.373 0.02 0.381 0.040 0.415 0.093 0.3961 n. S01 0.22t0.4800 0.384 0.04$ 0.3-2 0.026 0.514 0.24" 0.4-0 0.49t, 0 .210.6000 0.299 -0.087 0.361 ((.009 . 9 0.192 0.5984 0.439 0.l~'0.7500 0.313 -0.065 0.373 0.028 0.445 0.140 0.-483 ).453 OIS!0.8500 0.208 -0.088 0.408 0.082 9.461 1()9 0.8491 0.4t" o 1 t,6
Compare figure 372 329 372C
Table 5.7-3 Sesenth 5tandard 'onfiquration: Tire o \ r ikidu ', r ; f,
Pressure [)ist ribut ion for the 4j Recorinrede,\d { ;i,\,
c
y
154
xx
X2
M xcc
77 Y ' 7
x 1
AERCELRSTICITY IN TURBOMACHINE-CASCROES.STRNOPRO CONFIGURATION NUMBER 7
P2
Xx
hy
0.5 -
k
0 X d
xx
-0.5 ,,
0. .5 1.x
.0.
FIG. 3.7-2A: SEVENTH STANDARD CONFIGURATION:
TIME AVERAGED BLADE SURFACE PRESSURE
DISTRIBUTION FOR OUTLET VELOCITT M2=I.25 .
C
/1 55
SM2 Ec :
PEROELRST[CITT [N TURBOM'1CHINE-CASCAOES. jSTPNDARD CONF[GURATION NUMBER :7
M2Y,x x
h :
0.5 -:
k
8 :
ox x d
P x x [] [ 12
0. .5 1.
FIG. 3.7-2B: SEVENTH STANDARD CONFIGURATION:TIME AVERAGED BLADE SURFACE PRESSUREDISTRIBUTION FOR OUTLET VELOCITY M2=1.14
156 TI
7 / 2 TI,
xx
P2.
oc M2 x= :
AERELASTICITT IN TURBOMACHINE-CASCRDES.
STANDARD CONFIGURATION NUMBER 7
P2
hx
h
0.5 _: k :
x o
X X
p__ x x1
-0.5 "0. .5 I
x
FIG. 3.7-2C: SEVENTH STANDARD CONFIGURATION:
TIME AVERAGED BLADE SURFACE PRESSURE
DISTRIBUTION FOR OUTLET VELOCITY M2=1.05
J
c
x
P2
Xc
REROELRSTICTr IN TURBBMRCh 'E-CRSCPDE5.
STRNOR CONFICURPT[ON NUMBER :7
M2
m 2
xh
0.5 __ _ (6
Xk8:
x ,-cP cc
0.5
0. .5 1.
xk
aNo,
FIG. 3.7-20: SEVENTH STANDARD CONFIGURATION:TIME AVERAGED BLADE SURFRCE PRESSURE
DISTRIBUTION FOR OUTLET VELOCITY M2=0.99 . ,.
1 %8
Aeroelasticity in Turbomachine-Cascades.
Seventh Standard Configuration:
Aeroelastic test case No :_
•0 0
II. p2/tl- ___ -_• 81= B 2- 0 k-
-(-2) -(-1) -(0)= (+1) (+2) (rads)
a(-2) = a(-l)= * (0)= 0 (+1) = (+2)= o
a) Global Aeroelastic Coefficients
M___ OL___ C )
b) Local Time Dependant Blade Surface Pressure Coefficients
X(-) C( 1S) ( s) (0) C(US) 4 ,(US) (0) A C (-) % (0)
a~i i
Table 3.7-4 Seventh Standard Configuration: Table for Presentation of
the 44 Recommended Aeoelastic Test Cases
• mf In • m m m Ii IiJ
AC
159
M X :
S,, Y, :
x mAEROELASTICITY IN TURBOMRCHINE-CPSCROES. 1STANORRD CONFIGURATION NUMBER 7
P2
h
h TY
k
0 ,. - -H -I
+360 -360N
STABLE
+180 -180 N
UNSTABLE(US) L)(s)STABLE
-180 +180
UNSTABLE
-360 + 360
.0 .5 1.x
FIG. 3.7-3A: SEVENTH STANDARD CONFIGURATION:MAGNITUDE AND PHASE LEAD OF BLADE SURFACEPRESSURE COEFFICIENT.
1 too
M2 x
PERO[LPSTICITT IN TURBOMPCHINE-CASCPES.5TANDPRD CONFIGURPTION NUMBER 7
20M 2P2
hx
h
p 10
k
:
~+360
*360STABLE
+180
UNSTABLE
AP 0
STABLE
-180UNSTABLE
-360 - - -
0. .5 1.x
FIG. 3.7-3B: SEVENTH STANDARD CONFIGURATION:MAGNITUDE AND PHASE LEAD OF BLADE SURFACE
PRESSURE DIFFERENCE COEFFICIENT.(W IN PITCH MOnF.NOIAT;:'N VPLIO UPSTRFQM OF PITCH PY5si
2 Xci
xM
AEROELAST[CITY IN TURBOMRCHINE-CASCADE5. I
STANE~qD CONFI, URAT[ON NUMBER 7 [2. m2
P2h :x
h y
c Mi
M :
k
0.:
0. 1- -I-- -H-- -,- --- d
+360
STABLE
+180
UNSTABLE
0M 0
STABLE
-180
UNSTABLE
-360 - ' + - --180 0. 180
FIG. 3.7-3C: SEVENTH STANDARD CONFIGURATION:AERODYNAMIC MOMENT COEFFICIENT AND PHASE LEADIN DEPENDANCE OF INTERBLADE PHASE ANGLE.
c
iY1 / y :
E ERE PSTICITf IN TURBOMP-HINE-CSCADES.
5 T N D 9 C C N !% ,R q A I O N N u M H R 7 j2. M2
p2h
hy
Icc
k
80:
+360
STABLE
+180
UNSTABLE
M 0.
STABLE
-180
UNSTABLE
-360 I
0.5 1. 1.5m 2
FIG. 3.7-3D: SEVENTH STANDARD CONFIGURATION:RERODTNAMIC MOMENT COEFFICIENT AND PHASE LEAD
IN DEPENDANCE OF OUTLET MACH NUMBER.
/ I
×c
/xcx
7p P2
m x
0 Y~x
h
x xx
RERCELA5TICITI IN TUR80MPC,!NE-CA5CA0ES. :
STANDARO C"NF IGuRATION NUGER : 7
10.
F "
" k :
a:
+360 "
. STRBLE
+180 4
. UNSTABLE
FSTABLE
-180 i.. UNSTABLE
-360 1 ----180 0. 180
FIG. 3.7-3E: SEVENTH STANOARD CONFIGURATION:
AERODYNAMIC FORCE COEFFICIENT AND PHASE LEADIN DEPENDANCE OF INTERBLAOE PHASE ANGLE. B
• 1 80
S/ c
/
FErjE7 ST IZITT IN TuRBOMC!-INE-CPSCPIJES. i¢ NTh2 ijDNF i R I ON NULOBE : 7
10. M2p2
x
k
,CN ; LR IO UM E
10. m--
+360- ___
S
+180
UN
F "ok
S-180
UN!
-360 - -I- .0.5 1. 1.5
M2
FIG. 3.7-3F: SEVENTH STANDARO CONFIGURATION:
RERODTNRMIC FORCE COEFFICIENT RND PHASE LEIIN DEPENORNCE OF OUTLET MACH NUMBER.
JC
y
xx7 __ P2
RERDELASTICITr [N TURBOMACHINE-CRSC OES. I iSTANDARD CONFIGURAT:N NUMBER 7
-2. P2
hx
h
1°
k
8
d
W • TI
+1.
1 1 +2.
-180 0. 180U
FIG. 3.7-3G: SEVENTH STANDARD CONFIGURATION:AERODTNAMIC WORK AND DAMPING COEFFICIENTS
IN DEPENDRNCE OF INTERBLADE PHASE ANGLE.
166 'r
7 / P2
A. ~xc
REROE ASTICITY IN TURBOMACHINE-CRSCROES. I 2.STAN5ARD CONFIGURPTION NUMBER 7 I
-2. P2
hx
h :y
k"8 :
d
c UNSTABLEW STABLE
+2.
- I- -f- -'-- '- +2.
0.5 1. 1.5M2
FIG. 3.7-3H: SEVENTH STANDARD CONFIGURATION:
AEROOTNAMIC WORK AND DAMPING COEFFICIENTS
IN DEPENDRNCE OF OUTLET MACH NUMBER.
3.8 L. iqhth Standard ( onfiquirat iou
The eighth arid raritih stwdaiitirtF i rit i t rt' dirt( tt't ird w [ii 1 ,
investigation of has i-c w roel ist 1 rt ,,, t ,, i ii ri I i 1t Ii i fr t' tf , i.,
effects on numerical cale u itlioiurs'. f-; ( i 1 i,, rhw 1 r,;
Configuration nuRhper eniitt ui ,rt,i at 1wr -([I-ttl rll I w < t
flat plates. ttrJuir(,t w al aa I ,,; ot 'rh I i I it
been performed for riitrI \eai, li uw, tit ihe ira(t'htl I I
interest, mainly due to the following fa-tr.;:
o In modern compressors, operat tog i the t rios int -ic anTii snlrt'r I W) II
flow regimes, the actual blades are rather thin arid ha e a low caIitwit.
They can thus mostly be fairly well approxmated as flat plates.
o Supersonic two-dimensional flat plate prediction models are oft eri
one of the main aeroelastic tools used bv the designer of large turboreac-
tors.
o In the incompressible flow domain, anak tical flat plate soltitons
are available.
o It is possible to establish, with different theories and for the purpose
of the present comparative work, the aeroelastic response of a flat plate
cascade over the whole Mach number range from incompressible to superso-
nic flow conditions.
0 The strip theory assumption should be validated, in the transonic
flow domain, in a fairly simple case. This requires validation not onil,
of theoretical results, but also of two dimensioral and quasi three-dimen-
sional experimental data on thin airfoils.
In this chapter, the main emphasize will be laid upon the change in the
aeroelastic behaviour of the cascade in dependance of inlet flow velocity.
pressure ratio through the cascade, stagger angle and solidity. The unsteady
blade surface pressure distributions will thus only be compared in detaii
for a few aeroelastic cases.
It is assumed that the two-dimensional airfoils oscillates in pitch about
mid chord (0.5, 0.), with an amplitude of 20 (0.0349 rad.
As the main interest for this configuration lies in the ariation of the
time averaged parameters the calculations should be performed. at zero
mean incidence, with a constant interblade phase angle of 900 and with
a fairly high reduced frequency, k-1.0.
The cascade configuration is given in Figure 3.8-1 and a recommendation
for ') aeroelastic cases to be calculated is given in Table 3.8-1. If possi-
ble, the results should be represented as in Figures and Tables 3.8-2.
The 35 aeroelastic cases are situated in different velocity domains, where-
fore it is not expected that one single program can calculate all cases.
However, it would be of interest for the comparisons if all participants
could calculate the cases their program(s) can handle.
cascade leadingedge plane
Y l~upper surface
M
411wersurface I
Flat platesc = 0.1 m a = 2.0° (0.0349 rad)
camber = 0° a = 900
(xa,yc ) z (0.5,0.) k = 1.0
i = 00
Fiqure 3.8-1 Fighth Standard Configuration: Cascade Geometry
1 () 9
Recommended Fepresentation
M_ Normal C ,'C CM
shock ?
0m 0- I (-Io-(1 ( )
I Inlcompressible 3 30 0 .75 1 2 3,6 7
3 604 90
5 0.5 30 4 76 0.6 X7 0.78 0.8 12 3, ,5 6, ,89 0.9
I1 0.95
1I 3.3 45 3 612 6013 i 90
30 3. 8
S 1 0.75 - 4 7
17 at L.E. -1" at T.E.
.t L.E. -
t TE.
1 3 1 2 ,5
2t L.E. 3, ,5 6.
a - t T . .
* at LE.7 Tit T.E.
,9 ± at L.E.3:) at T.E.
32 1,3 at L.E. 0.534 11.035 45 0. 75
Notes 1) c as a function of x 5) CM as a function of
2)6) S
3) CM ' 7) M
4) C M1 8)M
Table 5.8-1 Fighth Standard Configuration: 35 Recommended Aeroelastic
(ases
170
P2p Yc :
x m,
/
M1
AEROELRSTICITT IN TURBOMACHINE-CASCRAES. iP
5TANDARD CONFIGURATION NUMBER 8
P2
-X
h
[p ' h
k
L
8:
a :
III , I Id
:
+360 -360
STRBLE
+180 -180
UNSTABLE
STABLE
-180 +180
UNSTABLE
-360
-1- 360
.0.5.x
FIG. 3.8-2A: EIGHTH STANDARD CONFIGURATION.
MAGNITUDE AND PHASE LEAD OF UNSTEROT BLADE SURFACEPRESSURE DISTRIBUTION.
(w:IN PITCH MODE.NOTATION VALID UPSTREAM OF PITCH AXIS)
171
2 X :
x I
REROELASTICITT IN TURBOMRCHINE-CRSCRES5TNOQPRO CONFIGURATION NUMBER S J
P2
h
AcP CA)
k
+360
STABLE M
+l80UNSTABLEM
0 0.as
STABLE
-180
UNSTABLE
-360 ' ' - - --0. .5 1.
x
FIG. 3.8-2B: EIGHTH STANDARD CONFIGURATION.MRGNITUDE AND PHASE LERD OF UNSTERDT BLADE SURFACEPRESSURE DIFFERENCE DISTRIBUTION.
(w:IN PITCH MODE.NOT TION VRLIO UPSTREAM OF PITCH A[IS)
c
172
X P2M ~ X-
m m 2
REROELRSTICITT IN TURBOMACHINE-CASCAOES. ISTANDARD CONFIGU PTION NUMBEM M8
P2
hx
hy
M (a
k
r:
I i I
+360
STABLE
+180
UNSTABLE
M
STABLE
-180
UNSTABLE
-360 l
0 50 1007
FIG. 3.8-2C: EIGHTH STANDARD CONFIGURATION.AERODTNAMIC MOMENT COEFFICIENT AND PHASE LEAD
IN DEPENDANCE OF STAGGER ANGLE.
xxP
P2
P , Y a :
M mp×
REROELP5STIC[TY IN TURBUM;CH[NE-CRSCRDES. I ,
STANDARO CONFIGURATION NUMBER 8
P 2
hxh
M
STABLE
+180
UNSTABLE
-180 -UNSTABLE
-360 -
.0 1. 2.
FIG. 3.8-20: EIGHTH STANDARD CONFIGURATION.
AERODTNAMIC MOMENT COEFFICIENT AND PHASE LEAD
IN DEPENDANCE OF INLET MACH NUMBER.
/// C
/ X
x
PLREA -ST ,: TT IN IuROMP'HiNE CfSCK4JES.
hx
hm -Wk
+360
STABLE
+180
UNSTABLE
0.M
STABLE
-180
UNSTABLE
-360 - -,
0. 1. 2.
FIG. 3.8-2E: EIGHTH STANDARP CONFIGURATION.RERO2TNRMIC MO,,NT COEFFICIENT AND PHASE LEAD
IN DEPEr4DANCE OF SOLIDITY.
I 1 I o
7 P2
Al m D
pC Yx
M1
x1REAOELASTICITY IN TURBOMACHINE-CSCA ES. I 7..STPNDPRO CONFIGurPTION NUMBER 8 I
M2
hx
h
k
5 :
a
d
UNSTABLE
- -40 50 100
7
FIG. 3.8-2F: EIGHTH STANDARD CONFIGURATION.
AERODTNAMIC WORK AND DAMPING COEFFICIENTSIN DEPENDANCE OF STAGGER ANGLE.
yL _ / /d
M3 /
/
2
c
k :
r8:•
d :
xS
0. 1. 2.M7
FIG. 3.8-2G: EIGHTH STANDARD CONFIGUATION.
RERODTNAMIC WORN AND DAMPING COEFFICIENTSIN DEPENDANCE OF INLET MACH NUMBER. ,
pI[ 2 x7xx
P 2
p 2a
AEROELRSTICITT IN TURBIMRCHNE-CRSCADES. 1 2STANOAR CONFIruRIPT]N NUBER 8 M
P 2
hx
k :h
UNSTRBLEW STABLE
0. 1. 2.
FIG. 3.8-2H: EIGHTH STANDARD CONFIGURATION.AERODYNAMIC WORK AND DAMPING COEFFICIENTS
IN DEPENDANCE OF SOLIDITY.
1 -. : it vs .It in~ I urt .Ik, id v-ca5Cadc5
]it plaites at :crkc i1 Ii. )IL
N I ii' i-49 rad. - L .
Ihc hp
Acroclasticity in Turbomachine-Cascades.Eighth Standard Configuration.
Aeroelastic test case No:
Flat plates at zero mean incidence.
(xa,y)=(0.5,0.). 0-0.0349 rad. o=90 ° k=.0.
MI= _. Shock at _ .Y= 0. _=
a) Global Aeroelastic Coefficients
C: >CL= - CW=-- oL =
,1 = l L= 0 o
b) Local Time Dependant Blade Surface Pressure Coefficients
( _ ( IS _ (s ) ( o 0 ( S ( ( u s ) ( ) 0 - _-
Table 3.8-2 h Li ihth Stardard C'orfiquration: Table for Representati
of thn 5') Rcono nwrided Aeroelast i' ( ases
3.9 Ninth Standard L;onfiquration
The ninth standard configuration is selected to be a continuat icr of the
flat plate in estration. The emphasize is now placed upon blade thirkness
influence. especialI% in the high subsonic flow region, on the runierical
results from the different prediction models.
To this end. a s~rmmetric circular-arc profile. with thickness/chord ranging
from .P 1 to 0.10., is defined ,see Figure 3.9-1.
Apart iom the profile thickness, the influence cf inlet Mach number
on the aeroelastic response of the cascade will be investigated.
For this configuration, the same \ibration mode, reduced frequr, nc\ and
interblade phase angle as in the eighth configuration 1.11 and 9 00 resp.,
are choosen. The stagger angle has been defined to te 30', mainl, to
allow for realistic conditions at high \elocities. This stagger angle na
in some computations introduce influence of distorted calculation grids.
wherefore it is of importance to gie indications about the computational
scheme together with the numerical results.
In the confiriuration, 24 aeroelastic cases are defined for comparison
,see table 3.9-1). The incidence in the subsonic cases is 01. For the super-
sonic cases, the unique incidence is calculated with a program based
upon the method of characteristics. The 11 supersonic cases are defined
as to ha\e attached leading edge shock waves, and they should be calcula-
ted with supersonic throughflow. The results should be represented as
in Figures 3.9-2 and in Table 3.9-2.
As for the eighth configuration, it is here not the purpose to calculate
all the cases with the same prediction model. It is instead proposed that
the participants calculate the cases their programs can handle, whereafter
the different results will be compared and anal'sied.
y
Symmetric Circular Arc Profiles.
Maximum Thickness at x = 0.5.
Vibration in pitch around (x ,y,) (0.5,0.)a
u. = 2.00 (0.0349 rad)
c = 0.1 m i = 00
= 0.75 camber 0
d thickness 0.01 . 0.1 y = 30 ochord
k = 1.0
i h t " ." 7 ,[ r t + :r : ' + J r , :, ! ' : l , : : ! ! : , , ,, l l 'l ;
rI,' C'
I I II I II ' I I
Ii I II I
S I~ ; j' '~ ' I I
__ _____ I ~ '~
~~iIi II
I: I I I. . Ii i,~ j
ii .. ; -.- ~-. ~ -. 1 ~ -ii..
V. -~* II I I I
4' LLiIiI I _ U .i.~ ~LLiisLe .. TI z~. . ~,' ~. fT... t:i H ~ liultQ viti, 'he r:ethii.J of I
~1 Ill
I v -
A e ) c I \s t i ls tj c o °
__ oil o , eC ., , ()
pe 10, 1 e 11,n t d Sur fa c','- Pressurc Coefficion ts
X_____ C_____ -1_____)_
!s A
__ __ , A.....j xi
_______ V) 2
o f _ H f__ _ __ _ _ __ __ _ _ __ _ _ __ _ ___ __ _ . . ,__ __ _ 1
[,__ _ I _ _ _ _ _ _ _ _ _ , ,,_ _ _ _- _
____ ___ __ ____ _ 4 ___ ___ ___ ___ _ _ ____ __ ___ ___
t I . I
-h
(l IS1..0(LS
-0 .
P . -B L
.0 .5~
F I G 36 N I i
- L- E- L- i
PF360SJP r ---JF------ I-CIL,!
x I
h h
± k
+360.
STIOBL E
+ 180 - -. r
0. - - iUNSTRBLE
-180
0. .5 1.
FIGC. 3.9-5 NI NTH STAN'LA fl -F6LiTIOmRC n c UFJ tIN PIAS LruD, LAID OF UNSTEAIDY BLf1BIE
SUHFACE FFRE'.)fwJVE B IFiV[13El--JCc COEFF IL11[T. '
-C' -Y
I
t' T h r! ..1 - I x
I I
x ,
GO0 . ..
J4.
.. .0 ..
FIG.
A E 0 j I P i ' ;
I I ci
+300 -r ...... .
I_
+I -N p L T L
FiG 3. J [ !i ST<FKD KIG3
• -3IO F ' 'K Ff . [.~ 1 IiIf" i I A
[~1
ii
C.)
I I(3
I Cr _ _ __
__ ___ _ ____ .... - ....- ~ LIN I 3''
.1* l*~'-I..
I I
t I
__ __ ~ ------- :..--,-- I
I I
1.
I
~i- - - -
P:I-
I h
I k
. I
I I
S I
.1..1
I-.
. -~ ~ _ IC'.
~1
r I
.1 (.I~ . -
r:,, . - . ,
1 . -,.~ .
!,Iitt id . Iii~ I iI Ift j iitn I
ti W Ii i ' c l :fIt Lj' I I it 1% c i f w Ic I:, I c 1 i t I
rI cI i ic I\ I Ii , t ' I c kcc ccr i I 1 t c i it 1 i fi sit i ~ ic s t ci if i
hir fu iiit I I' Ir'l~ rI~i IcC .I I cI I ti'~ Ii e ic crcts L i
h !; I I I i Ii is II t(f It, (I;, t- I.cs [ w III I I " IS cSO c ic t af S I f p'\] 1c; IT If (i Ii
Ii ci )I.ii I cc it lcat c I, f ccc'; II ( I ccc al ;' 5pe thiet I im' 1, Ice c i I !i ccca I f~ i,' I !: ic ct
o kti pt t ci:f~ e t C al t 1wc I Nicc~ I ( r ic i ll I cc' "Ae of' It SiI :i ic c' ii'I t ii ;I1 , 'i t
fic if c i ll whc' I I s I l rc' s f t ' aec l Id tI(. r !Il I . l i
e\ii if iccIi dI , ( rcc :i III -c ciri turn' t cci I ow t huovel ccii cc! al lth crcfsIc 11 cc1I-,
inn a'I if ' Ii \ ci . ! i i t ri rlul~ ticic ' i Isc I tIc vI ll C t In r li ci ici'
tocw '\ c, 1t t if tc 'SciIT t1 o fc> it iccic ci'/ s.i' u I tc cc 5cc i
cIr i I csIf u c t cI I ''I t Ii a r I Ic c' s'ic c ci!. 1)( ii a i I c Iw I i' I !f 1 s. It I t; Ic ccI c In o Ia-
ti'rneics cii I'Vt 11cc c rCIccic' ci'icc Sci ii'CAUi c it i Wc- i l tc f fl ic cccictc
ccr'cd ic T , if h i'~n ( ciccccc'i. h ia ( o t ( c ll l l e o t ( [T 1L 1i
twvm & pehtin m dl ndI \n m ns
l-Ao f'\ [-, it IT' WSLltS l[L no wihdi wn, the wi~ be com~ we l t
,-ow
AD-A141 004 IWO.OIUMENSICNAL AMl QUASI lNItE.DIENSIISAL3II IPERIIIENIAL STANDARD CSIIU. UP [COLE POLVICIUIOUII PDERALI DE LAUSANE ISUITZISLAIUII LAS Of.
UNCLASSIF IED T FRANSION ET AL. 30 SEP 53 F/d 20/4 Nt*flfllflfllfl4
112- 12.2
11-.6
11111 E~ 1 112.58i1g1,J_, __ 2
JIfJI25 JJJ1. 4 11111J.6
MICROCOPY RESOLUTION TEST CHART INATIONAL BUREAU OF STANOAROS- 93- A
A,'
9/
Aeroelast icity in lurborvichine-Cascades
Farticilants -ith ex;crin rtad data larticipanth with predicition iaodcls
Country / Institution Nmae Country / lnstitution Name
USA USAUnited Techno]ogies Researcb Center F.O. Carta Physical Sciences Inc. N.H. Kamp
NSA Lewis Research Center D.R. Boldman United Technologies Research Center J.%. Verdon/J.R. Caspar
Westinghouse Z. KovaLz NSA Levis Research Center M.E. Goldstoin/W.H. braun/F.B. Mblls
Hassachussetts Institute of Techn 1. Crawley University of btre Dame ii. Atassi
Stevens Institute of Technology .i. Sisto University of Tennesse Space J. Caruthers/MI. Kurosaka
Detroit Diesel Allison R.L. Jay Massachussetts Institute of Techn. E.F. Crawley
Naval Postgraduate School M.P. Platzet/K. Vogelet
Nielsen Engineering andResearch Inc. [. Nixon
General Electric R. Jutras
University of California P. Friedimann
Princeton University 0. Bendiksen
Jln
Japan
lokyo University S. Kaji/H. Tanaka/Y.Tan Tok3v University H. Shoji/S. Kji/il. Tanaka/
loshiba 1. Araki Y "
Tanida
Mitsubishi S. lakahara/M. Honjo Kuyushu University M. Namba
Isnikawajima-lHarLma Heay Industries S. Nagana itsubishi S. Takahara
\ational Aerospace Lab. i. hobay&hi
United bingcs United Kingdom
Cambridge Univcsity D.S. khitehead/R.J. Grant Cambridge University U.S. hlitehcad/S.N. SmithM1. Davies Imperial College . Graham
Roils - Royce D.G. erallieClll
Vrance France
ONI A J.Girault/E.Szechenyi OR A P. Salab
hist Germany West Germany
DIIA'l P. Bblitz/H. Triebstein DFVLR V. Carstens
ltchnische lbchschule Aachen H.E. Gallus/K. Vogeler/ Technische lkchschule Aachen H.E. Ga3lus/K. VogelerK.D. Broichhausen
EU D. ohn
Swit zer land S.'itzerland
Rrw1 B'eri A. Kirschner Lausanne Institute of Toc rology A. Wbicsil.1%. Fransson
Lausanne Institute of Technology A. lWlcs/M. Degen/D. Schlfli
"Il~taly
Florence University F. Martel I i
Table 4.1-1 Present Participation in the Project "Aeroelasticity in Turbo-
machine-Cascades"-f
193
& :j
f TC
C; r . 4,w Vu0CS
C-- -
-A
-
.c .-
S ~~A -- A-*'C
0C-4,4, .- r
0 ! C C04 ' -04, ' 1 1- 1 t
-- 4. t4.4: 4
t- t LILL I-- -- * 0.~.iC
__ > ~ > ~ V7iI________ ±21 LIK~I4 ~ 4C*.i(CtOS~~1 1 9 @ * 9 @~.~ A
4~0[0* *-'ooeee *, *e 0 0, 0 0 B
Table 4.1-2 ClsiiainofPeetPricpto in__ 7t7I71i7r 4 ntalPart o the rojec
194
4. t C K ' 4 Ej - 4
FO_________ I-- - --I X x x x -
i va1 uIS .44 -7 Kxx x x x x K x x x x
.4 x .1 tvT~-- --.-- ZY--
T - -7-- - -- - - r--i: 't l V- K K 4 4 K I K 4 I 4t .x I x4 x I xIK 4
z)Tu77S(Trr m -. r: XI T j x 4 K I4
___ ___ ___ ___I x
x K4 x x
x K K K _._ K K K
tX--
00
4,. . 4, 4'. -0
C~~ 'A .. >
7 4 -4-4 -
Tabl 4.1- b- Clsiicto of 44~ 0rsn Patcpto4- h hoeia
Part of the Project
195
Acknowledgement
This research project is sponsored in part by the United States Air Force
under Grants AFDSR 81-0251, AFOSR 83-0063 with Dr. Anthony Amos
as program inanager. and in part by the Lausarane Institute of Technology,
The authors express their thatiks to all the research collegues who ari-
participating in the project. It is needless to say that withbout their undcer-r
standing, patience and good will, these standard configurations would
ne\ er ha'.e been compiled.
196
| c r, erenl(c 5
Il "A6roC1asticit6 dans 1(,s turbcmachihes"
Proceeding.s of the Symposium held in Paris,
France, 1976
Revue M6caniqie Frarit'aise, Numn6ro sp6cial
1976
121 P. 5u1 er "Aeroelasticity in Turbomachines"
(Editor) Proceedings of the Symposium held in Lausanne,
Sept. 8-12, 1980.
Co, Imunicat ion di I aboratoire de Thernique
Appiiqu6e NO 10, Lausanne Institute of Technolo-
gy, Switzerland
131 F.O. Carta "Unsteady Gapwise Periodicil y of Oscillating
Cascaded Airfoils"
ASME Paper 82-GT-286, 1982
141 J.lM. Verdun "Development of a linear Unsteady Aerodynamic
J.R. Caspar Analysis for Finite-Defiection Subsonic Cascades"
AIAA Paper 81-1290, 1981
151 Y.C. Fung "An introduction to the Theory of Aeroelasticity"
Dover Publications, Inc., New-York, 1969,
page 82
161 H. Ashley "Princip -s of Aeroelasticity"
R.L. Bisplinghoff Dover iblications, Inc., New-York, 1969, page
202
171 F.O. Carta "Coupled Blade-Disk-Shroud Flutter Instabilities
in Turbojet Engine Motors"
Journal of Engineering for Power, July 1967,
p.p. 419-426
181 S.R. Bland "AGARD Two-Dimensional Aeroelastic Configura-
(Coordinator) tions"
AGARD Advisory Report NO 156, 1979
.. .. . . , .. , I - "
197
191 J.1A. Verdon "Unst eady Supersonic Cascade in SubsonicJ.F . Mv Cune Axial H OW"
AlAA JOUrnal Vol. 13, NO 2, 1975, pp. 193-201
1101 S. Fleeter "Aeroelast icity Research for Turbornachine
Appl icat ions".
.Journal of Aircraft, Vol.16, NO 5, 1979
tv
i t
199
Appendix: Aerovlasticily in Ttrhorachirie-Cascades
To be returned to
Mr. Torsten FranssonLaboratoire de Thermique Appliqu6eflcole Pol)technique I 6dr6'ale de LausanneCH- 1015 LA.J SANNESwit zerland
Are you interested in participating in the project on Aeroe-
lasticity in Turbomachine-Cascades and will you perform
calculations upon some of the standard configurations?
Vhich configuratiion(s) and aeroelastic cases will you calcu-
fote'?
Would you like to obtain the profile coordinates on cards
for these configurations?
Are >ou interested in receiving the aeroelastic test cases for
standard configuration number 4 when they are available? _
Name _
Affiliation
Address _ ___,
Telephone : _ _ _.___,
Telex __ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _
.-
AT