The forcing functions and structural responses characterizing gas turbine rotor/case system vibration due to rotating stall in an axial flow compressor are described. Two data sets with fundamentally different response characteristics are presented; one is supersynchronous and the other subsynchronous. Conventional beam element rotor dynamics analysis is shown to be severely limited in its ability to predict these responses. A new analytical approach, which significantly increases structural response predictive capability for these phenomena, is briefly discussed

Haley, P. J.

English

NASA Technical Reports Server

GAS TURBINE I_Y/DR/CASE S_ RESPONSE TO ROTATING STALL:
EXPi_I_AL _ATICIq AND ANALYTICAL APP--*
Philip J. Haley
Detroit Diesel Allison
Division of General Motors Corp.
Indianapolis, Indiana 46206
SUMMARY
This work presents experimental data describing the forcing functions and
structural responses characterizing gas turbine rotor/case system vibration
due to rotating stall in an axial-flow compressor. Two data sets with funda-
mentally different response characteristics are presented; one is supersynch-
ronous and the other subsynchronous. Conventional beam-element rotor dynamics
analysis is shown to be severely limited in its ability to predict these re-
sponses. A new analytical approach, which significantly increases structural
response predictive capability for these phenomena, is briefly discussed.
INTRODUCTION AND BACKGROUND
The emphasis on aerothermodynamic performance in the high-performance gas
turbine engine of today and tomorrow has focused attention on increased per-
formances from its components, one of which is the axial-flow compressor.
Compressor design trends, aimed toward high efficiencies and/ or high aerody-
namic loadings, have led to machines that are very sensitive to running tip
clearances between blades/vanes and their respective case/ rotor structures.
The controlling criterion in the selection of these clearances is often the
necessity to accommodate rotor and case excursions associated with surge/stall
instabilities. Closely related to clearance selection is the rotor dynamic
design of a given machine. The mechanical designer typically has only empiri-
cal guidelines based on severely limited data with which to design to accommo-
date surge/stall deflections and to simultaneously provide minimum running
clearances. This paucity of knowledge of structural dynamic response during
surge/stall instabilities renders the optimization of tip clearances, rotor/
case flexibility, and bearing placement a difficult and abstract task.
Detroit Diesel Allison (DDA) is currently working under Air Force con-
tract to experimentally document compressor structural response to the rota-
ting stall phenomenon and to improve state-of-the-art analytical techniques
for predicting such response. These efforts address some of the deficiencies
in knowledge noted above. This paper presents an abbreviation of some of the
results of this contractual effort with emphasis on the experimental data.
Rotating stall can be viewed as one or more regions or "cells" of low mo-
mentum, low-pressure fluid, each covering some sector of the flow annulus of
the compressor. Although rotating stall typically occurs near the compressor
surge line, some machines exhibit it away from surge, even near the operating
line. The number of cells can vary from one to eight or more. Multiple cells
seem to be uniformly spaced circumferentially. In the fully developed rota-
ting stall considered herein, the cells traverse the axial length of the tom-
*This work is associated with U.$. Air Force Contract No. F33615-79-C-2089.
399
https://ntrs.nasa.gov/search.jsp?R=19830007383 2020-03-21T23:47:10+00:00Z
pressor, so can be regarded as "tubes" of low-pressure fluid that are axially
twisted or "corkscrewed" through the machine. These stall cells result in net
forces exerted on both the compressor rotor and the case, assuming the cell
fills the flow passage span. These forces are radial and, if ramp angles are
present, can have axial components. The stall pattern rotates in the direc-
tion of the compressor rotor but at partial rotor speed, generally between 25%
and 75% speed, as viewed from the inertial frame. Thus a single-cell rotating
stall at 50% rotor speed acts as a subsynchronous excitation mechanism. A
two-cell stall at 50% speed appears as a synchronous force, while a two-cell
stall at 60% speed appears supersynchronous.
In contrast to the surge phenomenon, rotating stall can produce quasi-
steady, periodic forcing functions which can cause steady-state, periodic
rotor/case response manifested as structural dynamic instabilities. Such re-
sponses can, based on experience, lead to high amplitude vibration and/or
radial excursions beyond the design clearances, causing rub and potential
structural failures. This paper presents a classic set of experimental data
describing the violent nature of rotating stall-induced rotor/case system vi-
bration. The associated forcing functions are also presented, and Fourier
analysis is utilized to gain insight into the forcing function/response rela-
tionships. The new analytical approach developed at DDA to calculate stall-
induced system response is briefly outlined.
EXPERIMENTAL DATA AND DISCUSSION
The data presented herein were generated at DDA on a large, multistage,
axial-flow compressor rig, which is fairly typical of the compressors current-
ly found in high-performance, aircraft-type gas turbines. This rig is sketch-
ed in Figure i. Though not shown in this sketch, the bearing/rotor arrange-
ment of the rig is similar to that of the parent gas generator, of which this
compressor is a component. This rig was instrumented to measure the time-var-
iant forcing functions and structural responses associated with rotating
stall. The elements of this high-response instrumentation scheme are shown in
Figure 2, which depicts the compressor case unwrapped into a plane. These
sensors are all mounted on the compressor case in the stationary frame. The
dynamic pressure sensors are high-response transducers flush-mounted in the
outer gas-path wall. They measure the fluctuating component of endwall pres-
sure, which is assumed to characterize the stall cell at both its inner and
outer span. Vibration pickups measure case velocities, while rotor-to-case
relative motion is sensed with "whip" pickups, which are proximity probes lo-
cated over compressor blade tips. Rotor motion can be established by vector-
ially adding case motion and rotor-to-case relative motion after transforming
these measured parameters to compatible units.
Running of this compressor rig produced several rotating stall and/or
surge sequences, which were recorded on magnetic tape via the described in-
strumentation. The phenomenological sequence from which the data presented
herein were quantified consists of a high-speed surge followed by two-zone and
then single-zone rotating stall patterns. Figure 3 is a time record of the
rotor speed excursion showing the onset of surge and the subsequent initiation
of the stall patterns. As seen in this figure, the entire sequence of time-
variant phenomena lasted approximately 5 seconds, during which time the rotor
accumulated over 900 revolutions under the influence of the related rotating
forces. The data presented in the subsequent discussion were defined over the
two time intervals shown in Figure 3.
400
Following surge, a two-zone rotating stall pattern was spontaneously es-
tablished, traveling (one-per-circumference spatial propagation rate) at 57%
rotor speed. Time traces of the dynamic signals over the defined analysis
interval are presented in Figures 4, 5, and 6. A commontiming signal on
these plots is used to time-relate events. The responses shownin Figures 5
and 6 show high-amplitude compressor case structural vibration at the fre-
quency of the individual stall cell passage from Figure 4, i.e. at two times
the two-zone rotating stall rotational frequency. The whip signals of Figure
6 also indicate rotor-to-case relative motion at the samefrequency. These
responses and the associated forcing functions thus appear to be supersynch-
ro nOB S •
The two-zone rotating stall pattern evolved into a single-zone pattern
(Figure 3) with a propagation rate of 60% rotor speed. Figures 7, 8, and 9
present the traces of dynamic pressure, case vibration, and whip for this
stall occurrence. Again, high amplitude structural response is observed.
Both the compressor case response and the whip signals visually indicate major
components at the subsynchronous passing frequency of the Figure 7 forcing
functions. Clearly evident in some of the response signals are additional
higher frequency components.
Insight into the nature and relationships of the forcing functions and
structural responses characterizing these stall phenomena is afforded by Four-
ier analysis. The two-zone stall data of Figures 4 through 6 were digitized
over the common interval shown on Figure 4, and the single-zone data of Fig-
ures 7 through 9 were likewise digitized over the period shown on Figure 7.
Digitized data were harmonically analyzed to produce components for each sig-
nal according to the cosine Fourier form:
Um cos (m_t - m6+ am )
m=O
where:
Um = amplitude of mth harmonic (harmonic coefficient)
m = harmonic index
= fundamental frequency
= circumferential location of sensor
am = phase of mth harmonic
t = time
This procedure removes phase differences arising from the different circumfer-
ential locations of the various sensors. Note that in Figures 4 through 9,
representing fully developed stall patterns, all these dynamic signals, con-
sidered to represent transient phenomena in the sense of an operating steady-
state turbomachine, are relatively periodic functions.
The Fourier content of the pressure traces is presented in Tables I and II
for the two-zone and one-zone phenomena, respectively. Because eight one-per-
circumference spatial cycles were digitized (Figures 4 and 7), the first five
spatial harmonics of the waveforms correspond analytically to temporal harmon-
ics 8, 16, 24, 32, and 40, as listed. A comparison of Table I with Figure 4
for two-zone stall confirms the predominance of second harmonic content (first
401
harmonic of a single stall cell times two cells per circumference) and indi-
cates a strong fourth harmonic. Comparison of Table II with Figure 7 for one-
zone stall shows a predominant first harmonic content with significant higher
harmonic content, notably second harmonic.
Table III presents the Fourier content of the measured responses to the
two-zone rotating stall pattern. The first five spatial harmonics are listed.
The amplitude predominance of second harmonic is seen, followed by fourth
(first harmonic of second). This pattern corresponds to that noted in the
pressure traces. The highest amplitude forcing functions (pressures) from
Table I are seen to be axially toward the rear of the compressor, whereas the
highest amplitude case responses from Table III are seen to be in the compres-
sor inlet area, suggesting a proximity to a resonance in the inlet. Compari-
son of these two tables does clearly show, however, direct structural response
to rotating stall. The presence and predominance of second and higher harmon-
ic case response show the importance of localized distortion and "egging" be-
havior in a flexible gas turbine case. Beam-like behavior, corresponding to
first harmonic force and response components, is a relatively minor contrib-
utor to case response in these data. Figure I0 further clarifies these de-
scriptions.
Table IV presents the Fourier content of the measured responses to single-
zone stall. The amplitude predominance of first harmonic is apparent, along
with a strong second harmonic contribution, especially in the inlet. This
same pattern is seen in the rotor-to-case whip signal. The relative Fourier
contents of these response signals are comparable to those of the forcing
functions (Table II), again suggesting the approach of comparing forces and
responses on a harmonic basis. These data indicate the primary case response
to be beam-like, unlike that observed in the two-zone phenomenon.
As shown in Figure 2, axially-redundant signals were obtained for several
parameters. Examination of the Fourier content of these signals in Tables III
and IV reveals circumferentially asymmetric responses throughout this compres-
sor in both first and second harmonic components for both case and rotor-to-
case signals. The significance of these observations is that the responses of
this "axisy_metric" turbomachine to these stall-induced forcing functions are
not at all axisymmetric. The asymmetric case response in the first harmonic
indicates asymmetric mounting of the case to ground for the beam-like motion.
Asymmetric case response in the second and higher harmonics is due to asym-
metry in the case itself, caused by holes, split lines, bleed manifolds, and
other deviations from pure axisymmetry.
A conclusion from these experimental data is that stall-induced response
of the compressor case, an important contributor to system dynamic response
and to rotor-to-case clearance response, cannot always be adequately described
by first harmonic, beam-like motion. Furthermore, significant circumferential
asymmetry is present in the different modes of case response. Obvious from
these observations is the fact that the beam-element analytical approach wide-
ly used 'in rotor dynamic analyses is generally inadequate for modeling either
of the forced response problems described herein. Since the supersynchronous
two-zone stall is seen to have only minor components of forcing functions and
responses that can be described by the first spatial harmonic, the beam-ele-
ment approach is inherently grossly inadequate. Although forcing functions
and responses of the subsynchronous single-zone stall have predominant first
harmonic content, the higher harmonic components are not negligible but are
ignored in beam-element analysis.
402
NEWANALYTICAL APPROACH
DDA has developed a capability for predicting rotor/case structural re-
sponse to dynamic forcing functions. This analysis has been developed specif-
ically for the rotating stall phenomenon in compressors. The analysis in-
cludes the ability to predict localized motions of the static structure (i.e.,
compressor case), including "egging" modes. The approach entails using a
beam-element rotor analysis along with an axisy_metric finite-element case
analysis. Egging and localized motions are calculated for the case alone and
are assumed to be decoupled from the rotor. Beam-like motion is calculated
for the coupled rotor/case system using finite-element case modes modally
coupled to the conventional beam-element rotor model. Deviations from pure
axisymmetry are recognized: (I) in the beam-element calculation, through al-
lowance for asymmetric support modeling, and (2) in the finite-element case
analysis, through availability of a discontinuous element for modeling struts,
vanes, holes in the case, bleed manifolds, and other variances from pure axi-
symmetry. This technique has substantially addressed the shortcomings of con-
ventional beam-element rotor dynamics analysis in the modeling of stall-in-
duced response and has produced reasonable analytical simulations of both the
subsynchronous and supersynchronous preceding experimental data sets.
403
TABLEI. - FOURIERDECOMPOSITONOFDYNAMICPRESSURESFROMTWO-ZONESTALL
8talie
_I _2 _3 _5 _6 7 _8 _9 10
TemporaJ harmonic - 8
Anpll[ude 0.2143 0.0346 0.0613 0.0670 0.0562 0.0475 0.1012 0.0924 0.2463
Ptmse -103.1 -75.9 97.0 -144.7 135.5 -149.5 -174.5 60.7 77.7
Temporal harmonic - 16
_plltude 0.1050 0.1597 0.1961 0.9671 1.784 2.711 2.622 3.878 2.340
Phase -1.5 -122.6 78.1 -160.2 -176.8 -175.6 159.5 136.4 106.1
Temporal harmonic - 24
Amplitude 0,0498 0.0334 0.0260 0.0513 0.0620 0.0561 0,0688 0.0974 0.1809
Phsse 47.3 18.4 115.3 -74.0 140.6 153.8 166.4 88.4 61.6
Temporal harmonic - 32
_mplltude 0.1022 0.1339 0.1023 0.1286 0.3121 0.5181 0.4338 0.8993 0.1992
Phase -22.9 -24.8 -28.0 -164.8 -171.1 -154.2 141.5 102.6 117.0
Temporal harmonic = 40
Amplitude 0.0380 0.0026 0.0001 0.0311 0.0495 0.0188 0.0526 0.0914 0.0211
Phase 0.0 -180.0 -180.0 0.0 -180.0 0.0 0.0 0.0 0.0
Amplitude In psi.
Phase in degrees.
TABLE II. FOURIER DECOMPOSITION OF DYNAMIC PRESSURES FROM SINGLE-ZONE STALL
StaSe
1 2 3 5 6 7 8 9 10
Amplitude
Pha_
Amplitude
Phase
&aplltude
Phase
Temporal harmonlc + 8
0.2323 0.2519 0.3808 1.041 1.576 2.222 2.122 2.139 0.7372
17.3 149.3 176.0 -157.3 -172.7 -173.5 177.1 155.6 128.1
Temporal hermonlc - 16
0.1429 0.0926 0.1158 0.4098 0.7246 1.111 0.9731 0.9519 0.4192
-7.6 38.3 -108.3 -134.4 -147.7 -155.3 179.7 166.4 108.8
Temporal harmonlc = 24
0.1128 0.0888 0.1165 0.1704 0.3000 0.4062 0.3069 0.2796 0.OO43
-26.2 7.0 -47.2 -146.3 -145.2 -150.8 -164.6 -127.8 169.1
Temporal harmonic " 32
0.0399 0.0845 0.0883 0.0797 0.1446 0.1212 0.0718 0.1437 0.1235
-32.8 32.1 -32.6 -124.5 -143.3 176.6 -40.8 -30.1 127.2
Temporal harmonlc " 40
0.0085 0.0129 0.0245 0.0408 0.0491 0.0655 0.0659 0.1723 0.0220
0.0 0.O 0.0 -180.0 -180.0 -180.0 0.0 0.0 0.0
Amplitude in psi,
Phase £n degrees.
404
ZI'--
0
Z
!
I--
0
I.L
LIJ
0
0_
..d
I--
I.U
0-
X
U.I
I
hi
_00_0000
_I O00000000000
ql II
=I _ooooooooooo .• ° • • ° . . . ° ° . °
oooooooooooo "
g'l _ "
oo
• • • .... ° ....
,_ c-_,_O O0 O000000
000000000000
_ c_c_c_c_c_c__ c__ _ c_ ""
• ._ ...... ._
• _D _ _ _ _ 0. _ _. _ c_,-_ _'_
_ g
_Ng_gP, g_g_ 2_
_ _ _ _ l_ _ _ 04 III' II
,._1
-J
l-
eD
I--
0
L_
0
!
_1
0
0
I--
L_
0
I--
L_
0
0
0
I
_1
I--
o_o_o_oo_o_
I I llIIll
_m_o._g_o_ _o
000000000000
o o. o. o. o o. o. o..? o o o.
000000000000
77 7_ 7
m ,--t ,--t
_I o,_,_ o _._ o o o _.a O. -
000000000000
ddddddSggdd_
_ °I ''_ _ ''_
I I I I
_I o._.._.o._._g_.o.o. ..
o%%°°_ o ° ° ,_
o c_r_ ooo
_" 0 0 0 0 - - 0
405
--Plenum
I
l
- Diffuser assembly
Rear compressor [Pineapple
t-, Inlet. | r"lnlet bell t'_
\oous'ngI __._ __---_--- _
lid',-_', J _ 270 901,
9thJtl|l Looking forward
sth-qll
7th--tl 1
6th-I h4th _7 _ \ _L_
Compressor stages
Front mount Sealing
asse mb I y boot
Figure 1. - Compressor rig on test stand.
J
TE-6657
Figure
...._ _!L
i
" 1-
I
:'rT::T:::: : :I
"i......i:i_ :i!q!iii!i!__
!t:
;,, i I.:IF.:
0 o
i Dynamic pressure
O Vibration
Whip
_, , _ _ Inlet
: 3
4
7
i
_ = t_ !t
t i......... ,_ 10
: _ _ Exit
_0 o
Angular position (clockwise)
UNCLASSIFIEO
TE-6714
2. - High-response instrumentation scheme.
406
EI
n,,,
1300O
12OO0
11000
10000
9OO0
800O
11:50
Surge
1
, Digitizedinterval
2-zone stall _ -'-11= Digitizedinterval
initiation II
_z,,,o_Sn="ll,_
II _.. End stall zones
-- 1 sec
I I I I I I I I
0:.09 0:10 0:11 0:12 0:13 0:.14 0:15 0:.16
Time_ TE82-20_
Figure 3. - Sequence of phenomena following surge.
407
I__:_I '_ _I
o
• --, ; !i J
ii ""
;I
F_
_h
o.
;\
o.
• _ 5.T
,I ql, #
_ :,
.... t ,
408
iJ i1_]
i !! _
!
I
I11
u
.|
I-..
i.
!
S,.
e-
o
N
!
0
U
°r-
c-
O
l.
! .
0r-
U.
409
OJ
0
N
t_
e-
0
°_,
!
g
S.
._.
L_
410
c-
o
N
!
°_
c
!
&.
411
i, I
i
i!i
I
i°
_i i
c-
O
N
e-
U
e'-
o_..
0
0_
t_
e_
.r-
I
_g
f,.
.,,j
412
i,
...(
e,,.
0
N
!
_J
e-
°_
U_
U
e"
e_
0
°_,..
L
.e.-
I
413
Beam-like behavior
Q Arrows indicate
inducedmotion
Eggingmotion
Localdtstortlon
UNCLAS S IF IED
TE-6745
Figure lO. - Case motion descriptions.
414


Gas turbine rotor/case structural response to rotating stall: Experimental documentation and analytical approach

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server