Clearance on Effects of Asymmetric Tip

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Effects of Asymmetric Tip Clearance on
Compressor Performance and Stability
by
Thomas S. Wong
B.S. Aerospace Engineering
Illinois Institute of Technology, Chicago, Illinois, 1994
SUBMITTED TO THE DEPARTMENT OF AERONAUTICS AND ASTRONAUTICS
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE IN AERONAUTICS AND ASTRONAUTICS
AT THE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
JUNE 1996
© Massachusetts Institute of Technology, 1996. All rights reserved.
-
Z?~
Signature of Author
Depa
eof Aeronautics and Astronautics
/7
May 17, 1996
Certified by
f-I
Professor Edrd M. Greitzer, Thesis Advisor
H.N. Slater Professor of Aeronautics and Astronautics
Certified b
Dr. Choon S. Tan, Thesis Advisor
Principal Research Engineer
Accepted by
Professor Harold Y. Wachman
Professor of Aeronautics and Astronautics
Chairman Departmental Graduate Committee
OF TECHNOLOGY
JUN 111996
AerO
Effects of Asymmetric Tip Clearance on
Compressor Performance and Stability
by
Thomas S. Wong
Submitted to the Department of Aeronautics and Astronautics
on May 17, 1996
in Partial Fulfillment of the requirements for the degree of
Master of Science in Aeronautics and Astronautics
ABSTRACT
An experimental study has been carried out to assess effects of asymmetric tip clearance on
compressor performance and stability. The experiments were designed using a theoretical
model of compressor behavior with asymmetric tip clearance and were conducted in a four
stage, low speed compressor at the General Electric Aerodynamic Research Laboratory.
It was found that the reduction in stability margin with asymmetric clearance is significantly
more severe than that estimated based on an average clearance. Specifically, the stall point
can be closer to that obtained with axisymmetric flow at the largest clearance of the
asymmetry than to that obtained with the average clearance. Further, the circumferential
harmonic content (length scale) of the asymmetry is an important factor in determining the
amount of the stability margin reduction. For the same average clearance, an asymmetry
with wavelength equal to the compressor circumference showed a reduction in peak
pressure rise at stall one-and-a-half times as large as that for an asymmetry with half the
wavelength, both having the same average clearance.
The theoretical model was shown to capture the loss in steady-state pressure rise and stable
operating range associated with the clearance asymmetry. The model also reproduced the
trend of increasing velocity asymmetry as compressor axial velocity parameter is reduced.
Finally, the time resolved data showed that the stability limiting process can be linked to the
unsteady structure of the calculated disturbance modes in the compressor.
Thesis Supervisor:
Edward M. Greitzer
Title: H.N. Slater Professor of Aeronautics and Astronautics
Thesis Supervisor:
Dr. Choon S. Tan
Title: Principal Research Engineer
Acknowledgments
I would like to thank everyone involved in this research project. In particular, I wish to
thank:
Professor Edward Greitzer and Dr. Choon Tan for their support, guidance,
experience, and encouragement that were greatly needed in the completion of the project and
this thesis.
Dr. Martin Graf whose theoretical contribution lead to this experiment.
Dr. David Wisler for his support that made the experiment at GE Aerodynamic
Research Laboratory possible.
Dr. Hyoun Shin for his assistance and guidance at GE. His expertise in flow
measurements was invaluable to the success of this experiment.
Mr. Don Menner for his assistance in preparing the Low Speed Research
Compressor for testing and his support on data reduction.
Dr. Brent Beacher, Dr. Dave Halstead, and Mr. Bill Groll for their knowledge and
experience on the LSRC.
Professor Frank Marble and Professor Alan Epstein for their insightful discussions
and suggestions.
Roommate and pal John Brookfield, all my friends, and the staff at the MIT Gas
Turbine Laboratory for their help and friendship.
I would especially like to thank my parents and sister for their unconditional love and
constant encouragement which kept me going at the worse of times.
This research was supported by the Air Force Office of Scientific Research, under Grant
Number F49620-93-1-0015, Dr. J. M. McMichael, Program Manager, and General Electric
Aircraft Engine Company, D.C.Wisler, Program Manager.
Table of Contents
Chapter 1
Introduction
1.1
Background .............................................................
1.2
Overall Background....................................................
1.2.1 Tip Clearance Effects on Compressor Performance........
1.2.2 Asymmetric Clearance........................................
1.3
Thesis
1.4
Scope of the Thesis....................................................
Chapter 2
Objective.......................................................
Formulation of the Compressor Model with
Asymmetric Tip Clearance
13
2.1
A ssum ptions............................................................
13
2.2
Brief Description of the Compressor Model........................
14
2.2.1
14
Steady Flow Field.............................................
2 .2 .2 S tab ility .........................................................
17
2.3
Overall Performance Calculations.....................................
17
2.4
S um m ary ................................................................
18
Experimental Setup
22
3.1
Low Speed Research Compressor Rig Description................
22
3.2
Experimental Configurations..........................................
23
3.3
Instrum entation.........................................................
24
Chapter 3
3.4
Chapter 4
4.1
Error
Analysis.......................................................
Experimental Results and Assessment of Model
29
Steady State Performance..............................................
29
4.1.1
Pressure R ise...................................................
29
4.1.1.1
Axisymmetric Tip Clearance.......................
29
4.1.1.2 Non-Axisymmetric Tip Clearance.................
30
4.1.2 E fficiency .......................................................
31
4.1.2.1
4.2
Chapter 5
Reference
Axisymmetric Tip Clearance.......................
31
4.1.2.2 Non-Axisymmetric Tip Clearance.................
31
4.1.2 Circumferential Flow Distribution in the Compressor.....
31
Unsteady Compressor Response
32
4.2.1 Unsteady flow in compressors...............................
32
4.2.2 Stall inception..................................................
33
Summary and Conclusions
45
47
List of Figures
Chapter 1
Page
1.1
Effects of tip clearance on peak pressure rise. [Smith (1958)]
11
1.2
Effects of tip clearance on stalling pressure rise coefficient
[Koch (1981)].
11
Effects of increasing tip clearance on overall compressor performance
[Wisler (19840].
12
1.3
Chapter 2
2.1
Pressure rise characteristics of a three-stage compressor with
axisymmetric tip clearance of 1% to 5% of chord.
19
2.2
Local compressor operating points around the annulus.
19
2.3
Steady-state circumferential flow coefficient variation.
20
2.4
First mode wave envelope
20
2.5
Stall points for axisymmetric and non-axisymmetric compressor.
21
2.6
Stall points for clearance asymmetry of cos (0), cos (20) and cos (40).
21
Chapter 3
3.1
Schematic of the General Electric Low Speed Research Compressor.
27
3.2
Casing panel positions for a) the one-lobed configuration and
b) the two-lobed configuration.
28
Axial location of the instrumentation
28
3.3
Chapter 4
4.1
Compressor pressure rise characteristics for axisymmetric tip clearance.
35
4.2
Compressor pressure rise characteristics with axisymmetric tip clearance.
35
4.3a Change in peak pressure rise relative to the baseline configuration.
36
4.3b Change in stalling flow coefficient relative to the baseline configuration.
36
4.4
Compressor efficiency for axisymmetric tip clearance.
37
4.5
Compressor efficiency with asymmetric tip clearance.
37
4.6
Circumferential steady flow coefficient variation for the one-lobed
configuration.
38
Circumferential steady flow coefficient variation for the two-lobed
configuration.
39
4.8
Harmonic amplitudes of time-mean flow coefficient distribution.
40
4.9
First mode wave envelope.
41
4.7
4.10 Mode shape harmonic content.
41
4.11 Normalized RMS static pressure fluctuation.
42
4.12 Pressure transducer traces for axisymmetric baseline configuration.
42
4.13 Pressure transducer traces for one-lobed configuration.
43
4.14 Pressure transducer traces for two-lobed configuration.
43
4.15 Histogram of stall inception locations.
44
CHAPTER 1
INTRODUCTION
1.1
Background
Tip clearance is the gap between rotor blade tips and the casing of a turbomachine. There is
a large body of experimental information which shows that increases in tip clearance have a
significant adverse effect on axial compressor performance and stability. An operational
problem for gas turbine engines connected with can be the development of a clearance
asymmetry due to such effects as casing distortion or rotor eccentricity. Almost all the
studies of tip clearance in the literature, however, have focused on the situation with
axisymmetric clearance, and the impact of such asymmetry is much less understood. This
thesis thus addresses the effect of non-axisymmetric tip clearance on compressor
performance and stability.
Clearance asymmetry can be separated into two categories. The first is stationary
asymmetry which can be caused by relative displacement (off-center) between rotor and
casing or by deformation of the casing. The second category is rotating asymmetry, which
can be generated by non-uniform blade height in the rotor, by a whirling rotor, or by a socalled "bowed rotor." The focus of the present investigation will be the first of these
stationary asymmetry.
1.2
Overall Background
1.2.1 Tip Clearance Effects on Compressor Performance
As stated, a number of investigations have demonstrated the effect of tip clearance on axial
compressors performance and stability. Examples are the data shown in the studies by
Smith (1958) and Koch (1981) which are given in Figure (1.1) and Figure (1.2).
The curves shown in the figures illustrate the decrease in stalling pressure rise associated
with the increase in tip clearance. Increasing the mean level of clearance causes a decrease
in the range of compressor stable operation. Tip clearance also affects the peak efficiency
performance of a compressor as seen in Figure (1.3) [Wisler (1984)] which shows pressure
rise and efficiency characteristics for a multistage compressor run at two different
clearances. The data demonstrate the decrease in both pressure rise capability and efficiency
due to increased clearance.
1.2.2 Asymmetric Clearance
This thesis is complementary to a previous study by Graf (1996) which described the
formulation of a model to calculate the steady and unsteady behavior of a compressor with
asymmetric tip clearance. The results of that study indicated that asymmetric tip clearance
could have a significant impact on compressor pressure rise capability and stall margin.
Also, changes in behavior due to asymmetric tip clearance were linked to the sensitivity of
the compressor to axisymmetric clearances. Parametric studies showed that the severity of
the effect depends strongly on the wavelength of the asymmetry. Data for an asymmetric
clearance are given by Freeman (1985) but no information is provided about the test details.
1.3
Thesis Objective
The objective of the present study is to provide steady and unsteady performance data which
can not only serve as a guide to the magnitude of the effects expected with asymmetric tip
clearance but can also help evaluate the analytical model. The experiment was carried out at
the Low Speed Research Compressor (LSRC) at the Aerodynamic Research Laboratory
(ARL) of General Electric Aircraft Engine Division. There were two phases to the
experiment. The first was aimed at obtaining the performance and stability characteristics of
the compressor at different axisymmetric clearance levels. Those were needed for input to
the model. The second set of tests then examined the performance of the compressor with
two different casing asymmetries.
1.4
Scope of the Thesis
In Chapter 2, the asymmetric tip clearance model is briefly described and the trends of
Grafs results (Graf, 1996), which served as a guide to the design of the experiment, are
illustrated and discussed. The experimental facility and setup are described in Chapter 3. In
Chapter 4, the results of the experiment are presented and discussed. The summary and
conclusions are given in Chapter 5.
130
120
110
100
90
80
70
0
2
1
5
6
Clearance / Chord,
/Ct, %
3
4
7
8
9
Figure 1.1. Effects of tip clearance on peak pressure rise. [Smith (1958)]
1.25
1.20
1.15
1.10
1.05
1.00
0.95
0.90
0.85
0.05
0.10
Tip Clearance: dg
0.15
Figure 1.2. Effects of tip clearance on stalling pressure rise coefficient. [Koch (1981)
/
\
90
\
89
87
/
\
/
1.5 pt
l
II
88
Nominal Rotor
Tip Clearance
e/h = 1.38%/
Increased Rotor
Tip Clearance
85
/h = 2.80%
Rotor B/Stator B
Four-Stage Configurations
DA
0.30
0.40
0.50
Flow Coefficient, po
Figure 1.3. Effects of increasing tip clearance on overall compressor efficiency. [Wisler (1984)]
CHAPTER 2
FORMULATION OF COMPRESSOR MODEL
WITH ASYMMETRIC TIP CLEARANCE
2.1
Assumptions
The asymmetric tip clearance model (Graf, 1996) described in this Chapter is an extension
of the approach used by Hynes and Greitzer (1987) to assess effects of circumferentially
non-uniform inlet flow on compressor performance and stability. It is assumed that the
compressor has a high hub-to-tip ratio so that the flow through it can be considered as two
dimensional (the variations are in the axial and circumferential directions). The relevant
Mach numbers and the compressor pressure rise are assumed to be low enough that
compressibility effects can be neglected. A simple accounting for blade row viscous losses,
similar to that described by Haynes et al. (1993), is also included. From the outset the
model is not designed to capture the detailed fluid mechanics of the clearance flow but is
aimed at giving useful information about overall compressor and compression system
behavior, including stability.
Steady state performance characteristics of the compressor with difference axisymmetric
clearances are input to the model. To illustrate the manner in which these are used, consider
Figure (2.1) which shows three steady state total-to-static pressure rise characteristics of a
compressor with axisymmetric clearance values ranging from "tight" (say 1% of rotor chord
length) to "loose" (say 5% of rotor chord length). The characteristic with the highest
pressure rise capability corresponds to the tightest clearance, and the lowest curve belongs
to the largest clearance. The curve in the middle would correspond to performance of the
compressor with nominal clearance of 3% chord.
The view taken is to regard a non-axisymmetric situation as composed of a distribution of
different "compressors in parallel" around the annulus, each with a characteristic that
corresponds to the local tip clearance level as shown in Figure (2.2). In the figure, the locus
of operating points around the annulus for a compressor with a sinusoidal clearance
asymmetry is shown as the heavy dashed lines along with the three characteristics
previously shown in Figure (2.1). The clearance asymmetry implies that the compressor
operates over a range of flow coefficients. The local slope of the compressor pressure rise
characteristic is also varying around the circumference. It is, therefore, possible for a
portion of annulus to operate on a positively sloped region of the local characteristic, a
situation which is associated with a tendency toward instability.
2.2
Brief Description of the Compressor Model
2.2.1 Compressor Steady Flow Field
A full description of the model has been given by Graf (1996). In this section, we present
only a summary of some of the features. An implicit equation for asymmetric steady flow
through a compressor has been given by Hynes and Greitzer (1987) as
Pexit - Ptinlet
d
(2.1)
pU 2
dO
(2.1)
In equation (2.1)
j~(O)
is the pressure rise characteristic with axisymmetric flow and 4 is
the steady state flow coefficient. X is an unsteady blade inertia parameter defined as follows
bx
IUCOS2,)
ucos2 ,
U:
U
With a non-axisymmetric tip clearance, the compressor pressure rise characteristics around
the annulus are functions of both local flow coefficient and local clearance (the local
pressure rise characteristics depend on the tip clearance distribution around the
circumference). The steady state performance of the compressor is thus given by Graf
(1996) as
d=
4~
dO
Pexit - Ptinlet
pU 2
(2.2)
where E is the tip clearance normalized here by rotor chord length. The asymmetric steady
flow is obtained by the solving equation (2.2) along with an equation to determine the
circumferential average flow through the compression system. This is a non-linear
description of the asymmetric steady flow around the annulus. Although it is to be
emphasized that Grafs analysis for the background flow is non-linear, we present here a
simple linear description to illustrate some of the basic parameter dependence. Linearizing
equation (2.2) yields the following expression for the steady flow variations
8Pexit - pU
8Ptinlet
- I8
=
o
2
p U2
+
8 - ,d
88
O
dO
(2.3)
(2.3
(E
We can expand the axial velocity parameter variations and the clearance variations in a
Fourier series
80 = I Ane ino
(2.4)
8E = _ Bne ine
(2.5)
There are no losses upstream of the compressor, so the total pressure is circumferentially
uniform at the inlet. Further because the flow is assumed to exit the last stator, exit static
pressure of the compressor is also uniform (Lonley and Greitzer, 1992). This exit condition
is verified experimentally from the results of this investigation. Using these inlet and exit
conditions along with the equation (2.4) and (2.5), the variation in axial velocity is
described by
54 =
Bne in0
8,
inx -v
(2.6)
The extent of the velocity variations around the annulus thus depends on 1) the harmonic
content of the clearance variation, 2) the flow inertia parameter X, 3) the compressor
pressure rise sensitivity to axisymmetric clearance 8/8E, and 4) the local slope of the
pressure rise characteristics 8V/50. In general, a more negative slope of the compressor
characteristic, a larger inertia parameter, a higher harmonic content of the clearance
variation, and a decreased sensitivity to clearance in the asymmetric situation will all tend to
promote smaller variations in axial velocity parameter, and thus, presumably, less of an
adverse effect on overall performance and stability.
Figure (2.3) gives an example of the steady flow at the compressor face obtained by solving
equation (2.2) and the mean flow equation of the compression system. The figure illustrates
the non-uniformity in steady state inlet flow to the compressor, due to asymmetric tip
clearance, which has developed from uniform flow far upstream of the compressor.
2.2.2 Compressor Stability*
Once the distorted steady flow through the compressor is obtained, the stability of the
compression system is assessed by adding a small unsteady perturbation to the steady flow
and determining whether it grows or decays. This involves solving the linearized equations
of the compression system for small unsteady perturbations. The details of their
development can be found in (Graf, 1996). The loss model employed in the asymmetric
clearance model and a summary of the compression system equations can also be found in
Appendix A of Haynes et al. (1993).
Stability of the compression system is defined by the eigenvalues of the linearized
equations. The mode shape of the first eigenmode (least stable) for the three-stage
compressor example is shown in Figure (2.4). The wave envelope of this particular mode
represents the axial velocity perturbation wave at neutral stability, at different times. While
traveling around the annulus, the fluctuations grow in certain regions and are damped in
other regions as indicated. The growth or decay in a particular region depends on the
location of the local operating point on its pressure rise characteristic (i.e. positively sloping
or negatively sloping). The magnitude of the flow fluctuations is thus not constant around
the annulus.
2.3
Overall Performance Calculations
To assess effects of asymmetric tip clearance on compressor stall margin, the stall point of
the example compressor with axisymmetric clearance can be compared to that of the
compressor with asymmetric clearance. Both compressors have the same average tip
* Note that the results of this and subsequent sections are obtained using the non-linear
model of Graf (1996)
clearance. Figure (2.5) shows the stall points for the two configurations; the clearance
asymmetry causes a 3.7% reduction in peak pressure rise.
The case illustrated is for a sinusoidal tip clearance distribution with wavelength equals to
the circumference of the compressor (cos 0). Two other cases with wavelength of a half
(cos 20) and a quarter (cos 40) of the compressor circumference are also shown. Their stall
points are given in Figure (2.6) along with those of the baseline and the cos 0 clearance
distribution. As the wavelength of the asymmetry is reduced, the reduction in stall margin
becomes smaller because of the increased importance of unsteadiness which causes the
circumferential flow variation to decrease in magnitude. The locus of operating points
around the annulus [shown in Figure (2.2)] thus reduces in width. As a result, the
performance of the compressor with "short wavelength" clearance asymmetry approaches
that of the axisymmetric baseline compressor.
2.4
Summary
The effect of asymmetric clearance is modeled using steady-state compressor design
parameters and system dynamic parameters. Non-axisymmetric clearance distribution
causes a circumferential distortion of the steady flow through the compressor and a
reduction in stability. The predicted decrease in stability of a compressor with asymmetric
clearance is more severe than based on average clearance.
0.9
0.8
0.7
0.6
Loose
Clearance
0.5
0.4
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
4,
Figure 2.1.
Pressure rise characteristics of a three-stage compressor with
axisymmetric tip clearance of 1% to 5% of chord.
10.95
0.9
0.85
r
0.8
0.75
0.7
0.65
0.6
-
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0
Figure 2.2. Local compressor operating points around the annulus.
0.7
0.7
0.65
S0.6
Z
0
0.55
0
o 0.45
0
. 0.45
.
0.4
0.35
....
0.3
0.5
0
1
1.5
2
Circumferential Location (PI)
Figure 2.3. Steady-state circumferential flow coefficient variation.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
(Theta. - Pi)
Figure 2.4. First mode wave envelope
1.8
2
0.84
Stability Point with
Axisymmetric
0.82
0.8
0.78
v
/
0.76
Stability Point with
Non-Axisymmetric
Clearance
0.74
0.72
0.7
-
I
0.35
I
0.45
0.65
0.55
Figure 2.5. Stall points for axisymmetric and non-axisymmetric compressor.
0.84
-
0.82
0.8
0.78
v
0.76
0.74
cos(e)
0.72
0.7
-
0.35
0.45
0.55
0.65
Figure 2.6. Stall points for clearance asymmetry of cos 0, cos 20 and cos 40.
CHAPTER 3
DESCRIPTION OF EXPERIMENT
3.1
Low Speed Research Compressor (LSRC)
The experiment was performed at the General Electric Low Speed Research Compressor
(LSRC). The facility is shown schematically in Figure (3.1). Flow enters from the top
through the cylindrical filter. A ring of eleven wall static pressure taps located at the flow
measurement plane shown in the figure serve to meter the flow rate. The air passes through
the four stages and exits to a plenum below the test floor and through a circular throttle plate
to atmosphere. The throttle plate moves vertically to change the exit area, regulating the
flow through the machine. In the configuration tested, the compressor had a constant casing
diameter of 1.524 meter (60 inches) and a hub-to-tip ratio of 0.85. There were four
identical blade rows. The casing is comprised of forty-eight Plexiglas windows mounted on
steel frames. They were shimmed to provide the non-uniform clearance variation. There is
extensive instrumentation associated with the rig which will be referred to as needed. A
detailed description of the LSRC can be found in Wisler (1984).
The compressor consisted of fifty-three inlet-guide-vanes. For each stage, there are fiftyfour rotor blades and seventy-four stator blades. The blading used in this experiment was
representative of modem designs. Chord lengths and stagger angles for the compressor are
summarized in Table (3.1). The Reynolds number was 3.5x10 5 based on rotor chord
length and mid-span blade velocity. The tip Mach number was 0.2, so that the flow can be
considered incompressible.
Blade type
Chord (inches)
Stagger angle (degree)
IGV
3.300"
-3040'
Rotor
3.590"
46050 '
Stator
3.114"
13040 '
Table 3.1. LSRC Blading geometry.
3.2
Experimental Configurations
The tip clearance of the compressor was altered to assess performance sensitivity with
axisymmetric and non-axisymmetric tip clearance. To alter the clearance, the twelve
Plexiglas windows over each stage were shimmed out to the desired clearance values. The
shimming was done for all four stages to assess the performance of the entire compressor.
In the first set of experiments, the first characteristics of the compressor with different
axisymmetric clearance levels were attained; these serve as input to the analytical model.
Three clearances were tested having 2%, 4%, and 6% of rotor chord. The performance of
the 4% chord axisymmetric configuration served as the baseline case to which the
performance of the other configurations will be compared.
The second set of experiments involved two different asymmetric clearance distributions.
The circumferential harmonic content of the clearance variation was predicted to have a
significant influence on the severity of the effects of asymmetric clearance and the tests thus
included one configuration with a single lobed clearance variation around the circumference
and one with two lobes. The two configurations are illustrated schematically in Figure
(3.2). Both the one-lobed and two-lobed configurations had an average tip clearance of 4%,
the same as the baseline configuration.
A summary of the axisymmetric and non-axisymmetric test configurations examined is
shown in Table (3.2).
Test
Average
Clearance/chord
Configuration
Clearance
Asymmetry/chord
J
Wavelength of
Asymmetry
Axisymmetric:
1
2%
2%
N/A
N/A
2
4% (baseline)
4%
N/A
N/A
3
6%
6%
N/A
N/A
Non-axisymmetric:
4
One-lobed
4%
±2%
circumference
5
Two-lobed
4%
±2%
one-half
circumference
Table 3.2. Summary of test cases.
3.3
Instrumentation
The overall compressor parameters of interest include compressor pressure rise and
efficiency. The pressure rise characteristic is presented as the overall total-to-static pressure
rise of the four stages [Wisler (1984) gives details of the instrumentation]. The efficiency,
which is obtained from overall torque and pressure rise, is also a value for the four stages.
In addition to overall performance parameters, the time mean flow field associated with
asymmetric clearance is also of interest. At the inlet of the compressor, steady flow
measurements were obtained by eleven Kiel probes and eleven static pressure taps upstream
of the IGV and evenly spaced around the circumference. Data were acquired at three points
on the compressor characteristic corresponding to the wide open, design, and near stall.
The exit static pressure was measured at the fourth stage exit by eleven static taps. It was
circumferentially uniform as expected (uniform to within 0.6% of the mean dynamic
pressure).
Unsteady compressor pressure measurement were also obtained using eight evenly spaced
Kulite high-response pressure transducers mounted on the casing over the first-stage rotor.
The transducers had a response up to 20,000 Hz. The sampling frequency used is 5000 Hz
with anti-aliasing filter settings at 1000 Hz. In comparison the compressor has a rotor
frequency of less than 15 Hz. Table (3.3) is a summary of all the instrumentation used.
Station#
Location
Instrumentation
Parameter
1
1/2 chord in front
of IGV
11 Kiel Probes (steady
state)
Pt0
1
1/2 chord in front
of IGV
11 casing static pressure
taps (steady state)
P1
2
1/2 chord of 1st
stage rotor
8 Kulite high-response
pressure transducer
P2
3
1/2 chord behind
4th stage rotor
11 casing static pressure
taps (steady state)
P3
Rig standard
Pressure rise, flow
shaft speed, power
i 0, '1
Table 3.3. Summary of instrumentation.
3.4
Error Analysis
Pressure Coefficient, 1.:
The instrumentation for pressure coefficient measurements is
accurate to within 0.15 percent. Day-to-day variation was observed to have a precision of
0.16 percent. The overall error, calculated using Root-Sum-Square Method, is 0.22
percent.
Flow Coefficient,
(:
The instrumentation for flow coefficient measurements are
accurate to within 0.15 percent with day-to-day variation of 0.36 percent. The overall error
is 0.39 percent.
Flow Coefficient Variation,
&:
The instrumentation error of variation in flow
coefficient is 0.7 percent with day-to-day variation of 0.5 percent. The overall error in flow
coefficient variation is 0.73 percent of mean.
Efficiency, 1:
Efficiency measurements are accurate to within 0.15 point.
Flow Direedoc
Flow
Straightening
Vanes
Bellmont
Inlet Screen
Figure 3.1. Schematic of the General Electric Low Speed Research Compressor.
.
.
,-
.
6% chord
\
.
4% chord
..
2% chord
a) One-Lobed
360 degree
0 degree
-
-6%
\ /\-4%
-
chord
chord
-
2% chord
b) Two-Lobed
Figure 3.2. Casing panel positions for a) the one-lobed configuration and b) the two-lobed configuration
*1 *I
1-1.
6
6
C
C
S
Y-
-
-
Y'I
T
f
'1
Y
?
X
A
A
6
Inlet e
'
IGV
A
A
R1
A
x
x
x
x
S1i I R2
S2 I IR31 IS3 I IR4 I IS4
x
x
x
x
A
A
A
0 Kiel Probes
x Exit
x
x Static Taps
A Kulite Transducers
Figure 3.3. Axial location of the instrumentation.
CHAPTER 4
EXPERIMENTAL RESULTS AND ASSESSMENT
OF MODEL
4.1
Steady State Performance
Steady state compressor pressure rise characteristics were obtained with both axisymmetric
and non-axisymmetric tip clearance. The baseline configuration had a 4% clearance/chord
and this was also the average clearance of the two non-axisymmetric clearance
configurations. The other two axisymmetric configurations had clearance level equal to the
maximum and the minimum clearance of the non-axisymmetric configurations.
4.1.1 Pressure Rise
4.1.1.1 Axisymmetric Tip Clearance
Figure (4.1) shows the total-to-static pressure rise characteristics of the compressor with
different axisymmetric tip clearance values. The increase in tip clearance decreases the
pressure rise and increases the stall mass flow. When the tip clearance was increased from
2% to 4% of chord, the compressor was less sensitive to clearance change than for the
increase from 4% to 6%. The implication drawn was that the machine was hub critical at
tight clearance (Wisler, 1996).
4.1.1.2 Non-Axisymmetric Tip Clearance
The compressor measured pressure rise characteristics for non-axisymmetric clearance are
shown as the data points in Figure (4.2). The axisymmetric clearance data of Figure (4.1)
are given as dashed lines. The figure demonstrates the effects of non-axisymmetric tip
clearance. If we compare the 4% axisymmetric data (the middle dash line) with the nonaxisymmetric data (points), we see a degradation in pressure rise and in flow range of the
latter.
At high flow coefficients (design point or higher, say), the characteristics for asymmetric
clearance are close to the baseline characteristics and the largest deviations between the
configurations occur at low flow. Also the degradation in compressor performance is
reduced when the dominant wavelength of the clearance halved with the two-lobed clearance
variation where the behavior more closely approaches that for axisymmetric clearance.
The theory is shown as solid lines in the Figure. The model appears to capture both the
effect of asymmetry and of reduced frequency in the overall curves. The experimental and
calculated stall points also show good agreement.
To assess the change in stall margin for the different configurations in more detail, the
change in peak pressure coefficient and in stalling flow coefficient, relative to the baseline
configuration's stall point, are shown in Figure (4.3a) and Figure (4.3b). As a reference,
the left hand side of the figure shows the results for axisymmetric clearance. The alterations
in stall conditions for the two asymmetric configurations can be seen to be significant
compared to the alterations for the same clearance change in an axisymmetric configuration.
The one-lobed experiment shows a decrease in peak pressure rise of more than eight percent
compared to that of the baseline configuration. The stall point for this asymmetric
configuration is in fact closer to the stall point with the loosest axisymmetric clearance than
the average.
4.1.2 Efficiency
4.1.2.1 Axisymmetric Tip Clearance
Efficiency characteristics for the three different levels of clearance are shown in Figure
(4.4). The efficiency has been normalized by dividing by the peak value at the tightest
clearance. The data indicate a roughly two percent change in peak efficiency for 2% chord
change in tip clearance.
4.1.2.2 Non-Axisymmetric Tip Clearance
Efficiency measurements for the one-lobed and two-lobed non-axisymmetric configurations
are shown as the data points in Figure (4.5). The axisymmetric data of Figure (4.4) are
given as dashed lines. The peak efficiency for the two asymmetric configurations are close
to the that of the axisymmetric configuration so asymmetric clearance has only a small
impact on peak efficiency of the compressor. This trend is consistent with that of pressure
rise characteristics for asymmetric clearance which show only a small deviation from the
baseline at design mass flow. This point will be addressed subsequently.
4.1.3 Circumferential Flow Distribution in the Compressor
Figure (4.6) shows the time-mean inlet axial velocity around the circumference of the
compressor with the one-lobed clearance variation. As described in Chapter 2, the velocity
distortion increases as the flow and the average compressor pressure rise characteristic slope
decreases. This can be explained if one notes that the axisymmetric clearance characteristics
are far apart near stall and closer together near design and high-flow conditions. Flow field
variations are thus greater at low flow than at high flow. The model captures this trend and
the shape of the axial flow variations.
The circumferential flow distributions for the two-lobed clearance configuration are shown
in Figure (4.7). There are two essentially identical lobes around the annulus and the
amplitude of the axial velocity variation has decreased. The two-lobed configuration is a
more demanding test of the assumptions on which the model is based but there is still good
agreement between theory and data.
The calculated and experimentally measured amplitudes of the flow variation at design point
and stall point are shown in more detail in Figure (4.8) which gives the first and second
harmonics of the velocity variation. For the one-lobed clearance distribution, the amplitude
of the first and second harmonics of the variation are shown. For the two lobed
distribution, only the second harmonic is given. The figures show an increase in amplitude
as the overall flow is throttled from design conditions to near stall. They also show the
effect of reduced frequency on decreasing the flow variation amplitude from the one-lobed
clearance distribution to the two-lobed.
4.2
Unsteady Compressor Response
4.2.1 Unsteady Flow in Compressors
Now thus turn to examination of the unsteady flow processes that limit stability. For a
compressor with asymmetric clearance, the steady flow field entering the compressor is
non-axisymmetric. As the rotor moves through this spatially non-uniform flow, it perceives
the distorted flow as an unsteady inlet flow, similar to the situation with circumferential inlet
distortion. Also similar to inlet distortion, both experiment and calculation indicate that
lower spatial harmonics produce the largest loss in stability. The wave shape of the
calculated least stable eigenmode is illustrated in Figure (4.9), which shows the
circumferentially traveling wave at different times. Because of clearance asymmetry, the
local damping of this traveling wave is different at different circumferential location, so the
wave grows at certain locations and decays at others. Figure (4.10) shows the harmonic
content of the eigenmode. For this configuration the largest harmonic is the first but others
harmonics are also strong.
The calculated wave envelope Figure (4.9) indicates that the local amplitude of the velocity
fluctuation varies circumferentially. The level of unsteadiness will thus be a strong function
of annulus location. Eight equally-spaced, high-response pressure transducers were used to
measure the unsteadiness in the compressor. The normalized root-mean-square values of
the static pressure fluctuation are shown in the Figure (4.11). The data indicate a widely
varying level of fluctuation for the eight locations. The highest level of measured fluctuation
coincides with the calculation of the location of the peak level of unsteadiness.
4.2.2 Stall Inception
The onset of stall is characterized by a rapid increase in fluctuation amplitude from the
growth of an underdamped circumferentially traveling wave. Figure (4.12) shows traces of
the normalized unsteady data from the eight pressure transducers from a test of the baseline
axisymmetric configuration. The data are taken at times just before and during the
development of a stall cell. The horizontal axis is time in units of rotor revolutions. The
vertical axis is the circumferential locations of the eight transducer. The time traces are
normalized static pressure fluctuation. The origin (defined here as have pressure
fluctuation, 8W, of 0.1) of the stall cell can be traced roughly to the location at 250 degrees
but the traveling wave shows similar growth over all the annulus.
With asymmetric clearance, the unsteady flow is quite different. Figure (4.13) shows
normalized pressure transducer data with the one-lobe configuration. The measured level of
fluctuation are now much higher at locations near 150 degrees and the stall cell can be traced
back to this same location. The cell begins to grow at roughly 150 degrees mark and its
amplitude increases until it reaches roughly 200 degrees. From 250 to the 50 degrees
however, the amplitude does not increase, and there is growth at some locations and decay
at others. This phenomenon is also shown by the model.
Data from the two-lobe configuration indicate the same behavior as shown in Figure (4.14).
For this configuration, the traveling wave experiences two growth and two decay regions as
it travels once around the annulus.
Examination of the stall cell inception location from different test runs of the baseline
axisymmetric configuration and from the one-lobe asymmetric configuration are also useful.
To determine these locations, the inception points are defined by the onset of a prescribed
value of the RMS pressure fluctuation amplitude (6 w=0.1).
A histogram of the stall cell inception locations is shown in figure (4.15). The compressor
with axisymmetric clearance does not appear to have one specific location from where the
stall cells emerge, but stall cells in the asymmetric compressor seem to always appear at the
location with highest unsteadiness. The model shows that the locations with the highest
unsteadiness offers the most favorable environment for the growth of small traveling
disturbances.
1.5
1.4
1.3
I
1.2
1.1
--
----h
0.9
2% chord
4% chord
6% chord
0.8
0.4
0.45
0.5
0.55
0.6
0.65
0.7
Figure 4.1. Compressor pressure rise characteristics for axisymmetric tip clearance.
1.6
1.5 ---
1.4
Two Lobe
1.3
One Lobe
1.2 ------- 2% chord
1.1 ------- 4% chord
----- 6% chord
1
O
Experiment, one lobe
Theory, one lobe
0.9
A
0.8
0.4
..
0.45
',,
Experiment, two lobe
Theory, two lobe
0.5
0.55
0.6
0.65
0.7
Figure 4.2. Compressor pressure rise characteristics with asymmetric tip clearance.
10
Axisymmetric Clearance
Non-axisymmetric Clearance
5
0-
-5
, -
-2%
chord
from
Nominal
%
rd
m
N
inal
E LSRC Data
-10
8 Calculation
-15
Figure 4.3a. Change in peak pressure rise relative to the baseline configuration.
15
Axisymmetric Clearance
Non-axisymmetric Clearance
10
5
=
0%
&rd
-5
m
inal
-2%
chord
from
Nominal
Two
Lobe
One
Lobe
at
0 LSRC Data
E3 Calculation
-10
Figure 4.3b. Change in stalling flow coefficient relative to the baseline configuration.
100
99
98
92
---
4% chord
91
-
6% chord
90
..
0.4
0.45
0.5
0.55
0.6
0.65
C
Figure 4.4. Compressor efficiency for axisymmetric tip clearance.
100
.
-
99 1
98
II
97
•
,i,'
A 0
A-
10•
0
96
0
k
0
95
94
-
93
------- 2% chord '
------- 4% chord
92
------- 6% chord
91
-
90 !
0.4
0
Experiment, one lobe
A
Experiment, two lobe
0.45
0.5
0.55
0.6
0.65
Figure 4.5. Compressor efficiency with asymmetric tip clearance..
0.7
A
Theory
-
0.65
-A A
Experiment
LI
A ......iiillll " tX
ZX
0.6
0.55
0lillilllllIIIIIII A0 12 ,
24
00
3 0
A8
0
0
Ui 0.5
0
8
Tight LIClearance
0j
8
Loose Clearance
0.45
Casing
Geometry
0
60
120
180
240
300
360
Circumferential Location (degrees)
Figure 4.6. Circumferential steady flow coefficient variation for the one-lobed configuration.
0.7
A
Experiment
Theory
0.65
0.6
4 0.55
o
o
M 0.5
0
0
-J
..a
Loose Clearance
0.45
Tight Clearance
Casing
Geometry
0
60
120
180
240
300
360
Circumferential Location (degrees)
Figure 4.7. Circumferential steady flow coefficient variation for the two-lobed configuration.
15
One Lobe
Two Lobe
Near
Stall
0
Cu
U Experiment
d.O
E Calculation
Design
• =
St
St
CPoint
5
Design
NPoint
Near
Stall
o
Design
Point
7
0
I~
1st Harmonic
L
2nd Harmonic
2nd Harmonic
Figure 4.8. Harmonic amplitudes of time-mean flow coefficient distribution.
0.5
0
-0.5
-1
0
50
100
150
200
250
300
350
Figure 4.9. First mode wave envelope.
1
0.5
-
I.. in I- [jL
N
0
0
1
2
3
4
5
Harmonic Number
Figure 4.10. Mode shape harmonic content.
41
6
7
8
1
0.5
0
0
60
120
180
240
300
360
Circumferential Location (degrees)
Figure 4.11. Normalized RMS static pressure fluctuation.
-10
-5
0
# of Revolutions to Stall
Figure 4.12. Pressure transducer traces for axisymmetric baseline configuration.
5
250
0
200
0
150
00
C,
E
0
.'100
# of Revolutions to Stall
Figure 4.13. Pressure transducer traces for one-lobed configuration.
350
300
0
250
0
O
a
100
# of Revolutions to Stall
Figure 4.14. Pressure transducer traces for two lobe configuration.
43
O Axisymmetric
4
SOne-Lobed
E3
0
0
20
65
110
155
200
245
290
Circumferential Location (degrees)
Figure 4.15. Histogram of stall inception locations.
335
CHAPTER 5
SUMMARY AND CONCLUSIONS
5.1
Summary and Conclusions
1)
Experiments have been performed at the General Electric Low Speed Research
Compressor to investigate effects of asymmetric tip clearance on compressor performance
and stability.
2)
It was found that asymmetric tip clearance resulting from casing distortion can
significantly reduce compressor peak pressure rise and stable flow range. The decrease in
stability is more severe than based on average clearance.
3)
The harmonic content of the asymmetry is an important factor in determining the
severity of the impact on compressor performance. Asymmetry with lower harmonics is
more detrimental than asymmetry with higher harmonics. Clearance asymmetry with
wavelength of its dominant spatial harmonic equal the circumference of the compressor
produces the greatest reduction in stability margin.
4)
There is a reduction in peak efficiency due to asymmetric clearance, but the
percentage change will generally be smaller in magnitude than for the stall pressure rise
because of the generally steeper speedline slopes at peak efficiency flows. As example, the
change in peak efficiency of the compressor with asymmetric clearance was less than 0.5 %
compared to a change of 8% for peak pressure rise.
5)
Sensitivity to asymmetric clearance is a function not only of steady-state compressor
design parameters but also of the parameters that reflect the unsteady response of the
compressor.
6)
The theoretical model (Graf, 1996) gave a good description of both the steady state
(overall as well as local) and the unsteady behavior with asymmetric clearance.
References
Freeman, C., Effect of Tip ClearanceFlow on CompressorStability and Engine
Performance. von Karman Institute for Fluid Dynamics, Lecture Series 1985-05, 1985.
Graf, M.B., Effects of Asymmetric Tip Clearanceon CompressorStability, Master Thesis,
MIT Department of Aeronautics and Astronautics, June 1996.
Longley, J.P. and Greitzer, E.M., Inlet DistortionEffects in Aircraft PropulsionSystem
Integration,AGARD Lecture Series -183, May 1992.
Haynes, J.M., Hendrick, G.J., and Epstein, A.H., Active Stabilizationof Rotating Stall
in a Three-Stage Axial Compressor,ASME Paper No. 93-GT-346. 1993.
Hynes, T.P. and Greitzer, E.M., A Methodfor Assessing Effects of CircumferentialFlow
Distortionon CompressorStability, ASME Journal of Turbomachinery, 1987, Vol. 109,
371-379.
Koch, C.C., Stalling PressureRise Capabilityof Axial Flow CompressorStages, ASME
Paper No. 81-GT-3. 1981.
Smith, L.H., Jr., The Effect of Tip Clearanceon the Peak PressureRise of Axial-Flow
Fans and Compressors,ASME Symposium on Stall, 1958, 149-152.
Wisler, D.C., Loss Reduction in Axial-Flow Compressors Through Low-Speed Model
Testing, ASME Paper No. 84-GT-184. 1984.
Wisler, D.C., personal communication, 1996.
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