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Printed in USA.
91-GT-88
Active Control of Rotating Stall in a
Low Speed Axial Compressor
J. PADUANO, A. H. EPSTEIN, L. VALAVANI, J. P. LONGLEY
*,
E. M. GREITZER, G. R. GUENETTE
Gas Turbine Laboratory
Massachusetts Institute of Technology
Cambridge, MA 02139
ABSTRACT
The onset of rotating stall has been delayed in a low speed,
single-stage, axial research compressor using active feedback control.
Control was implemented using a circumferential array of hot wires
to sense rotating waves of axial velocity upstream of the compressor.
Circumferentially travelling waves were then generated with
appropriate phase and amplitude by "wiggling" inlet guide vanes
driven by individual actuators. The control scheme considered the
wave pattern in terms of the individual spatial Fourier components.
A simple proportional control law was implemented for each
harmonic. Control of the first spatial harmonic yielded an 11%
decrease in the stalling mass flow, while control of the first and
second harmonics together reduced the stalling mass flow by 20%.
The control system was also used to measure the sine wave response
of the compressor, which behaved as would be expected for a second
order system.
NOMENCLATURE
C
n
complex spatial Fourier coefficient (Eq. (5))
IGV
inlet guide vane
n
mode number
P
static pressure
P
T
total pressure
R
n
controller gain (R
n
=
IZ
n
I)
r
mean compressor radius
t
non-dimensional time (= Ut/r)
U
mean compressor blade speed
V
k
axial velocity measurement (Eq. (5))
Zn
controller complex gain and phase
l3
n
controller phase for n'th mode
(O
n
=
IZ
n
I)
y
IGV stagger angle
S()
perturbed quantity
0
circumferential coordinate
X
rotor inertia parameter
µ
rotor
+
stator inertia parameter
* Current Address: Whittle Laboratory, Cambridge University,
Cambridge, England
P IG V
IGV inertia parameter
p
density
local flow coefficient (axial velocity/U)
area averaged flow coefficient
Nr
compressor pressure rise (P
-P
T
) / (pU
2
)
Subscripts
n
n'th circumferential Fourier mode
R
real part of complex quantity
I
imaginary part of complex quantity
INTRODUCTION
Axial compressors are subject to two distinct aerodynamic
instabilities, rotating stall and surge, which can severely limit
compressor performance. Rotating stall is characterized by a wave
travelling about the circumference of the machine, surge by a
basically one-dimensional fluctuation in mass flow through the
machine. Whether these phenomena are viewed as distinct (rotating
stall is local to the blade rows and dependent only on the compressor,
while surge involves the entire pumping system -- compressor,
ducting, plenums, and throttle) or as related (both are natural modes
of the compression system with surge corresponding to the zeroth
order mode), they generally cannot be tolerated during compressor
operation. Both rotating stall and surge reduce the pressure rise in
the machine, cause rapid heating of the blades, and can induce severe
mechanical distress.
The traditional approach to the problem of compressor flow
field instabilities has been to incorporate various features in the
aerodynamic design of the compressor to increase the stable
operating range. Balanced stage loading and casing treatment are
examples of design features that fall into this category. More
recently, techniques have been developed that are based on moving
the operating point close to the surge line when surge does not
threaten, and then quickly increasing the margin when required,
either in
an
open or closed loop manner. The open loop techniques
are based on observation, supported by many years of experience,
that compressor stability is strongly influenced by inlet distortions
and by pressure transients caused by augmentor ignition and, in turn,
that inlet distortion can be correlated with aircraft angle of attack and
yaw angle. Thus, significant gains have been realized by coupling
Presented at the International Gas Turbine and Aeroengine Congress and Exposition
Orlando, FL June 3-6, 1991
This paper has been accepted for publication in the Transactions of the ASME
Discussion of it will be accepted at ASME Headquarters until September 30, 1991
Copyright © 1991 by ASME
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r —
Performance
/
A
Improvement
Operating Point
Without Control
Without Control
Surge Line
Speed Line
Constant
The existing models for rotating stall inception in multi-row
Inlet Guide
C)
U)
G)
i
N
N
C)
a
^mpressor
the aircraft flight control and engine fuel control so that engine
operating point is continually adjusted to yield the minimum stall
margin required at each instantaneous flight condition (Yonke et al.,
1987).
Closed loop stall avoidance has also been investigated. In
these studies, sensors in the compressor were used to determine the
onset of rotating stall by measuring the level of unsteadiness. When
stall onset was detected, the control system moved the operating
point to higher mass flow, away from the stall line (Ludwig and
Nenni, 1980). While showing some effectiveness at low operating
speeds, this effort was constrained by limited warning time from the
sensors and limited control authority available to move the
compressor operating point.
This paper presents the initial results of an alternative and
fundamentally different means for attacking the problem posed by
rotating stall. Here, we
increase
the stable flow range of an axial
compressor by using closed loop control to damp the unsteady
perturbations which lead to rotating stall. In contrast to previous
work, this dynamic stabilization concept increases the stable
operating range of the compressor by moving the stall point to lower
mass flows, as illustrated conceptually in Fig. 1. There appear to be
at least two advantages of this new technique. One is that engine
power always remains high with dynamic stabilization while power
must be cut back with stall avoidance (often at critical points in the
flight envelope). A second advantage is that the gain in operating
range can be potentially greater. In the following sections, we briefly
describe those elements in the the theory of compressor stability that
are relevant to active stability enhancement, discuss the design of the
experimental apparatus, and present the experimental results.
Conceptual View of Compressor Stability.
and Active Stall Control
We consider rotating stall to be one of the class of natural
instabilities of the compression system, as analyzed for example by
Moore and Greitzer (1986) for low-speed machines of high hub-to-
tip radius ratio. Their model predicts that the stability of the
compressor is tied to the growth of an (initially small amplitude)
wave of axial velocity which travels about the circumference of the
Surge Line
Stabilized
With Control
With Active
Control
,!
Actively Stabilized
,'
Operating Point
compressor. If the wave decays (i.e. its damping is greater than
zero), then the flow in the compressor is stable. If the wave grows
(wave damping negative), the flow in the compressor is unstable.
Thus, wave growth and compressor flow stability are equivalent in
this view.
One prediction of this model that is useful for present
purposes is that rotating waves should be present at low amplitude
prior to stall. McDougall (1988, 1989) has identified these waves in
a low speed, single-stage compressor, and Gamier, et al (1990)
observed them in both a single and a three-stage low speed
compressor, and in a three-stage high speed compressor. The waves
were often evident long (ten to one hundred rotor revolutions) before
stall. It was found that the waves grew smoothly into rotating stall,
without large discontinuities in phase or amplitude, and that the wave
growth rate agreed with the theory of Moore and Greitzer (1986).
Further, the measurements showed how the wave damping, and thus
the instantaneous compressor stability, could be extracted from real
time measurements of the rotating waves.
In 1989, Epstein, Ffowcs Williams, and Greitzer suggested
that active control could be used to artificially damp these rotating
waves when at low amplitude. If, as the theory implies, rotating stall
can be viewed as the mature form of the rotating disturbance,
damping of the waves would prevent rotating stall from developing,
thus moving the point of instability onset as in Fig. 1. It was
proposed that the compressor stability could be augmented by
creating a travelling disturbance with phase and amplitude based on
real time measurement of the incipient instability waves. This paper
presents an experimental investigation of this idea.
The basic concept is to measure the wave pattern in a
compressor and generate a circumferentially propagating disturbance
based on those measurements so as to damp the growth of the
naturally occurring waves. In the particular implemerltation
described herein, shown schematically in Fig. 2, individual vanes in
an upstream blade row are "wiggled" to create the travelling wave
velocity disturbance. The flow which the upstream sensors and the
downstream blade rows see is a combination of both the naturally
occurring instability waves and the imposed control disturbances.
As such, the combination of compressor and controller is a different
machine than the original compressor - with different dynamic
behavior and different stability.
At this point, it is appropriate to present the rotating stall
model and connect it with the idea of control. Here, it is the structure
of the model that is most important rather than the fluid mechanic
details. Since the structure provides a framework for design of the
control system, the quantitative details can be derived by fitting
experimental data to the model.
Mass Flow
Fig. 1: The intent of active compressor stabilization is to move the
surge line to lower mass flow
Velocity at
Circulation
Velocity Field
Compressor Inlet
Changes
Due to
(Sense This)
(Move This)
Blade Motion
Fig. 2: Conceptual control scheme using "wiggly" inlet guide vanes
to generate circumferential travelling waves
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axial compressors are typified by an equation for the velocity and
pressure perturbations of the form
Pcompressor —
SP
Tcom ressor
exit
inlet
=
µ aS^
(1)
PU
2
dp
ae
at
Here, SP and SPT are the static and total pressure perturbations
respectively, S0 is the non-dimensional axial velocity perturbation, ?
and µ are non-dimensional parameters reflecting the fluid inertia in
stator and rotor passages respectively, (dV/do) is the slope of the
non-dimensional compressor characteristic, and t is a non-
dimensional time, t = tU/r. Equation (1) has been shown in several
publications (e.g. Hynes and Greitzer, 1987; Longley, 1988) and we
will not present its development here. The equation is an expression
of the matching conditions (across the compressor) for flowfields
upstream and downstream of the compressor and, as such, upstream
and downstream flow field descriptions are needed to be able to find
a solution.
Using these, Longley (1990) has shown that one can put Eq.
(1) in a wave operator form. For the nth spatial Fourier coefficient,
this is
{I^^
+µ
ac
+t
ae)
s
doI80
(2)
The left-hand side of Eq. (2) is a convective operator corresponding
to circumferential propagation with velocity i/(2/(Inl + p)) • (rotor
speed). In addition, the growth rate of the wave is dependent on the
slope of the compressor characteristic. If (dyi/d4) is positive the
waves grow; if negative they decay. Neutral stability (wave
travelling with constant amplitude) occurs at (dw/d4) = 0.
We can cast Eq. (2) in a form that is more useful for control
by considering a purely propagating disturbance. The first Fourier
mode will be of the form eie, so Eq. (2) can be written as
(2
+ µ)
at +1ia, -I
d
s )1 s0 = 0
Thus far, the equations presented have been for flow associated with
uncontrolled compressor dynamics. If, in addition, we model the
control as due to perturbations in IGV stagger, &y, we obtain the
following equation for the first Fourier mode:
(2 + t)
a
4+1ia,—(i)]
+ [ii IGV(
a
)
—
(
ay
—
IGV x)]87
at
L
—
i$µIGV(
1
+µ
-µ
2^)
_
=0
(4)
at
where $ is the axisymmetric (annulus averaged) flow coefficient,
IaIGV is the fluid inertia parameter for the IGV's, and (at{i/ay)
represents the incremental pressure rise obtainable from a change in
IGV stagger, y.
This is formally a first order equation for S0, however it
must be remembered that the quantity of interest is the real part of
S0. If we express So in terms of its real and imaginary parts, S0 _
SO
R
+ i&&
t
, then Eq. (4), which is a coupled pair of first order
equations for SC
R
and i&, becomes mathematically equivalent to a
second order equation for S4
R
. The form thus used in the system
identification discussed below is thus second order. Another way to
state this is that a first order equation with a complex (or pure
imaginary) pole is equivalent to a second order system in the
appropriate real valued states.
The second order model of compressor behavior is useful for
two reasons. First, it can be tested experimentally in a
straightforward manner. Second, it provides both a conceptual
qualitative framework about which to design a control system (i.e.
the stabilization of a second order system) and, given the results of
the experimental test, the quantitative inputs required to do the control
system design.
EXPERIMENTAL APPARATUS
A 0.52 meter diameter, single-stage low speed research
compressor was selected as a test vehicle due to its relative
simplicity. The general mechanical construction of the machine was
described by Lee and Greitzer (1988), and the geometry of the build
studied here is given in Table 1. The apparatus can be considered to
consist of four sections: the compressor (described above),
instrumentation for wave sensing, actuators for wave launching, and
a signal processor (controller). The design of the last three
components is discussed below.
TABLE 1
SINGLE-STAGE COMPRESSOR GEOMETRY
Tip Diameter
0.597 m
Hub-to-Tip Ratio
0.75
Axial Mach No.
0.10
Operating Speed
2700 RPM
IGV
Rs1r
Stator
Mean Line Stagger
0
350
22.5°
Chamber Angle
0
25°
25°
Solidity
0.6
1
1
Aspect Ratio
0.9
2.0
1.9
The sensors used in the present investigation are eight hot
wires evenly spaced about the circumference of the compressor, 0.5
compressor radii upstream of the rotor leading edge. The wires were
positioned at midspan and oriented so as to measure axial velocity.
Hot wires where chosen because their high sensitivity and frequency
response are well suited to low speed compressors. The sensors
were positioned relatively far upstream so that the higher harmonic
components of the disturbances generated by the compressor would
be filtered (the decay rate is like
e-nl)d/r,
where n is the harmonic
number). This reduced the likelihood of spatial aliasing of the signal.
With eight sensors, the phase and amplitude of the first three distur-
bance harmonics may be obtained. The outputs of the anemometers
were filtered with four pole Bessel filters with a cutoff frequency of
22 times rotor rotation. The axial location of the sensors is important
in determining the signal to noise ratio (SNR) of the rotating wave
measurements; this question was studied by Gamier et. al. (1990),
who showed the SNR to be greatest upstream of the stage.
There are many ways to generate the required travelling
waves in an axial compressor. Techniques involving oscillating the
inlet guide vanes (IGV's), vanes with oscillating flaps, jet flaps,
peripheral arrays of jets or suction ports, tip bleed above the rotor,
whirling the entire rotor, and acoustic arrays were all considered on
the basis of effectiveness, complexity, cost, and technical risk. For
this initial demonstration in a low speed compressor, oscillating the
IGV's was chosen on the basis of minimum technical risk.
Considerable care was taken in design of the actuation system
to maximize effectiveness and minimize complexity and cost. An
unsteady singularity method calculation of the potential flow about a
cascade was carried out first to evaluate tradeoffs between blade
angle of attack and flow turning angles versus cascade solidity,
fraction of the cascade actuated, and airfoil aspect ratio (Silkowski,
(3)
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12
d
r
c
G)
.
La)
C)>
C)-
C)
in
n
a
ao
50
100
Percent of Blades Moved
Fig. 3: Calculated blade stagger angle change required to generate a
given first harmonic axial velocity perturbation as a function
of the fraction of the blade row actuated
1990). The unsteady flow was examined since, although the reduced
frequency of the IGV airfoil relative to rotating stall is about 0.3 for
the first harmonic, several harmonics may be of interest.
Calculations were also performed to evaluate the relative
effectiveness of bang-bang actuation versus continuous airfoil
positioning. As an example of these actuation studies, the tradeoff
between the peak airfoil angle of attack excursion and the fraction of
the cascade actuated is shown in Fig. 3. As the fraction of the airfoils
which is actuated is increased, the angle of attack requirements on
individual blades are reduced.
The limits to blade motion are set by both mechanical
constraints (i.e., actuator torque limits) and airfoil boundary layer
separation at large angles of attack. A NACA 65-0009 airfoil section
was chosen due to its good off-angle performance and relatively low
moment. The airfoils were cast from low density epoxy to reduce
their moment of inertia. A coupled steady inviscid-viscous solution
of the flow over the blades indicated that the boundary layers would
stay attached at angles of attack up to fifteen degrees (Drela, 1988).
In this experiment, blade actuation torque requirements are
set by the airfoil inertia since the aerodynamic forces are small. Both
hydraulic and electric actuators are commercially available with
sufficient torque and frequency response. Hollow core D.C. servo
motors were selected because they were considerably less expensive
than the equivalent hydraulic servos. The blades and motors have
roughly equal moments of inertia.
For a given IGV solidity, the number of actuators required
can be reduced by increasing the blade chord, but this is constrained
by actuator torque and geometric packaging. The final IGV design
consists of twelve untwisted oscillating airfoils with an aspect ratio of
0.9 and a solidity of 0.6 (Fig. 4). The complete actuation system has
a frequency response of 80 Hz (approximately eight times the
fundamental rotating stall frequency) at plus or minus ten degrees of
airfoil yaw. The flow angle distribution measured at the rotor leading
edge station (with the rotor removed) for a stationary ten degree
cosine stagger pattern of the IGV's is compared in Fig. 5 to a
prediction of the same flow made by Silkowski (1990).
The control law implemented for the tests described here is a
simple proportionality; at each instant in time, the nth
spatial mode of
the IGV stagger angle perturbation is set to be directly proportional to
the nth mode of the measured local velocity perturbation. The
Fig.
4:
Compressor flow path
complete control loop consisted of the following steps. First, the
sensor signals are digitized. Then, a discrete Fourier transform is
taken of the eight sensor readings. The first and/or second discrete
Fourier coefficients are then multiplied by the (predetermined)
complex feedback gains for that mode. Next, an inverse Fourier
transform is taken which converts the modal feedback signals into
individual blade commands. These, in turn, are then sent to the
individual digital motor controllers. Additional housekeeping is also
performed to store information for post-test analysis, limit the motor
currents and excursions (for mechanical protection), and correct for
any accumulated digital errors.
The controller hardware selection is set by CPU speed
requirements (main rotating stall control loop and individual blade
position control loops), I/O bandwith (sensor signals in, blade
positions out, storage for post-test analysis), operating system
overhead, and cost. The final selection was a commercial 20 MHz
80386 PC with co-processor. A multiplexed, twelve bit analog to
digital converter digitized the filtered hot wire outputs. The D.C.
servo motors were controlled individually by commercial digital
motion control boards. Using position feedback from optical
encoders on the motors, each motor controller consisted of a digital
proportional, integral, derivative (PID) controller operating at 2000
Hz. The entire control loop was run at a 500 Hz repetition rate.
Motor power was provided by 350-watt D.C. servo amplifiers. The
complete hardware arrangement is shown in Fig. 6.
10
•
Calculated Flow Angle
E
c
2
1ladT
e
Stagger
•
•
Angle
10
0
120
240
360
Circumferential Position (Deg)
Fig. 5: A comparison of the measured and calculated flow angle
generated 0.3 chords downstream by a 10 degree cosine
stagger pattern distribution of 12 inlet guide vanes
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Control Computer
(80386)
AID
E> IGV Position i
•
Detection
Control Loop
•
Wave
Tracking
• Control Loo
RPM
Axial
Velocity
Anemometers
&
Filters
p
I
(12)
IGV Position
6
Servo Amp
(350 W)
(12)
Fig. 6: Hardware component of actively stabilized axial flow compressor
OPEN LOOP COMPRESSOR RESPONSE
The inputs and outputs that characterize the fluid system of
interest (the compressor and associated flow in the annular region)
are the inlet guide vane angles (inputs) and the axial velocity
distribution (outputs). In the present configuration this consists of
twelve inputs (twelve inlet guide vanes) and eight outputs (eight hot
wires) so that the system is multiple input-multiple output. Because
the disturbances of interest are of small amplitude, the system
behavior can be taken as linear and we can thus express the spatial
distribution of the input and output perturbations (or indeed of any
other of the flow perturbations) as a sum of spatial Fourier
components, each with its own phase velocity and damping. This
representation, which is consistent with Eq. (2), allows us to treat the
disturbances on a harmonic-by-harmonic basis, and reduces the the
input-output relationship to single input-single output terms, an
enormous practical simplification.
The complex spatial Fourier coefficient for each mode n is
given by
K-1
C
n
= K
I
V
k exp
f
_
2in
l
n
(5)
k=0
L
J
where K is the number of sensors about the circumference (8 in this
case), and Vk is the axial velocity measured at angular position k.
The magnitude of
CI
is thus the amplitude of the first harmonic at
any time and its phase is the instantaneous angular position of the
spatial wave Fourier component.
An important concept in the present approach is the
connection between rotating stall and travelling wave type of
disturbances in the compressor annulus. In this view, the wave
damping and the compressor damping are equivalent and determine
whether the flow is stable. At the neutral stability point, the damping
of disturbances is zero, and close to this point , the damping should
be small. (The measurements given by (lamier, et al. (1990) show
this.) Thus, for a compressor operating point near stall, the flow in
the annulus should behave like a lightly damped system, i.e., should
exhibit a resonance peak when driven by an external disturbance. As
with any second order system, the width of the peak is a measure of
the damping.
The present apparatus is well suited to establishing the forced
response of the compressor since the individual inlet guide vanes can
be actuated independently to generate variable frequency travelling
waves. The sine wave response of the compressor was measured by
rotating the ±10 degree sinusoidal IGV angle distribution shown in
Fig. 5 about the circumference at speeds ranging from 0.05 to 1.75
of rotor rotational speed. Figure 7 shows the magnitude of the first
spatial Fourier coefficient, as a percentage of the mean flow
coefficient, as a function of input wave rotation frequency, i.e. the
transfer function for the first spatial mode.
The peak response to the forcing sine wave is seen in Fig. 7
to be at 23% of the rotor rotation frequency. This is close to the
frequency observed for the small amplitude waves without forcing
(20%) and for the fully developed rotating stall (19%). This behavior
supports the view stated previously that the compressor behaves as a
second order system.
CLOSED LOOP EXPERIMENTS — ROTATING STALL
STABILIZATION OF THE FIRST FOURIER MODE
While the open loop experiments described above are of
interest in elucidating the basic structure of the disturbance field in the
compressor annulus, this work is principally aimed at suppressing
rotating stall using closed loop control. To assess this, experiments
were performed using a control scheme of the form
[S71GVIn'th mode
- Zn Cn
(6)
where
Z
n
= R
n
ei0n
(7)
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