aeromechanical control of high-speed axial compressor stall
TRANSCRIPT
AEROMECHANICAL CONTROL OF HIGH-SPEED AXIAL COMPRESSOR STALL
An Undergraduate Honors Thesis
Presented in Partial Fulfillment of the Requirements for the
Bachelor of Science of Civil Engineering with Distinction in the
College of Engineering at The Ohio State University
By
Keith LaMar Coleman
* * * * *
The Ohio State University 2006
Examination Committee: Approved By Dr. Oliver G. McGee III, Advisor Dr. Patrick J. Fox
Advisor
Department of Civil & Environmental Engineering & Geodetic Science
First and foremost, I would like to dedicate this work to my Lord and Savior Jesus Christ. With Him all things are possible. This is also for my family for their continual support.
Thanks Mom and Jess.
i
ABSTRACT
General methodologies will be developed in this work for the evaluation of passive high-
speed compressor stabilization strategies using tailored structural design and aeromechanical
feedback control. These passive stabilization strategies will be compared in their
performance of several aeromechanical stabilization approaches which could potentially be
implemented in high-speed axial compressors used by industry. The stability of
aeromechanically-compensated high-speed compressors will be determined from linearized,
compressible structural-hydrodynamic equations of stall inception developed in this study.
This work offers a systematic study of the influence of ten aeromechanical feedback
controller schemes to increase the range of stable operation of two high-speed laboratory
compressors, using static pressure sensing and local structural actuation to postpone modal
(long wave) stall inception. The maximum operating range for each scheme is determined for
optimized structural parameters, and the various schemes are compared. Ten passive
stabilization schemes that could potentially be used by industry were discussed and examined
in a high-speed compressible flow environment. The concept of elasticity was introduced
and implemented to examine the effects of flow non-uniformity, entropic loss, and
unsteadiness on thermodynamic state changes within the compression system. Finally,
pumping and aeroelastic characteristics of these laboratory compressors both with and
without feedback were analyzed.
ii
ACKNOWLEDGEMENTS
I would like to first thank my advisor and friend, Dr. Oliver G. McGee III, for inspiring me
and also believing in my potential. I appreciate you for spending those longs nights in your
office with me to make sure that I understood the material. Thanks for ‘hurtin’ my head’ so
that I may become a better thinker. I truly believe that you have prepared me to be successful
in the next stage of my academic career. I look forward to the times ahead. Here’s to a long
lasting friendship.
Secondly, I thank Dr. Chih Fang, for his advice and support. I wish you and your family well.
I am grateful for the support of The Ohio State University Summer Research Opportunities
Program, The OSU Civil and Environment Engineering & Geodetic Science Department,
and The OSU Engineering Experiment Station for deeming my work as “worthy of research”.
Last and certainly not least, I must thank my lab partners and friends, Celeste Chavis and
Dan Work, for making my undergraduate research experience worthwhile. You two will truly
be missed. Best wishes in your future endeavors. Maybe someday we may work together as
colleagues. Only time will tell.
Thank you all!
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TABLE OF CONTENTS
Abstract ………………………………………………………………………………….. . i
Acknowledgements ………………………………………………………………….. …... ii
Table of Contents …………………………………………………………………………. iii
List of Figures …………………………………………………………………………….. iv
List of Tables ……………………………………………………………………………... vi
Chapter 1 ………………………………………………………………………………….. 7
Chapter 2 ………………………………………………………………………………….. 14
Chapter 3 ………………………………………………………………………………….. 21
Chapter 4 ………………………………………………………………………………….. 27
Chapter 5 ………………………………………………………………………………….. 42
Chapter 6 ………………………………………………………………………………….. 64
References ………………………………………………………………………………… 71
Appendix ………………………………………………………………………………….. 72
iv
List of Figures
Figure 1.1a……………………………………………………………………………….. 8 Figure 1.1b……………………………………………………………………………….. 9Figure 2.1a……………………………………………………………………………….. 14 Figure 3.2a……………………………………………………………………………….. 22 Figure 3.4a……………………………………………………………………………….. 24 Figure 4.2a……………………………………………………………………………….. 29 Figure 4.2b……………………………………………………………………………….. 29 Figure 4.2c……………………………………………………………………………….. 30 Figure 4.2d……………………………………………………………………………….. 30 Figure 4.3a……………………………………………………………………………….. 31 Figure 4.3b……………………………………………………………………………….. 32 Figure 4.4.1a……………………………………………………………………………... 33 Figure 4.4.1b…………………………………………………………………………….. 33 Figure 4.4.2a……………………………………………………………………………... 34 Figure 4.4.3a……………………………………………………………………………... 35 Figure 4.4.3b……………………………………………………………………………... 36 Figure 4.4.4a……………………………………………………………………………... 36 Figure 4.4.4b……………………………………………………………………………... 37 Figure 4.5.1a……………………………………………………………………………... 38 Figure 4.5.1b……………………………………………………………………………... 38 Figure 4.5.2a……………………………………………………………………………... 39 Figure 4.5.3a……………………………………………………………………………... 40 Figure 4.5.3b……………………………………………………………………………... 40 Figure 4.5.4a……………………………………………………………………………... 41 Figure 4.5.4b……………………………………………………………………………... 41 Figure 5.2a……………………………………………………………………………….. 44 Figure 5.2b……………………………………………………………………………….. 44 Figure 5.3a……………………………………………………………………………….. 45 Figure 5.4a……………………………………………………………………………….. 46 Figure 5.4b……………………………………………………………………………….. 47 Figure 5.4c……………………………………………………………………………….. 47 Figure 5.5a……………………………………………………………………………….. 48 Figure 5.5b……………………………………………………………………………….. 48 Figure 5.5c……………………………………………………………………………….. 49 Figure 5.6a ………………………………………………………………………………. 50 Figure 5.6b……………………………………………………………………………….. 51 Figure 5.6c……………………………………………………………………………….. 51 Figure 5.6d……………………………………………………………………………….. 52 Figure 5.6e……………………………………………………………………………….. 52 Figure 5.7a ………………………………………………………………………………. 53 Figure 5.7b……………………………………………………………………………….. 54 Figure 5.7c……………………………………………………………………………….. 54 Figure 5.7d……………………………………………………………………………….. 55 Figure 5.7e……………………………………………………………………………….. 55 Figure 5.8a……………………………………………………………………………….. 56
v
List of Figures (cont’d)
Figure 5.8b……………………………………………………………………………….. 56 Figure 5.8c……………………………………………………………………………….. 57 Figure 5.9a……………………………………………………………………………….. 58 Figure 5.9b……………………………………………………………………………….. 59 Figure 5.9c……………………………………………………………………………….. 59 Figure 5.9d……………………………………………………………………………….. 60 Figure 5.9e……………………………………………………………………………….. 60 Figure 5.10.1a……………………………………………………………………………. 61 Figure 5.10.1b……………………………………………………………………………. 62 Figure 5.10.2a……………………………………………………………………………. 63 Figure 5.10.2b……………………………………………………………………………. 63
vi
List of Tables
Table 1…………………………………………………………………………………….24 Table 2………………………………………………………………………………….... 26
7
CHAPTER 1: Introduction
1.1 Introduction
The operating range of aeroengine compression systems is limited by two classes of
aerodynamic instabilities known as rotating stall and surge (Emmons et al, 1955). Rotating
stall is a multi-dimensional instability in which regions of low or reversed mass flow (i.e.,
stall cells) propagate around the compressor annulus due to incidence variations on adjacent
airfoils (Greitzer, 1976, 1980, 1981). Surge is primarily a one-dimensional instability of the
entire pumping system (compressor, ducts, combustion chamber, and turbine). It is
characterized by axial pulsations in annulus-averaged mass flow, including periods of flow
reversal through the machine. In high-speed compressor hydrodynamics (Fréchette, 1997),
rotating stall is generally encountered first, which then (loosely) “triggers” surge (often after
a few rotor revolutions, Greitzer, 1976). Therefore, the focus of this work will be on rotating
stall. With either instability, the compression system experiences a substantial loss in
performance and operability, which sometimes result in mechanical failure.
8
Fig. 1.1a Illustration of rotating stall and surge. A sketch of the transient signatures that would be given by high response pressure probes in the compressor (for rotating stall) or in the combustor, or other volume downstream of the compressor (for surge). (Fréchette 1997)
An experience-based approach for avoiding such performance loss is to operate the
compressor at a safe range from the point of instability onset (i.e., with stall margin). The
stall margin ensures that the engine can endure momentary off-design operation. The margin
also reduces the available pressure rise and efficiency of the machine (see Fig 1.1b). It is
proposed here that addition of tailored structural dynamic components or aeromechanical
feedback controllers, locally sensed by unstable perturbations in annulus pressure and
actuated by non-uniformities in the high-speed flow distribution around the annulus, can be
shown to inhibit the inception of rotating stall of high-speed compressor devices. As a result,
the stable operating range will be effectively extended, allowing higher performance
operating conditions.
9
Fig. 1.1b Compressor map illustrating the surge margin (from Fréchette 1997).
Aeromechanical feedback can be loosely defined as the dynamic interaction between
flexible structures and fluid dynamics of the compression system, without external
electromechanical input. When approaching the stall line, flow disturbances induce local
pressures on the structures. When tailored with the appropriate dynamic characteristics, the
structure deforms to counteract flow disturbances, either directly or by modifying the local
unsteady pressure rise of the compressor. High-speed compressor stabilization using
aeromechanical feedback control is investigated here as a passive means of improving
stability so that the compressor can operate safely at lower mass flows. This approach
incorporates tailored structural feedback control within the machine that can alter the fluid
dynamic behavior, so that the performance of the compressor can be extrapolated to
operating ranges outside the empirical database generated by years of experience. Passive
approaches to high-speed compressor stability have received no previous attention in the
open literature. However, some important fundamentals in aeromechanical control of low-
speed devices have been achieved (Gysling and Greitzer, 1995; McGee et al, 2004; Fréchette
et al, 2004).
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1.2 Objectives and Scope of Study
This work presents a systematic development and evaluation of tailored structural
design and aeromechanical feedback stabilization of rotating stall in high-speed axial
compressors. The focus of this research is to evaluate aeromechanical feedback stabilization
strategies of long wave- length, high-speed compressible, modal stall (Fréchette, 1997) that
employ static pressure sensing and structural actuation for dynamic compensation. Ten
aeromechanical feedback stabilization strategies are considered, which generally include: (1)
aeromechanically incorporating variable duct geometries for dynamic impedance control, (2)
dynamically restaggered inlet guide vanes and rotor blades for diffusing or contracting blade
passage control, (3) movable casing walls for dynamic tip clearance flow control, and (4)
dynamic fluid injection for unsteady circumferential flow and pressure rise control across the
compressor. To quantify the effectiveness of the various schemes, the analysis is applied to
two laboratory compressors (ideally modified for high speeds) for which the empirical
modeling inputs have been previously determined: (i) the MIT single-stage compressor
(Gsyling and Greitzer, 1995) and (ii) the MIT three-stage compressor (Haynes et al, 1994).
The proof-of-concept studies of Gysling and Greitzer (1995), McGee et al (2004), and
Fréchette et al (2004) demonstrated the feasibility of aeromechanical control of low-speed
stalled compressors. However, some additional questions remain for high-speed devices. The
motivation of the present modeling development and evaluation is to address three
overarching questions: (1) What is the high-speed stall control capability of other
aeromechanical feedback stabilization strategies, and how do they compare to that modeled
and demonstrated by Gysling and Greitzer (1995), McGee et al (2004), and Frechette et al
(2004)? (2) Are there destabilizing high-speed, compressible fluid-structural interactions
which should be avoided through tailored structural design? (3) How do the aeromechanical
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feedback dynamics couple with the pre-stall compressible fluid dynamics (Fréchette, 1997)
to postpone or induce the inception of high-speed rotating stall?
The significance of the problem posed here is extremely unique and timely. Fluid-
structural interaction effects are not only essential in devising high-speed compressor
stabilization strategies, but also useful in establishing constraints on the structural design of
compressors used by industry. As lightweight, less rigid structures are incorporated into new
high-speed compressor designs, the level of fluid-structure interactions is likely to increase
and result in reduced stall margin if the structures are not properly tailored. The practical
insight and motivation here is to achieve light-weight, more efficient compressor builds using
tailored, less rigid structures, while preventing potential stall margin reductions. There is
therefore a need for broader study evaluating the potential of various passive control schemes
to better assess the effect of aeromechanical interaction on high-speed compressor stability.
The overarching goals of this study are to evaluate the role of flexible structures on
compressor stability, and to elucidate that a proper choice of local structural dynamic
compensation close-coupled to the compressor affects (either beneficially or detrimentally)
the stability of the system. The paper presented here re- introduces the ten aeromechanical
feedback schemes developed by McGee et al (2004) and the nonlinear measured high-speed
compression system dynamics calculated from a MIT single-stage and a MIT three-stage
compressor characteristics employed therein (Fréchette et al, 2004; Gysling and Greitzer,
1995 (MIT single-stage); Haynes et al, 1994 (MIT three-stage)).
1.3 Methodology
An extensive literature review of low-speed and high-speed compressor system
hydrodynamic stability models and aeromechanical feedback approaches for passive control
of such devices was conducted. Specifically, a state-of-the-art high-speed, compressible
12
hydrodynamic model (Fréchette 1997) was examined and extending to a linearized,
compressible structural-hydrodynamic model of stall inception examined herein.
Subsequently, proof-of-concept schemes of aeromechanical control technologies were
developed in order to describe how such feedback can be utilized to stabilize high-speed
compressor stall of axial compressors, and how different tailored structural designs impact
high-speed compression system stability. Optimal structural parameters for aeromechanical
compensators were determined to maximize the stable operating range of the high-speed
compression system. The use of optimized aeromechanical feedback control to stabilize the
system and extend the operating range will be discussed later. The theoretical basis of ten
aeromechanical control schemes examined here was evaluated under a compressible flow
environment. These schemes are broadly classified as: (1) dynamic fluid injection upstream
of the compressor for control of inlet flow non-uniformities, (2) variable compressor inlet
and exit duct geometries for impedance control inside the ducts, (3) flexible compressor
casing wall providing control of tip clearance flow processes, and (4) dynamically re-
staggered inlet guide vanes and rotor blades for control of deviation and dissipation loss
mechanisms.
Completing the evaluation of the aforementioned aeromechanical control
methodologies developed, the low-speed computer codes of McGee et al (2004) was
modified and extended to high-speed, compressible flow regimes. Off-design operation of an
aeromechanically-controlled (or dynamically-compensated) high-speed compressor can
dramatically affect the performance characteristic curve shape of the device. Any change in
inlet conditions can change the discharge pressure and gas horsepower. Besides changing the
characteristic pressure and horsepower curves, the characteristic head curve and the head
curve sensitivity (associated with the stability of the high-speed compressor) also changes.
This phenomenon is due to specific volume or gas density ratio effects and equivalent speed
13
effects on the compressor. Since the performance map curves change with speed (higher
losses at higher speeds), the overall shape of these curves change, which can be compounded
by compressibility (specific volume or gas density ratio) effects closely-coupled with
dynamic compensation associated with aeromechanical feedback controls.
The modified computer codes were utilized in order to construct the essential
performance maps, discharge pressure vs. flow (bringing forth a measure of gas density and
speed changes affecting a dynamically-compensated compressor’s stability).
14
Fig. 2.1a Compressor characteristics used in this study: (a) MIT single stage (Gysling and Greitzer 1995), (b) MIT three-stage (Haynes et al, 1994)
CHAPTER 2: Thermodynamics and the Compressible Rotating Stall Inception Model
2.1 Compressor Characteristic
As previously mentioned, empirical compressor
characteristics associated two low-speed laboratory
compressors were used in this study by way of
simplicity and illustrative purpose of the concepts
proposed herein. Characteristic curves and pressure
loss buckets for the MIT single-stage compressor
(Gysling and Greitzer, 1995) and the MIT three-stage
compressor (Haynes et al, 1994) are shown in Figure
2.1a. The polynomial expressions for the MIT single-
stage compressor are as follows:
94.14.104.1475.5 23 −+−=Ψ φφφts (2-1)
1039.1 +−=Ψ φisen (2-2)
198.0 +−=Ψ φideal (2-3)
The MIT three-stage compressor expressions are:
85.1430.94.10 2 −+−=Ψ φφts (2-4)
15
φφφ
011.1374.3995.8499.7 2 +−+−=Ψisen (2-5) 3559.2547.0 2 +−−=Ψ φφideal (2-6)
φγ
02.1−=∂
Ψ∂ ideal (2-7)
Where, Ψ ,φ , and γ are the pressure rise coefficient, flow coefficient, and stagger angle
respectively.
The thermal loss due to viscous dissipation is estimated by:
tsisenL Ψ−Ψ=φ (2-8)
and the propulsive loss due to blade flow incidence deviation changes was estimated by :
isenidealdL Ψ−Ψ= (2-9)
These compressor characteristics were used to create critical performance maps, which will
be discussed in the proceeding sections. The compressor input parameters are assumed as
follows:
o design shaft speed - 10,000 rpm
o axial velocity ratio - 0.5
o density of atmospheric air - 1.229 kg/m3
o specific heat ratio - 1.4
o atmospheric pressure - 101.3 kPa
Through manipulation of the total- to-static pressure rise coefficient equation shown above
and assuming the given inlet pressure, P1, inlet density, ?o and wheel speed, U, the
performance map for a MIT single-stage and MIT three-stage compressor can be developed.
This map can then be used to evaluate essential thermodynamic properties (Gresh 2001).
First, the exit to inlet pressure ratio must be obtained for the compressor. The total-to-static
pressure rise coefficient equation can be defined as:
16
2
12
21 U
PP
o
ts
ρ
−=Ψ (2-10a)
Solving for P2,
Ψ+= 2
12 21
UPP ots ρ (2-10b)
Finally, dividing by the inlet pressure, yields the pressure ratio
1
2
1
2 21
1P
U
PP ots
Ψ
+=ρ
where P2= pressure at the compressor exit (2-10c)
Now that we have attained the exit-to-inlet pressure ratio, we can now develop the
exit-to- inlet temperature ratio using the laws of thermodynamics for a polytropic process
using the following relation (Gresh 2001):
( ) nn
PP
TT
/1
1
2
1
2
−
= where n=polytropic exponent (2-11)
Finally, the exit-to-inlet density ratio can be found by dividing the pressure ratio by
the temperature ratio (Gresh 2001):
=
1
2
1
2
1
2
TT
PP
ρρ
(2-12)
2.2 Losses and Efficiency
The propulsive pressure loss due to deviation (Ld) was estimated by taking the
difference between the ideal pressure rise characteristic (? ideal) and the isentropic
characteristic (? isen). Similarly, the thermal pressure loss due to viscous dissipation (Lf ) was
estimated from the difference between the isentropic pressure characteristic (? isen) and the
measured total-to-static characteristic (? ts). To obtain a reasonable measure of loss at each
17
speed, both deviation and viscous loss were proportioned appropriately. For example, if the
engine operates at 70 percent design speed, loss is then reduced by 30 percent. Accordingly,
if the engine is sped up to 110 percent design, loss is then increased by 10 percent.
Propulsive, thermal, and overall efficiency can be found by considering the losses.
Thermal efficiency is:
ϕη Lt −= 1 (2-13)
Propulsive efficiency is defined as:
dp L−= 1η (2-14)
The total loss experienced by the compressor is:
ϕLLL dtot += (2-15)
Therefore, the overall efficiency of the compressor can now be simply described as
follows:
tottot L−=1η (2-16)
Now that all efficiencies of the machine have been defined, the work and head can
now be considered (Gresh, 2001). Specifically, propulsive head, thermal head, propulsive
work, and thermal work will be evaluated.
Propulsive head is:
−
−=
−
11
/)1(
1
2
1
1
nn
p PPP
nn
Hρ
(2-17)
Thermal head is:
−
−=
−
11
/)1(
1
2
1
1
kk
t PPP
kk
Hρ
(2-18)
where k=specific heat ratio
Propulsive work is:
18
p
p
HW
=η
(2-19)
Thermal work is:
t
tHW
=
η (2-20)
2 .3 Compressible Rotating Stall Inception Model
The stability model of McGee et al (2004) was similar to the model of Moore and
Greitzer (1986), which was an extension of Emmons’ original work on stall inception in
1955. Emmons theorized that the stall cell starts as a flow separation in a single blade
passage, which causes blockage in the passage. As a result, approaching flow is diverted to
the adjacent blade passage causing the stalled cell to propagate. Circumferentially, the length
of this type of disturbance was short scale, meaning that it was limited to a small number of
blade passages. The more inclusive model of Moore and Greitzer (1986) idealized a multi-
stage compressor mathematically as a two-dimensional, incompressible flow machine of
large hub-to-tip ratio, with three-dimensional unsteady effects at the casing walls. Their
model assumes that the flow and its perturbations are radially uniform. This model also
assumes that the initial harmonic wave-like disturbance is circumferentially longer than that
of the Emmons-type disturbance. As the point of instability is approached, this disturbance
grows in intensity until it becomes a fully developed stall cell. The low-speed model of
McGee et al (2004) captures the same essential physics and mathematics as that of Moore
and Greitzer (1986) with the addition of several aeromechanical feedback stabilization
schemes. McGee’s low-speed stability model, however, made a few simplifying assumptions
such as, constant shaft speed, constant axial velocity, constant density ratio, and constant
19
temperature ratio suggesting that the fluid is incompressible. This notion is fairly valid at
relatively low speeds. However, as the compressor approaches higher speeds this theory
collapses and the fluid is, in fact, compressible. Since the current study involves high-speed
compressible fluid, the low-speed stability model of McGee et al (2004) and Frechette et al
(2004) had to be modified to account for variable shaft speed, variable axial velocity,
variable density ratio, and variable temperature ratio to incorporate compressibility affects.
To achieve this, Fréchette’s (1997) fluidic compressibility parameters were integrated into
the model. These parameters are (Fréchette, 1997):
o axial velocity-density ratio,
1,1
2,2
x
x
VV
AVDRρρ
= (2-21)
o blade row continuity parameter,
21 cI br
+= where 1,
2,
x
x
VV
c = (2-23)
These two compressibility parameters modify the fluidic blade row inertias of McGee
et al (2004) in the rotors, ?, and also in the rotors + stators, µ. The blade row inertia
parameters are now defined as:
AVDRIrcbr
rotors
ox
= ∑ γ
λ2cos/
(2-24)
AVDRIrcbr
statorsrotors
ox
= ∑
+ γµ
2cos/
(2-25)
with cx , ro , and γ representing the axial chord, mean radius, and blade row stagger angle,
respectively.
For low-speed incompressible flow assumptions, the velocity and density are held
constant, thus, the AVDR and Ibr is unity. In addition, the fluidic blade row inertia parameters
(equations 2-24 and 2-25) are identical to the low-speed model of McGee et al (2004) and
20
held constant. In the present study, the Ibr is constant at 0.75 and AVDR is variable due to the
changes in the density ratio.
21
CHAPTER 3: Aeromechanical Feedback Control
3.1 Static Pressure Sensing, H(s)
The structural feedback responds to fluctuations in static pressure in the ducts either
upstream, downstream, or within the compressor depending on the scheme. These unsteady
pressure disturbances are then used to serve as input parameters to the structural controller. A
transfer function for the sensor was developed by McGee et al. (2004) relating the upstream
or downstream velocity with the pressure disturbance. The transfer function is defined as
follows:
Φ+−= um
ssH 2)( where s=iω (3-1)
with m and Fu representing the mth spatial harmonic mode and steady sate upstream axial
flow, respectively. In the present analysis m was set to unity, assuming the instability of the
first harmonic as the initial inception of stalling condition, and Fu was variable. By definition,
the disturbance rotational frequency is:
n
mµ
λω −= where µµ +=mn
4 (3-2)
3.2 Structural Controller, C(s)
22
McGee et al (2004) also developed a transfer function for the structural controller.
This structural controller provides the feedback to the compression system. This controller is
defined as:
22 2
)(QsQs
WsC
++=
ξ (3-3)
with W , Q , and ξ as the mass ratio, frequency ratio, and critical damping ratio, respectively.
In McGee et al (2004) these parameters were restricted to constructible sizes for low-speed
compressor builds using materials that were readily obtainable. In the current high-speed
compressor study, these parameters carry the same restrictions. The constraints restricted the
mass ratio to 583.0=W , the frequency ratio within 9.23.0 ≤≤ Q , and the critical damping
ratio within 9.23.0 ≤≤ Q (Gysling & Greitzer, 1995). These ranges of values for the
frequency and critical damping ratio were chosen to maximize stability in the compression
system and are shown in Figure 3.2a below (McGee et al, 2004; Frechette et al, 2004).
Fig. 3.2a Structural control parameters for maximum stable extension. Optimal structural frequency, Q, and damping ratio, ξ are shown for the various aeromechanical
schemes. (McGee et al, 2004) Note: Time lags are not considered in the present study and the frequency needed to be increased from 0.3 to 1.1 for the 3-stage scheme # 10 in order to achieve reasonable stability.
23
3.3 Effective Slope
In order to delay the inception of stall in the machine, the compression system was
aeromechanically dampened instantly. To achieve this, McGee et al (2004) defined the
“ideal” effective growth rate of the compression system at neutral stability as:
βφφ
cosHCbrts
eff
ts +∂Ψ∂
=
∂Ψ
(3-4a)
with φ∂
Ψ∂ ts representing the slope of the steady-state compressor characteristic and rb
denoting the essential feedback control parameter for this study. The β term measures the
degree to which the fluid is in phase with the structural response of the controller. In this
study we ideally assume that the fluid is 180 degrees out of phase with the structural response
thus reducing the equation to:
HCbrts
eff
ts −∂Ψ∂
=
∂Ψ
φφ (3-4b)
with the term HCbr defined as the ideal control authority. The rb parameter is defined
differently for each scheme. These definitions are presented in Table 2 of the next section.
The equation of the best fit line through the points that create the effective slope versus
corrected flow scatter plot is integrated with a certain initial condition to produce an effective
total-to-static characteristic curve ( )efftsΨ . The initial condition simply implies that ( )efftsΨ
must initially equal ( )tsΨ at stall.
24
Fig. 3.4a Illustration of the ten aeromechanical feedback schemes (McGee et al, 2004)
3.4 Description of Aeromechanical Feedback Stabilization Schemes
The aeromechanical feedback
strategies studied are shown in Fig. 3.4a
and listed in Table 1. They are
categorized as (i) dynamic fluid injection
(with and without exit flow recirculation)
to supplement the axial momentum
entering the compressor, implemented
with a circumferential array of reed valve inj ectors that react to local static pressure (Gysling
and Greitzer, 1995) (Schemes
#1-#4); (ii) movable compressor
inlet and exit duct walls for flow
field impedance control,
potentially implemented as
flexible wall liners or as a
structurally tuned case that
resonates with the pre-stall, local
static pressure fluctuations
(Schemes #5-#7); (iii) flexible
compressor casing wall to
provide dynamic control of rotor tip clearance flow processes, implemented through
structurally- tuned casing or flexible casing treatment (Scheme #8); and (iv) dynamically
restaggered inlet guide vanes and rotor blades, possibly implemented through flexible root
attachments or structurally tuned blades (Schemes #9 & #10). (McGee et al, 2004)
25
The broad range of control schemes are considered without limiting the study to the
most feasible schemes to implement. This provides further insight on the impact of the
interactions between the fluid and structure during the inception of stall. It also indicates
which phenomena are most beneficial or detrimental in stabilizing the compression system.
Different combinations of actuation principles and sensing locations (upstream, downstream,
and average) are investigated. Further design work would be necessary to construct a
practical configuration that implements the most promising approaches.
A schematic of the system considered is shown in Fig. 3.4a. Flow enters through an
inlet duct, a compressor then pumps the flow through an exit duct to a plenum, which then
exhausts through a throttle (not shown) and an exit nozzle (not shown). The aeromechanical
components are integrated at one of the various locations shown. The table shown below
defines the essential feedback control parameter for the current study, br. As mentioned in the
previous section, this br factor is an essential component of the ideal control authority of
McGee et al (2004).
26
*Note that br is divided by µn for all schemes. For schemes #2 and #4 64.0=∂Ψ∂
i
ideal
α, for scheme
#8 8.0=∂
Ψε
ideal , and for scheme #10 ϕγ
02.1−=∂
Ψ∂ ideal (McGee et al, 2004).
Table 2 Essential Feedback Control Parameter, br*
# 1
Φ−Φ+
∂Ψ∂
Φ )(2 uits
i φ
#2 ( )2/ uii
ideal ΦΦ
∂Ψ∂
α
#3
Φ+
∂Ψ∂
Φ )2 iideal
i φ
#4 ( ) uiuii
ideal ΦΦ+ΦΦ
∂Ψ∂
2/ 2
α
#5
Φ−
∂Ψ∂
Φ )2 uideal
u φ
#6 22 uts Φ−Ψ
#7 uts
uts Φ
∂Ψ∂
−Φ−Ψφ
22
#8 ε∂
Ψideal
#9 igvuideal n µλγ
Φ−∂
Ψ 2
#10 γ∂
Ψideal
27
CHAPTER 4: Nonlinear Measured High-Speed Compression System Dynamics
4.1 Introduction
The following data has been produced for the MIT single-stage compressor using the
compressor characteristic of Gysling and Greitzer (1995). Subsequent data was produced for
the MIT three-stage compressor using the characteristic of Haynes et al (1994). The curves
were then manipulated to include aeromechanical feedback for each scheme. A detailed
explanation of findings will be presented using scheme #1 (radially mixed-out injection at the
compressor face) as the basis for discussion. The results for the remaining schemes can be
found in the Appendix section. A new metric called elasticity, which is a non-dimensional
measure of relativeness, will be discussed in the next chapter.
4.2 Corrected Pressure Ratio (Density Ratio)
Figure 4.2a depicts the Corrected Pressure Ratio vs. the Corrected Flow at variable
speed. In order to obtain these “corrected” quantities the pressure was divided by the
temperature ratio (T2/T1) and the flow was divided by the pressure ratio (P2/P1). The
corrected pressure ratio can now be defined as the density ratio. See Section 2.1 Compressor
Characteristic for the development of these quantities. The corrected T2/T1 values on the
opposite side of the y-axis depict lines of constant temperature ratios between the compressor
inlet (T1) and the compressor exit /combustor inlet (T2). Figure 4.2b also represents the
28
Corrected Pressure Ratio vs. the Corrected Flow; however, the values on the opposite side of
the y-axis depict lines of constant corrected T3/T1 ratios between the compressor inlet (T1)
and the combustor exit/turbine inlet (T3). The critical T3/T1 ratio was found to be 1.126 for
the MIT single-stage, as shown in the diagram, because it is the highest T3/T1 temperature
ratio that can be achieved at 70 percent design before the machine begins to stall. This value
was estimated by obtaining the slope from the highest point on the 70 percent corrected
pressure ratio curve to the origin at one. The remaining T3/T1 lines were then proportioned
accordingly. Notice that the safe operating line is not located along the maximum efficiency
line; instead, it is located a safe distance away from the surge line called the stall margin
(recall the discussion in Chapter 1).
The effective surge line with scheme #1 aeromechanical feedback is found in Figure
4.2c and Figure 4.2d. With the new surge line in place, the compressor will now be capable
of operating closer to the original maximum efficiency line. Also, notice how the T2/T1
(compressor exit to compressor inlet) temperature ratio lines shift as a result of the increased
corrected pressure due to the feedback scheme. The T3/T1 (combustor exit to compressor
inlet), however, remains unchanged; but, Figure 4.2d gives a new critical T3/T1 ratio of 1.24,
which is about a 10% increase in temperature.
29
Corrected Pressure Ratio (Density Ratio)
94.7%
95.2%
95.7%
96.2%
96.7%
0.99
1
1.01
1.02
1.03
1.04
1.05
1.06
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Co
rrec
ted
Pre
ssu
re R
atio
(Den
sity
Rat
io)
110% 100% 90% 80% 70% Surge Line
Maximum Efficiency Line
70 80% 90% 100% 110%
102.0E-2
101.5E-2
101.0E-2
100.5E-2
Corrected T2/T1
100.75E-2
101.25E-2
101.75E-2
102.2E-2
Safe Operating Line
Fig. 4.2a Corrected Pressure Ratio & Density ratio versus Corrected Flow of a MIT single stage compressor with lines of constant T2/ T1 temperature ratio.
Corrected Pressure Ratio (Density Ratio)
94.7%
95.2%
95.7%
96.2%
96.7%
0.99
1
1.01
1.02
1.03
1.04
1.05
1.06
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Co
rrec
ted
Pre
ssu
re R
atio
(Den
sity
Rat
io)
110% 100% 90% 80% 70% Surge Line
Maximum Efficiency Line
70 80% 90% 100% 110%
112.6E-2114.0E-2116.0E-2118.0E-2
110.0E-2
108.0E-2
106.0E-2
104.0E-2
102.0E-2
Corrected T3/T1
Safe Operating Line
Fig. 4.2b Corrected Pressure Ratio & Density ratio versus Corrected Flow of a MIT single stage compressor with lines of constant T3/ T1 temperature ratio.
30
Corrected Pressure Ratio (Density Ratio)with Scheme 1 Feedback
94.7%
95.2%
95.7%
96.2%
96.7%
92.6%
93.3%
94.0%
94.6%
95.3%
94.4%
93.6%
92.8%
92.0%
91.2%
1
1.01
1.02
1.03
1.04
1.05
1.06
1.07
0.1 0.15 0.2 0.25 0.3 0.35 0.4
Corrected Flow
Co
rrec
ted
Pre
ssu
re R
atio
(Den
sity
Rat
io)
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line
101.75E-2
101.5E-2
101.25E-2
101.0E-2
100.75E-2
100.5E-2
102.0E-2
102.2E-2
Corrected T2/T1
102.6E-2
102.3E-2
102.0E-2
101.7E-2
101.4E-2
101.1E-2
Fig. 4.2c Corrected Pressure Ratio & Density ratio versus Corrected Flow of a MIT single stage compressor with lines of constant T2/ T1 temperature ratio and aeromechanical feedback.
Corrected Pressure Ratio (Density Ratio)with Scheme 1 Feedback
96.7%
96.2%
95.7%
95.2%
94.7%
95.3%
94.6%
94.0%
93.3%
92.6%
91.2%
92.0%
92.8%
93.6%
94.4%
1
1.01
1.02
1.03
1.04
1.05
1.06
1.07
0.1 0.15 0.2 0.25 0.3 0.35 0.4
Corrected Flow
Co
rrec
ted
Pre
ssu
re R
atio
(D
ensi
ty R
atio
)
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line
112.0E-2
110.0E-2
108.0E-2
106.0E-2
104.0E-2
102.0E-2
114.0E-2
116.0E-2
118.0E-2Corrected T3/T1
120.0E-2122.0E-2124.0E-2126.0E-2
Fig. 4.2 d Corrected Pressure Ratio & Density ratio versus Corrected Flow of a MIT single stage compressor with lines of constant T3/ T1 temperature ratio and aeromechanical feedback.
31
4.3 Compressor Stability
Shown below is the stability of the compression system. It measures the slope of the
MIT single-stage compressor at various speeds. The surge line extends across the horizontal
axis at a value equal to zero. A negative slope means that the compression system is stable
and corresponds to the values below the surge line on Figure 4.3a. Note that the effective
surge line extends to the left of the original surge, thus enabling a dynamically-compensated
compressor using Scheme #1 aeromechanical feedback to reach stability at lower flow as
shown in Figure 4.3b.
Slope of the Pressure Rise Characteristic vs. Corrected Flow
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Slo
pe
110% 100% 90% 80% 70% Surge Line
UNSTABLE
STABLE
Fig. 4.3 a Corrected Compressor Stability versus Corrected Flow of a MIT single-stage compressor.
32
Slope of the Pressure Rise Characteristic vs. Corrected Flowwith Scheme 1 Feedback
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Slo
pe
of
Pre
ssu
re R
ise
Ch
arac
teri
stic
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Eff
ecti
ve S
lop
e o
f Pre
ssu
re R
ise
Ch
arac
teri
stic
110% 100% 90% 80% 70% Surge Line Effective Surge Line
UNSTABLE
STABLE
Fig. 4.3 b Corrected Compressor Stability versus Corrected Flow of a MIT single-stage compressor
with aeromechanical feedback.
4.4 Compressor Efficiency
The efficiency of the compression system can be divided into three categories-
thermal efficiency, propulsive efficiency, and overall efficiency. It should be duly noted,
however, that thermal efficiency is a more useful measure in analyzing high-speed
compressor performance. The efficiency was calculated and plotted using the compressor
characteristic equations. See the Section 2.2 Losses and Efficiency for a description of the
efficienc ies. Aeromechanical feedback causes maximum thermal and overall efficiency at
design speed to be regained by 95.794% and 96.660%, respectively (see Figs. 4.4.1b and
4.4.3b). The propulsive efficiency, however, is shown in Figure 4.4.2 exhibit negligibly small
change with shaft speed. This is because we are assuming the propulsive efficiency is not
affected by changes in the total- to-static pressure rise characteristic, although propulsive
efficiency is assumed to be affected by empirically-measured affected aerodynamic flow
losses due to blade flow incidence deviation changes, whose overall aggregated effects are
considerably smaller by comparison to viscous dissipation losses attributing to the
33
considerably larger thermal efficiency of the Scheme #1 dynamically-compensated
compression system.
4.4.1 Thermal Efficiency (refer to equation 2-13)
Thermal (Dissipation) Efficiency
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
1.05
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Ther
mal
Effi
cien
cy
110% 100% 90% 80% 70% Surge Line
Fig. 4.4.1a Thermal Efficiency versus Corrected Flow of a MIT single-stage compressor at
various speeds.
34
Thermal (Dissipation) Efficiency with Scheme 1 Feedback
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
1.05
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Ther
mal
Effi
cien
cy
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Fig. 4.4.1 b Thermal Efficiency versus Corrected Flow of a MIT single-stage compressor with
aeromechanical feedback at various speeds.
4.4.2 Propulsive Efficiency (refer to equation 2-14)
Propulsive (Deviation) Efficiency
0.94
0.945
0.95
0.955
0.96
0.965
0.97
0.975
0.98
0.985
0.99
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Pro
pulsive
Efficien
cy
110% 100% 90% 80% 70% Surge Line
Fig. 4.4.2a Propulsive efficiency versus Corrected Flow of a MIT single-stage compressor at various
speeds . Note: Propulsive efficiency is not affected by changes in the total-to-static characteristic according
to its definition. Hence, aeromechanical feedback will not affect the propulsive efficiency of the machine.
Refer to section on Losses and Efficiency.
35
4.4.3 Overall Efficiency (refer to equation 2-16)
Overall (Propulsive & Thermal) Efficiency
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Ove
rall
Eff
icie
ncy
110% 100% 90% 80% 70% Surge Line
Fig.4.4.3a Overall efficiency versus Corrected Flow of a MIT single-stage compressor at various
speeds .
36
Overall (Propulsive & Thermal) Efficiency with Scheme 1 Feedback
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Ove
rall
Effi
cien
cy
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Fig.4.4.3 b Overall efficiency versus Corrected Flow of a MIT single-stage compressor with
aeromechanical feedback at various speeds.
4.4.4 Efficiency Ratio (Propulsive/Thermal)
Efficiency (Propulsive/Thermal)
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Effic
iency
Rat
io
110% 100% 90% 80% 70% Surge Line
Fig. 4.4.4a Efficiency Ratio (Propulsive/Thermal) versus Corrected Flow of a MIT single-stage
compressor at various speeds.
37
Efficiency (Propulsive/Thermal) Ratiowith Scheme 1 Feedback
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Eff
icie
ncy
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Fig.4.4.4b Efficiency Ratio (Propulsive/Thermal) versus Corrected Flow of a MIT single-stage
compressor with aeromechanical feedback at various speeds.
4.5 Compressor Losses
The loss of the compression system can be divided into the same three categories as
efficiency- thermal loss, propulsive loss, and overall loss. The loss was calculated and
plotted using the compressor characteristic equations. See the Section 2.2 Losses and
Efficiency for a description of the losses. In accordance with compressor efficiency, notice
that aeromechanical feedback causes loss at design speed to be reduced to 95.794% and
96.660%, respectively (see Figs. 4.5.1b and 4.5.3b). The propulsive loss, however, remains
unchanged because of how it was defined in Section 2.2 Losses and Efficiency. We are
assuming the propulsive loss is not affected by changes in the total-to-static pressure rise
characteristic.
38
4.5.1 Thermal Loss (refer to equation 2-8)
Thermal (Dissipation) Loss
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Th
erm
al L
oss
110% 100% 90% 80% 70% Surge Line
Fig. 4.5.1a Thermal Loss versus Corrected Flow of a MIT single-stage compressor at various speeds.
Thermal (Dissipation) Losswith Scheme 1 Feedback
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Ther
mal
(Dis
sipat
ion)
Loss
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Fig. 4.5.1 b Thermal Loss versus Corrected Flow of a MIT single-stage compressor with aeromechanical
feedback at various speeds.
39
4.5.2 Propulsive Loss (refer to equation 2-9)
Propulsive (Deviation) Loss
0
0.01
0.02
0.03
0.04
0.05
0.06
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Pro
pu
lsiv
e L
oss
110% 100% 90% 80% 70% Surge Line
Fig. 4.5.2a Propulsive Loss versus Corrected Flow of a MIT single-stage compressor at various speeds.
Note: Propulsive loss is not affected by changes in the total-to-static characteristic according to its definition.
Hence, aeromechanical feedback will not affect the propulsive loss of the machine. Refer to section on
Losses and Efficiency.
40
4.5.3 Overall Loss (refer to equation 2-15)
Overall (Propulsive & Thermal) Loss
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Ove
rall
Lo
ss
110% 100% 90% 80% 70% Surge Line
Fig. 4.5.3a Overall Loss versus Corrected Flow of a MIT single-stage compressor at various speeds.
Overall (Propulsive & Thermal) Losswith Scheme 1 Feedback
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Ove
rall
Effic
iency
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Fig. 4.5.3b Overall Loss versus Corrected Flow of a MIT single-stage compressor with aeromechanical
feedback at various speeds.
41
4.5.4 Loss Ratio (Propulsive/Thermal)
Loss Ratio (Propulsive/Thermal)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Lo
ss R
atio
110% 100% 90% 80% 70% Surge Line
Fig. 4.5.4a Loss Ratio (Propulsive/Thermal) versus Corrected Flow of a MIT single-stage compressor
at various speeds.
Loss (Propulsive/Thermal) Ratiowith Scheme 1 Feedback
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Loss
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Fig. 4.5.4 b Loss Ratio (Propulsive/Thermal) versus Corrected Flow of a MIT single-stage compressor
at various speeds.
42
CHAPTER 5: Compressor Elasticity
5.1 Introduction
Compressor elasticity is a measure of the unsteadiness in the compression system.
This chapter will explain how to develop an elasticity quantity. Further explanation is
discussed in the Appendix. This chapter will also demonstrate the affect of aeromechanical
feedback on two elasticity measures (corrected pressure-flow and corrected pressure-density).
The effect of aeromechanical feedback on the other elasticity measures will be le ft for future
study. However, the open- loop (without aeromechanical feedback) results are presented. In
the subsequent sections, findings shown illustrate the unsteadiness of the compression system
with respect to several different thermodynamic properties. Also introduced in this chapter is
the concept of relative non-dimensional flow, which will be briefly explained. Finally, the
chapter ends with presenting the results of the pumping and aeroelastic characteristic for a
gas generator based on the MIT single-stage compressor with and without aeromechanical
feedback. The aeroelastic characteristic was only measured for the corrected pressure-flow
and corrected pressure-density elasticities, the measurement of the other aeroelastic
characteristics are left for future study. The results of other elasticities, pumping, and
aeroelastic characteristics for the MIT single-stage and MIT three-stage compressor for the
remaining schemes can be found in the Appendix.
43
5.2 Corrected Pressure -Flow (Pf ) Elasticity
In order to create an elasticity, or unsteadiness, measure you first need to develop a
relationship between two quantities- in this case corrected pressure ratio and corrected flow.
In Section 4.2 this relationship was formed and plotted (see Fig. 4.2a). Once the relationship
of the corrected pressure ratio and corrected flow has been obtained, the relative change in
the corrected pressure ratio to the relative change in the flow (or the slope of the corrected
pressure ratio vs. corrected flow curve) is measured. This quantity is then multiplied by the
original corrected flow to corrected pressure ratio. The result is a corrected pressure-flow
elasticity quantity. Mathematically, it is:
∆∆
=o
oelasticity P
PP
ϕϕ
ϕ
All other elasticities (other than the corrected pressure-density elasticity) were derived in a
similar manner. See the Appendix for a more general formulation.
Figures 5.2a and 5.2b show the corrected pressure-flow elasticity of a MIT single-
stage compressor at various speeds with and without feedback, respectively. Note the
similarity of the relationship between the slope of the pressure rise characteristic versus
corrected flow (Fig. 4.3b) and the corrected pressure-flow elasticity versus corrected flow
(Fig. 5.2b), which both show scheme #1 feedback enabling stability at lower flow; however,
the slope of the latter is flatter than the slope of the former, which suggests that the corrected
pressure-flow elasticity is less prone to fluctuate when the corrected flow changes.
44
Corrected Pressure- Flow (Pf) Elasticity vs. Corrected Flow
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Co
rrec
ted
Pre
ssu
re-
Flo
w (
Pf)
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line
STABLE
UNSTABLE
Fig. 5.2a Corrected Pressure-Flow Elasticity versus Corrected Flow of a MIT single-stage compressor
at various speeds.
Corrected Pressure-Flow Elasticity (Pf ) with Scheme 1 Feedback
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Co
rrec
ted
Pre
ssu
re-F
low
(Pf)
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line Effective Surge Line
UNSTABLE
STABLE
Fig. 5.2 b Corrected Pressure-Flow Elasticity versus Corrected Flow of a MIT single-stage compressor
with aeromechanical feedback at various speeds.
45
5.3 Corrected Pressure -Density (P?) Elasticity
The corrected pressure-density elasticity is the polytropic exponent, n, and was
derived from the propulsive efficiency, pη , and specific heat ratio, k. It is described as
follows (Gresh 2001):
( )
( ) 11
1
−==
−
−
kk
p
kk
pelasticity nP
η
ηρ
Note that it is assumed that aeromechanical feedback doesn’t affect the corrected
pressure-density elasticity because neither propulsive efficiency nor the specific heat ratio is
affected by changes in the total-to-static pressure characteristic.
Corrected Pressure-Density Elasticity (P?) vs. Corrected Flow
1.405
1.41
1.415
1.42
1.425
1.43
1.435
1.44
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Co
rrec
ted
Pre
ssu
re-D
ensi
ty (P
?) E
last
icit
y
110% 100% 90% 80% 70% Surge Line
Fig. 5.3a Corrected Pressure-Density Elasticity versus Corrected Flow of a MIT single-stage
compressor with aeromechanical feedback at various speeds. Note: Corrected Pressure-Density
Elasticity is not affected by changes in the total-to-static characteristic but rather changes in the polytropic
exponent.
46
5.4 Corrected Pressure-Specific Volume Elasticity (Pv) (see Appendix for basic elasticity derivation)
Since this is the first section where it is derived, it is fitting to discuss the relative
non-dimensional corrected flow. The relative non-dimensional corrected flow is simply a
quantity that measures the relative change in the corrected flow with respect to the original
flow. It is defined as follows:
oϕϕϕ ∆=′
Altering the x-axis from corrected flow to relative non-dimensional corrected flow has
significant consequences; particularly, the surge line becomes almost vertical, which means
that the relative non-dimensional corrected flow at surge is constant (see Fig. 5.4c).
Corrected Pressure Ratio vs. Corrected Specific Volume Ratio(WORK)
0.99
1
1.01
1.02
1.03
1.04
1.05
1.06
0.94 0.95 0.96 0.97 0.98 0.99 1 1.01
Corrected Specific Volume Ratio v2/v1
Co
rrec
ted
Pre
ssu
re R
atio
P2/
P1
100% 110% 90% 80% 70%
Fig. 5.4 a Corrected Pressure Ratio versus Corrected Specific Volume Ratio of a MIT single-stage
compressor at various speeds.
47
Corrected Pressure-Specific Volume (Pv) Elasiticity vs. Corrected Flow
-1.04
-1.02
-1
-0.98
-0.96
-0.94
-0.920 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Corr
ecte
d P
ress
ure
-Spec
ific
Volu
me
(Pv)
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line
Fig. 5.4 b Corrected Pressure-Specific Volume Elasticity versus Corrected Flow of a MIT single-stage
compressor at various speeds.
Corrected Pressure-Specific Volume (Pv) Elasiticity vs. Relative Non-Dimensional Corrected Flow
-1.04
-1.02
-1
-0.98
-0.96
-0.94
-0.920.01 0.012 0.014 0.016 0.018 0.02 0.022 0.024
Relative Non-Dimensional Corrected Flow
Corr
ecte
d P
ress
ure
-Spec
ific
Volu
me
(Pv)
E
lasi
ticity
110% 100% 90% 80% 70% Surge Line
Fig. 5.4c Corrected Pressure-Specific Volume Elasticity versus Relative Non-Dimensional Corrected
Flow of a MIT single-stage compressor at various speeds.
48
5.5 Corrected Pressure-Temperature (PT) Elasticity (see Appendix for basic elasticity derivation)
Corrected Pressure Ratio vs. Temperature Ratio (T2/T1)
0.99
1
1.01
1.02
1.03
1.04
1.05
1.06
0.995 1 1.005 1.01 1.015 1.02 1.025
Temperature Ratio (T2/T1)
Corr
ecte
d P
ress
ure
Rat
io
110% 100% 90% 80% 70%
Fig. 5.5a Corrected Pressure Ratio versus Corrected Temperature Ratio (T2/T1) of a MIT single-stage
compressor at various speeds.
Corrected Pressure- Temperature (PT) Elasticity vs. Corrected Flow
2.46
2.47
2.48
2.49
2.5
2.51
2.52
2.53
2.54
2.55
2.56
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
PT
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line
Fig. 5.5b Corrected Pressure-Temperature Elasticity versus Corrected Flow of a MIT single-stage
compressor at various speeds .
49
Corrected Pressure- Temperature (PT) Elasticity vs. Relative Non-Dimensional Corrected Flow
2.46
2.47
2.48
2.49
2.5
2.51
2.52
2.53
2.54
2.55
2.56
0.01 0.012 0.014 0.016 0.018 0.02 0.022 0.024
Relative Non-Dimensional Corrected Flow
PT
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line
Fig. 5.5c Corrected Pressure-Temperature Elasticity versus Relative Non-Dimensional Corrected Flow
of a MIT single-stage compressor at various speeds.
50
5.6 Corrected Temperature-Loss (Ts) Elasticity (see Appendix for basic elasticity derivation)
The elasticities that contain losses (thermal & propulsive) also have rather interesting
effects- most likely because of the strange relationships that it has with the other
thermodynamic properties in this study. In this section, the corrected temperature ratio (T2/T1)
and losses are compared (see Fig. 5.6a). Note the considerable amount of thermal loss in
comparison to propulsive loss during operation. As a result, it is apparent that when
considering the overall efficiency of the compressor, it is more appropriate to consider the
thermal efficiency versus the propuls ive efficiency of the machine. The peculiar shape of the
temperature ratio versus thermal loss curve leads to asymptotic elasticity curves around the
x-axis (Fig. 5.6b). In addition, because the surge line is also along the x-axis ranging from
about 0.18 to 0.27 in Fig. 5.6b, it becomes a point at about 0.0186 when this axis is altered in
Fig. 5.6c. This phenomenon occurs in a similar manner in all the elasticities that involve loss.
(see Sections 5.7 and 5.9)
Temperature Ratio (T2/T1) vs. Thermal & Propulsive Loss
0.995
1
1.005
1.01
1.015
1.02
1.025
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Loss
Tem
per
atu
re R
atio
110% 100% 90% 80% 70%
(solid) Denotes thermal Loss (dotted) Denotes propulsive Loss
Fig. 5.6a Corrected Temperature Ratio (T2/T1) versus Thermal & Propulsive Loss of a MIT single-
stage compressor at various speeds.
51
Temperature- Thermal Loss (Ts_o) Elasticity vs. Corrected Flow
-0.5
0
0.5
1
1.5
2
2.5
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Ts_
o E
last
icity
110% 100% 90% 80% 70% Surge Line
Fig. 5.6b Corrected Temperature-Thermal Loss Elasticity versus Corrected Flow of a MIT single-stage
compressor at various speeds.
Temperature- Thermal Loss (Ts_o) Elasticity vs. Relative Non-Dimensional Corrected Flow
-0.5
0
0.5
1
1.5
2
2.5
0.01 0.012 0.014 0.016 0.018 0.02 0.022 0.024
Relative Non-Dimensional Corrected Flow
Ts_
o E
last
icity
110% 100% 90% 80% 70% Surge Line
Fig. 5.6c Corrected Temperature-Thermal Loss Elasticity versus Relative Non-dimensional Corrected
Flow of a MIT single-stage compressor at various speeds.
52
Temperature-Propulsive Loss (T_sd) Elasticity vs. Corrected Flow
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
T_s
d E
last
icity
110% 100% 90% 80% 70% Surge Line
Fig. 5.6d Corrected Temperature-Propulsive Loss Elasticity versus Corrected Flow of a MIT single-
stage compressor at various speeds.
Temperature-Propulsive Loss (T_sd) Elasticity vs. Relative Non-Dimensional Corrected Flow
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.01 0.012 0.014 0.016 0.018 0.02 0.022 0.024
Relative Non-Dimensional Corrected Flow
T_sd
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line
Fig. 5.6e Corrected Temperature-Propulsive Loss Elasticity versus Relative Non-Dimensional
Corrected Flow of a MIT single-stage compressor at various speeds.
53
5.7 Corrected Pressure -Loss (Ps) Elasticity Elasticity (see Appendix for basic elasticity derivation)
Corrected Pressure Ratio vs. Thermal & Propusive Loss
0.99
1
1.01
1.02
1.03
1.04
1.05
1.06
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Loss
Co
rrec
ted
Pre
ssu
re R
atio
110% 100% 90% 80% 70%
(solid) Denotes thermal Loss (dotted) Denotes propulsive Loss
Fig. 5.7a Corrected Pressure Ratio versus Thermal & Propulsive Loss of a MIT single-stage
compressor at various speeds.
54
Pressure-Thermal Loss (Ps_o) Elasticity vs Corrected Flow
-1
0
1
2
3
4
5
6
0 0.1 0.2 0.3 0.4 0.5
Corrected Flow
Ps_
o E
last
icity
110% 100% 90% 80% 70% Surge Line
Fig. 5.7b Corrected Pressure-Thermal Loss Elasticity versus Corrected Flow of a MIT single-stage
compressor at various speeds.
Pressure-Thermal Loss (Ps_o) Elasticity vs Relative Non-Dimensional Corrected Flow
-1
0
1
2
3
4
5
6
0.01 0.012 0.014 0.016 0.018 0.02 0.022 0.024
Relative Non-Dimensional Corrected Flow
Ps_
o E
last
icity
110% 100% 90% 80% 70% Surge Line
Fig. 5.7c Corrected Pressure-Thermal Loss Elasticity versus Relative Non-dimensional Corrected Flow
of a MIT single-stage compressor at various speeds.
55
Corrected Pressure-Propulsive Loss (Ps_d) Elasticity vs. Corrected Flow
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Ps_
d E
last
icity
110% 100% 90% 80% 70% Surge Line
Fig. 5.7d Corrected Pressure-Propulsive Loss Elasticity versus Corrected Flow of a MIT single-stage
compressor at various speeds.
Corrected Pressure-Propulsive Loss (Ps_d) Elasticity with respect to Propulsive Loss vs. Relative Non-Dimensional Corrected Flow
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.01 0.012 0.014 0.016 0.018 0.02 0.022 0.024
Relative Non-Dimensional Corrected Flow
Ps_
d E
last
icity
110% 100% 90% 80% 70% Surge Line
Fig. 5.7e Corrected Pressure-Propulsive Loss Elasticity versus Relative Non-Dimensional Corrected
Flow of a MIT single-stage compressor at various speeds.
56
5.8 Corrected Specific Volume-Temperature (vT) Elasticity Elasticity (see Appendix for basic elasticity derivation)
Corrected Specific Volume (v2/v1) vs. Temperature Ratio (T2/T1)
0.94
0.95
0.96
0.97
0.98
0.99
1
1.01
0.995 1 1.005 1.01 1.015 1.02 1.025
Temperature Ratio
Cor
rect
ed S
peci
fic V
olum
e (v
2/v1
)
110% 100% 90% 80% 70%
Fig. 5.8a Corrected Specifc Volume (v2/v1) versus Temperature Ratio (T2/T1) of a MIT single-stage
compressor at various speeds.
Corrected Specific Volume-Temperature (vT) Elasticity vs. Corrected Flow
-2.65
-2.6
-2.55
-2.5
-2.45
-2.40.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
vT E
last
icity
110% 100% 90% 80% 70% Surge Line
Fig. 5.8b Corrected Specifc Volume-Temperature Elasticity versus Corrected Flow of a MIT single-
stage compressor at various speeds.
57
Corrected Specific Volume-Temperature (vT) Elasticity vs. Relative Non-Dimensional Corrected Flow
-2.65
-2.6
-2.55
-2.5
-2.45
-2.4
0.01 0.012 0.014 0.016 0.018 0.02 0.022 0.024
Relative Non-Dimensional Corrected Flow
vT E
last
icity
110% 100% 90% 80% 70% Surge Line
Fig. 5.8c Corrected Specifc Volume -Temperature Elasticity versus Non-dimensional Corrected Flow of
a MIT single-stage compressor at various speeds.
58
5.9 Corrected Specific Volume-Loss (vs) Elasticity Elasticity (see Appendix for basic elasticity derivation)
Corrected Specific Volume Ratio (v2/v1) vs. Thermal & Propulsive Loss
0.94
0.95
0.96
0.97
0.98
0.99
1
1.01
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Loss
Cor
rect
ed S
peci
fic
Vol
ume
Rat
io (
v2/v
1)
110% 100% 90% 80% 70%
(solid) Denotes thermal Loss (dotted) Denotes propulsive Loss
Fig. 5.9a Corrected Specific Volume Ratio (v2/v1) versus Thermal & Propulsive Loss of a MIT single-
stage compressor at various speeds.
59
Corrected Specific Volume-Thermal Loss (vs_o) Elasticity vs Corrected Flow
-6
-5
-4
-3
-2
-1
0
1
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
vs_o
110% 100% 90% 80% 70% Surge Line
Fig. 5.9b Corrected Specific Volume–Thermal Loss Elasticity versus Corrected Flow of a MIT single-
stage compressor at various speeds.
Corrected Specific Volume-Thermal Loss (vs_o) Elasticity vs Relative Non-Dimensional Corrected Flow
-6
-5
-4
-3
-2
-1
0
1
0.01 0.012 0.014 0.016 0.018 0.02 0.022 0.024
Relative Non-Dimensional Corrected Flow
vs_o
110% 100% 90% 80% 70% Surge Line
Fig. 5.9c Corrected Specific Volume–Thermal Loss Elasticity versus Relative Non-dimensional
Corrected Flow of a MIT single-stage compressor at various speeds.
60
Corrected Specific Volume-Propulsive Loss (vs_d) Elasticity vs. Corrected Flow
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
vs_d
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line
Fig. 5.9d Corrected Specific Volume–Propulsive Loss Elasticity versus Corrected Flow of a MIT
single-stage compressor at various speeds.
Corrected Specific Volume-Propulsive Loss (vs_d) Elasticity vs. Relative Non-Dimensional Corrected Flow
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.01 0.012 0.014 0.016 0.018 0.02 0.022 0.024
Relative Non-Dimensional Corrected Flow
vs_d
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line
Fig. 5.9e Corrected Specific Volume–Propulsive Loss Elasticity versus Relative Non-dimensional
Corrected Flow of a MIT single-stage compressor at various speeds.
61
5.10 Pumping and Aeroelastic Characteristics. Using the compressor map in Section 5.1
the pumping characteristic of a gas generator can be determined. In a similar manner the
aeroelastic characteristic with respect to density and flow can also be determined. The
purpose of these characteristics is to reveal the changes that occur to certain quantities when
the engine changes speed. The changes in corrected pressure ratio, corrected temperature
ratio, and corrected flow were measured at stall. The changes in these quantities at maximum
efficiency before and after stall were also compared.
5.10.1 Pumping Characteristic.
Compression System Pumping Characteristicat Maximum Efficiency & Stall
1
1.01
1.02
1.03
1.04
1.05
1.06
70% 80% 90% 100% 110%
Corrected Speed
Co
rrec
ted
Pre
ssu
re &
T
emp
erat
ure
Rat
ios
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Co
rrec
ted
Flo
w
Pressure Ratio @ Maximum Efficiency Temperature Ratio @ Maximum Efficiency
Pressure Ratio @ Surge Temperature Ratio @ Surge
Flow @ Maximum Efficiency Flow @ Surge
Design Line
Corrected T3/T1= 1.126
Fig. 5.10.1a Pumping Characteristic for a gas generator based on a MIT single-stage compressor.
62
Compression System Pumping Characteristicat Maximum Efficiency & Stall with Scheme 1 Feedback
1
1.01
1.02
1.03
1.04
1.05
1.06
70% 80% 90% 100% 110%
Corrected Speed
Co
rrec
ted
Pre
ssu
re &
T
emp
erat
ure
Rat
ios
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Co
rrec
ted
Flo
w
Pressure Ratio @ Maximum Efficiency Temperature Ratio @ Maximum Efficiency
Pressure Ratio @ Surge Temperature Ratio @ Surge
Flow @ Maximum Efficiency Flow @ Surge
Design Line
X Denotes Effective Surge Line - - Denotes Effective Maximum Efficiency
Corrected T3/T1= 1.24
Fig. 5.10.1b Pumping Characteristic for a gas generator based on a MIT single-stage compressor with
aeromechanical feedback .
63
5.10.2 Aeroelastic Characteristic.
Compression System Aeroelastic Characteristicsat Maximum Efficiency & Stall
1.41
1.412
1.414
1.416
1.418
1.42
1.422
1.424
1.426
70% 75% 80% 85% 90% 95% 100% 105% 110%
Corrected Speed
Co
rrec
ted
Pre
ssu
re-D
ensi
ty (
P?
) A
ero
elas
tici
ty
-0.45
-0.35
-0.25
-0.15
-0.05
0.05
0.15
0.25
0.35
0.45
Co
rrec
ted
Pre
ssu
re-F
low
(P
f)
Aer
oel
asti
city
P? Elasticity @ Stall P? Elasticity @ Maximum EfficiencyPf Elasticity @ Stall Design LinePf Elasticity @ Maximum Efficiency
Corrected T3/T1= 1.126
Corrected T2/T1= 1.01
Fig. 5.10.2a Aeroelastic Characteristic for a gas generator based on a MIT single-stage compressor.
Compression System Aeroelastic Characteristicsat Maximum Efficiency & Stall with Scheme 1 Feedback
1.41
1.412
1.414
1.416
1.418
1.42
1.422
1.424
1.426
70% 75% 80% 85% 90% 95% 100% 105% 110%
Corrected Speed
Corr
ecte
d P
ress
ure
-Den
sity
(P?) A
eroel
astic
ity
-0.45
-0.35
-0.25
-0.15
-0.05
0.05
0.15
0.25
0.35
0.45
Corr
ecte
d P
ress
ure
-Flo
w (P
f) A
eroel
astic
ity
P? Elasticity @ Stall P? Elasticity @ Maximum EfficiencyPf Elasticity & Effective Pf Elasticity @ Stall Design LinePf Elasticity @ Maximum Efficiency Effective Pf @ Max Efficiency
Note: Effective E_density= E_density
Corrected T3/T1= 1.24
Corrected T2/T1= 1.0139
Fig. 5.10.2 b Aeroelastic Characteristic for a gas generator based on a MIT single-stage compressor
with aeromechanical feedback.
64
CHAPTER 6: Summary and Future Work
6.1 Summary
General methods were developed in this work to evaluate passive high-speed
stabilization of two laboratory gas generator devices - the MIT single-stage and MIT three-
stage compressors. A high-speed compressible rotating stall inception model was developed
and compressible flow was analyzed along with the effects of changes in its thermodynamic
properties. Ten passive stabilization schemes that could potentially be used by industry were
discussed and examined in a high-speed compressible flow environment. The concept of
elasticity was introduced and implemented to examine the effects of flow non-uniformity,
entropic loss, and unsteadiness on thermodynamic state changes within the compression
system. Finally, pumping and aeroelastic characteristics of these laboratory compressors
both with and without feedback were analyzed.
65
6.1 Future Work
In the present research, we were able to answer two questions that lingered for high-
speed aeroengine devices: (1) Are there high speed fluid-structural interactions associated
flow non-uniformity, entropic loss, and unsteadiness, which can be avoided using tailored
structural design to dynamically compensate compression systems through aeromechanical
feedback passive control? (2) How do aeromechanical feedback dynamics combine with the
pre-stall compressible fluid dynamics to postpone or induce the inception of high-speed
rotating stall of aeroengine compressors? However, two additional questions still remain: (1)
What are other stabilization schemes associated with geometry, steady flow, fluidic
compressibility, and operating performance of high-speed (compressible flow) compressors
and engines in contrast to those fundamental to low-speed (incompressible flow) devices? (2)
How do changes in the parameters that govern the pre-stall dynamics affect the stability of
not only the compression system, but also the matching components (compressor, combustion,
turbine) of the entire pumping system of the engine?
It is proposed here that in addition to the ten aeromechanical schemes presented in the
current research, other innovative aeromechanical schemes exist, through a careful sensitivity
analysis on geometric, steady flow, fluidic compressibility, and operating performance
parameters that can indeed inhibit the inception of rotating stall in high-speed engine devices.
As a result, the stable operating range will be effectively extended, allowing higher
performance operating conditions.
In order to achieve the goals presented in this proposal, a reduced-order model of
fluid-structure interaction inside an axial compressor system used in modern aircraft engines
has been devised. First, proof-of-concept schemes of innovative aeromechanical control
technologies to describe how such feedback can be utilized to stabilize high-speed
compressor stall of axial compressors, and how different tailored structural designs impact
66
high-speed compression system stability will be developed. Optimal structural parameters for
these unique aeromechanical compensators will be determined to maximize the stable
operating range of the high-speed compression system. The use of optimized aeromechanical
feedback control to stabilize the system and extend the operating range will be discussed.
The theoretical basis of additional control methods examined here will be evaluated under a
compressible flow environment. To complete the evaluation of the aeromechanical control
methodologies developed, a sensitivity analysis of the parameters that govern the pre-stall
dynamics will be conducted. Thirteen input parameters are required in a high-speed
compressor stall inception model, which include: geometry, steady flow values, fluidic
compressibility, and overall performance slopes of the compressor device. Specifically these
parameters are (Fréchette, 1997):
1. Geometry
o axial chords (cx/ro)
o stagger angles ( γ )
2. Steady flow values
o inlet axial flow coeffient (ϕ )
o inlet swirl angle ( inα )
o axial velocity ratios (1
2
ϕϕ )
o density ratios (1
2ρρ )
3. Overall compressor performance slopes
o overall pressure rise sensitivity to inlet flow coefficient ( ϕ∂Ψ∂ ts )
o overall pressure rise sensitivity to inlet swirl angle (in
tsαtan∂
Ψ∂ )
o last blade row deviation sensitivity to inlet flow coefficient ( ϕα
∂∂ extan )
67
o last blade row deviation sensitivity to inlet swirl angle (in
exαα
tantan
∂∂ )
4. Fluidic Compressibility Parameters
o axial velocity-density ratio (AVDR)
o axial momentum ratio (Y)
o blade row continuity parameter (Ibr)
These parameters are all part of Fréchette’s extended stability model which is:
+
+
−=
µ
ϕσ
nAVDR
dYnTS exIR
1,
2
where:
in
tsintsRTS
αϕα
ϕ tantan
∂Ψ∂
∂−
∂Ψ∂=
in
exexI n
dαα
ϕ tantan1
, ∂∂
=
AVDRIrcbr
statorsrotors
ox
= ∑
+ γµ
2cos/
1,1
2,2
x
x
VV
AVDRρρ
=
2
11,
2,
x
x
br
VV
I+
=
2
1,
2,
1
2
=
x
x
VV
Yρρ
Differentiating this extended stability equation with respect to each of these
parameters results in the following:
1. Geometry
68
o axial chords (cx/ro)
( )
++
−−=
∂∂
γµ
ϕσ22
,2
cos1
AVDR
nAVDR
dYnTS exIR
rc
ox
o stagger angles ( γ )
( ) AVDRIr
c
nAVDR
dYnTSbr
o
x
exIR
++
−=
∂∂
γµ
ϕ
γσ
22
,2
cos1
2. Steady flow values
o inlet axial flow coefficient (ϕ )
( ) 2
,2
1
12tan
tan
++
++
−
∂Ψ∂
=∂∂
µ
µϕαϕ
α
ϕσ
nAVDR
nAVDRYdn exI
in
tsin
o inlet swirl angle ( inα )
( )
++
∂
Ψ∂
−=∂
∂
µ
αϕα
σ
nAVDR
in
ts
in 1
tan1
tan
o axial velocity ratios (1
2
ϕϕ )
( )
[ ]
2
1
22
1
2,
2,
1
22
1
21
cos112
12
++
++
−−
++
−
=∂
∂
µ
ϕϕ
γρρ
ϕµϕϕ
ϕ
σ
ϕϕ
nAVDR
rc
ndYnTS
nAVDRdn o
x
exIRexI
69
o density ratios (1
2ρρ )
( )
[ ]
2
21
2,
2,
2
1
2
1
cos11
12
+
+
+
−−
+
+
−
=∂
∂
µ
γϕϕ
ϕµϕϕ
σ
ρρ
nAVDR
Ir
c
ndYnTS
nAVDR
dn bro
x
exIRexI
3. Overall performance slopes
o overall pressure rise sensitivity to inlet flow coefficient ( ϕ∂Ψ∂ ts )
( ) 21
1
++
=∂∂
∂Ψ∂
µ
σ
ϕ
nAVDR
ts
o overall pressure rise sens itivity to inlet swirl angle (in
ts
αtan∂Ψ∂ )
( )
++
−=∂
∂
∂Ψ∂
µ
ϕα
σ
α
nAVDR
in
in
ts 1
tan
tan
o last blade row deviation sensitivity to inlet flow coefficient ( ϕα
∂∂ extan )
( ) 0tan
=∂
∂
∂∂
ϕα
σex
o last blade row deviation sensitivity to inlet swirl angle (in
ex
αα
tantan
∂∂ )
( )
++
−=∂
∂
∂∂
µ
ϕσ
αα
nAVDR
Y
in
ex 1tantan
4. Fluidic Compressibility Parameters
o axial velocity-density ratio (AVDR)
70
( )
[ ]
2
2,2
1
cos1
++
+−−
=∂
∂
µ
γϕ
σ
nAVDR
Ir
c
ndYnTS
AVDR
bro
x
exIR
o axial momentum ratio (Y)
( )[ ]
++
−=∂∂
µ
ϕσ
nAVDR
dnY
exI
1,
2
o blade row continuity parameter (Ibr)
( )
[ ]
2
2,2
1
cos
++
−−
=∂∂
µ
γϕ
σ
nAVDR
AVDRr
c
dYnTS
I
o
x
exIR
br
which is the basis for the sensitivity analysis posed.
71
References Emmons, H.W., Pearson, C.E., and Grant, H.P., 1955, “Compressor Surge and Stall Propagation,” Trans. ASME, 77, pp. 455-469. Frechette, L.G., 1997, “Implications of Stability Modeling for High-Speed Axial Compressor Design,” Master Thesis, Department of Aeronautics and Astronautics, M.I.T., Cambridge, MA. Frechette, L.G., McGee, O.G., and Graf, M.B., 2004, “Tailored Structural Design and Aeromechanical Control of Axial Compressor Stall – Part II: Evaluation of Approaches,” ASME J. Turbomachinery, 126, pp. 63-72. Greitzer, E.M., 1976, “Surge and Rotating Stall in Axial Flow Compressors, Part I & II,” ASME J. Eng. Power, 99, pp. 190-217. Greitzer, E.M., 1980, “Review: Axial Compressor Stall Phenomenon,” ASME J. Fluids Eng., 102, pp. 134-151. Greitzer, E.M., 1981, “The Stability of Pumping Systems, The 1980 Freeman Scholar Lecture,” ASME J. Fluids Eng., 103, pp. 193-242. Gresh, M. Theodore, 2001, “Compressor Performance: Aerodynamics for the User,” Butterworth & Heinemann, Boston. Gysling, D.L., and Greitzer, E.M., 1995, “Dynamic Control of Rotating Stall in Axial Flow Compressors Using Aeromechanical Feedback,” ASME J. Turbomachinery, 117, pp. 307-319. Haynes, J.M., Hendricks, G.J., and Epstein, A.H., 1994, “Active Stabilization of Rotating Stall in a Three-Stage Axial Compressor, “ ASME J. Turbomachinery, 116, pp. 226-239. McGee, O.G., Graf, M.B., and Frechette, L.G., 2004, “Tailored Structural Design and Aeromechanical Control of Axia l Compressor Stall – Part I: Development of Models and Metrics, ASME J. Turbomachinery, 126, pp. 63-72. McGee, O.G. and Coleman, K.L., 2006a, “Aeromechanical Control of High-Speed Axial Compressor Stall and Engine Performance– Part I: Development of Models, to be submitted, ASME J. Turbomachinery. Coleman, K.L. and McGee, O.G., 2006b, “Aeromechanical Control of High-Speed Axial Compressor Stall and Engine Performance– Part II: Evaluation of Approaches, to be submitted, ASME J. Turbomachinery.
72
APPENDIX
A.1 Introduction This appendix contains the formulation of the elasticity concept and the results of the
nonlinear measured high-speed compression sys tem dynamics for the MIT single-stage and
MIT three-stage compressor for schemes #1-#8 and schemes #1-#10 (including the open-
loop problem), respectively.
73
A.2 Basic Elasticity Formulation
Step 1: Begin with a relationship between two quantities, X and Y.
X vs. Y
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
X
Y
Fig. A.2 Plot of the relationship between X and Y.
Step 2: Find the slope, m, of the XY relationship.
XYm
∆∆=
Step 3: Multiply the slope at point (X,Y) by the X to Y ratio at that point to obtain a
cross-elasticity measure .
=
YX
mYX elasticity
74
A.3 Additional Nonlinear Measured High Speed Compression System Dynamics
MIT 1 Scheme 2
Corrected Pressure Ratio (Density Ratio)with Scheme 2 Feedback
94.7%
95.2%
95.7%
96.2%
96.7%
97.0%
96.6%
96.2%
95.7%
95.3%
92.6%
93.3%
94.0%
94.6%
95.3%
1
1.02
1.04
1.06
1.08
1.1
1.12
0.08 0.13 0.18 0.23 0.28 0.33 0.38
Corrected Flow
Co
rrec
ted
Pre
ssu
re R
atio
(Den
sity
Rat
io)
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line
Corrected T2/T1
10.75E-2
101.25E-2
101.75E-2
102.2E-2
104.1E-2
103.8E-2
103.5E-2103.2E-2
102.9E-2
102.6E-2
Corrected Pressure Ratio (Density Ratio)
with Scheme 2 Feedback
94.7%
95.2%
95.7%
96.2%
96.7%
97.0%
96.6%
96.2%
95.7%
95.3%
92.6%
93.3%94.0%
94.6%95.3%
1
1.02
1.04
1.06
1.08
1.1
1.12
0.08 0.13 0.18 0.23 0.28 0.33 0.38
Corrected Flow
Co
rrec
ted
Pre
ssu
re R
atio
(Den
sity
Rat
io)
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line116.0E-2
112.0E-2
108.0E-2
104.0E-2
Corrected T3/T1
120.0E-2
124.0E-2
128.0E-2
132.0E-2140.0E-2166.0E-2 148.0E-2156.0E-2
Efficiency (Propulsive/Thermal) Ratio
with Scheme 2 Feedback
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Eff
icie
ncy
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line Loss (Propulsive/Thermal) Ratio
with Scheme 2 Feedback
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Loss
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Work (Propulsive/Thermal) Ratiowith Scheme 2 Feedback
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
0 0.05 0.1 0.15 0 . 2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Wor
k R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line Head (Propulsive/Thermal) Ratio
with Scheme 2 Feedback
0.9999
1
1.0001
1.0002
1.0003
1.0004
1.0005
1.0006
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Hea
d R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line Pressure-Flow and Pressure-Density Cross-Elasticities
with Scheme 2 Feedback
1.405
1.41
1.415
1.42
1.425
1.43
1.435
1.44
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Co
rrec
ted
Pre
ssu
re-D
ensi
ty E
last
icity
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
Co
rrec
ted
Pre
ssu
re-F
low
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Pressure-Flow
Pressure-Density
Propulsive (Deviation) Efficiency and Loss
with Scheme 2 Feedback
0.94
0.95
0.96
0.97
0.98
0.99
1
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Pro
pu
lsiv
e E
ffic
ien
cy
0
0.01
0.02
0.03
0.04
0.05
0.06P
ropu
lsiv
e Lo
ss
110% 100% 90% 80% 70% Surge Line
Propulsive Efficiency
Propulsive Loss
75
Thermal (Dissipation) Efficiency and Losswith Scheme 2 Feedback
0
0.2
0.4
0.6
0.8
1
1.2
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Th
erm
al E
ffic
ien
cy
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Thermal Efficiency
Thermal Loss
Overall (Propulsive & Thermal) Efficiency and Loss
with Scheme 2 Feedback
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Ove
rall
Eff
icie
ncy
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Ove
rall
Lo
ss
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Overall Efficiency
Overall Loss
Compression System Aeroelastic Characteristics
at Maximum Efficiency & Stall
1.41
1.412
1.414
1.416
1.418
1.42
1.422
1.424
1.426
0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1
Corrected Speed
Co
rrec
ted
Pre
ssu
re-D
ensi
ty A
ero
elas
tici
ty
-0.45
-0.35
-0.25
-0.15
-0.05
0.05
0.15
0.25
0.35
0.45
Co
rrec
ted
Pre
ssu
re-F
low
Aer
oel
astic
ity
E_Density @ Stall E_Density @ Maximum EfficiencyE_Flow & Effective E_Flow @ Stall Design Line
E_Flow @ Maximum Efficiency Effective E_Flow @ Maximum Efficiency
Note: Effective E_density= E_density
Corrected T3/T1= 1.66
Corrected T2/T1= 1.03
Compression System Pumping Characteristic
at Maximum Efficiency & Stall
1
1.02
1.04
1.06
1.08
1.1
1.12
0.7 0.8 0.9 1 1.1
Corrected Speed
Co
rrec
ted
Pre
ssu
re &
T
emp
erat
ure
Rat
ios
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Co
rrec
ted
Flo
w
Pressure Ratio @ Maximum Efficiency Temperature Ratio @ Maximum Efficiency
Pressure Ratio @ Surge Temperature Ratio @ Surge
Flow @ Maximum Efficiency Flow @ Surge
Design Line
X Denotes Effective Surge Line - - Denotes Effective Maximum Efficiency Line
Corrected T3/T1= 1.66
Dynamically Compensated Compression System Stability
with Scheme 2 Feedback
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Slo
pe o
f P
ress
ure
Ris
e C
hara
cter
istic
s
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Eff
ectiv
e S
lop
e o
f Pre
ssu
re R
ise
Ch
arac
teri
stic
s
110% 100% 90% 80% 70% Surge Line Effective Surge Line
UNSTABLE
STABLE
76
MIT 1 Scheme 3
Corrected Pressure Ratio (Density Ratio)with Scheme 3 Feedback
96.7%
96.2%
95.7%
95.2%
94.7%
94.9%
95.4%
95.8%
96.3%
96.8%
95.3%
94.6%
94.0%
93.3%
92.6%
1
1.01
1.02
1.03
1.04
1.05
1.06
1.07
1.08
1.09
0.1 0.15 0.2 0.25 0.3 0.35 0.4
Corrected Flow
Co
rrec
ted
Pre
ssu
re R
atio
(D
ensi
ty R
atio
)
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line
Corrected T2/T1
101.75E-2
101.25E-2
101.75E-2
102.2E-2
103.0E-2
102.5E-2
102.0E-2
101.5E-2
Corrected Pressure Ratio (Density Ratio)
with Scheme 3 Feedback
96.7%
96.2%
95.7%
95.2%
94.7%
94.9%
95.4%
95.8%
96.3%
96.8%
95.3%
94.6%
94.0%
93.3%
92.6%
1
1.01
1.02
1.03
1.04
1.05
1.06
1.07
1.08
0.1 0.15 0.2 0.25 0.3 0.35 0.4
Corrected Flow
Co
rrec
ted
Pre
ssu
re R
atio
(Den
sity
Rat
io)
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line
118.0E-2
116.0E-2
114.0E-2
112.0E-2
110.0E-2
108.0E-2
106.0E-2
104.0E-2
102.0E-2
Corrected T3/T1
133.0E-2 128.0E-2 124.0E-2 120.0E-2
Efficiency (Propulsive/Thermal) Ratio
with Scheme 3 Feedback
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Eff
icie
ncy
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line Loss (Propulsive/Thermal) Ratio
with Scheme 3 Feedback
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Loss
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Work (Propulsive/Thermal) Ratiowith Scheme 3 Feedback
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
0 0.05 0.1 0.15 0 . 2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Wor
k R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line Head (Propulsive/Thermal) Ratio
with Scheme 3 Feedback
0.99995
1
1.00005
1.0001
1.00015
1.0002
1.00025
1.0003
1.00035
1.0004
1.00045
1.0005
0 0.05 0.1 0.15 0.2 0.25 0 . 3 0.35 0.4 0.45 0.5
Corrected Flow
Hea
d R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line Pressure-Flow and Pressure-Density Cross-Elasticities
with Scheme 3 Feedback
1.405
1.41
1.415
1.42
1.425
1.43
1.435
1.44
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Co
rrec
ted
Pre
ssu
re-D
ensi
ty E
last
icity
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
Co
rrec
ted
Pre
ssu
re-F
low
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Pressure-Flow
Pressure-Density
Propulsive (Deviation) Efficiency and Loss
with Scheme 3 Feedback
0.94
0.95
0.96
0.97
0.98
0.99
1
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Pro
pu
lsiv
e E
ffic
ien
cy
0
0.01
0.02
0.03
0.04
0.05
0.06
Pro
puls
ive
Loss
110% 100% 90% 80% 70% Surge Line
Propulsive Efficiency
Propulsive Loss
77
Thermal (Dissipation) Efficiency and Losswith Scheme 3 Feedback
0
0.2
0.4
0.6
0.8
1
1.2
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Th
erm
al E
ffic
ien
cy
0
0.1
0.2
0.3
0.4
0.5
0.6
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Thermal Efficiency
Thermal Loss
Overall (Propulsive & Thermal) Efficiency and Loss
with Scheme 3 Feedback
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Ove
rall
Eff
icie
ncy
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Ove
rall
Lo
ss
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Overall Efficiency
Overall Loss
Compression System Aeroelastic Characteristics
at Maximum Efficiency & Stall
1.41
1.412
1.414
1.416
1.418
1.42
1.422
1.424
1.426
0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1
Corrected Speed
Co
rrec
ted
Pre
ssu
re-D
ensi
ty A
ero
elas
tici
ty
-0.45
-0.35
-0.25
-0.15
-0.05
0.05
0.15
0.25
0.35
0.45
Co
rrec
ted
Pre
ssu
re-F
low
Aer
oel
astic
ity
E_Density @ Stall E_Density @ Maximum EfficiencyE_Flow & Effective E_Flow @ Stall Design Line
E_Flow @ Maximum Efficiency Effective E_Flow @ Maximum Efficiency
Note: Effective E_density= E_density
Corrected T3/T1= 1.33
Corrected T2/T1= 1.018
Compression System Pumping Characteristic
at Maximum Efficiency & Stall
1
1.01
1.02
1.03
1.04
1.05
1.06
0.7 0.8 0.9 1 1.1
Corrected Speed
Co
rrec
ted
Pre
ssu
re &
T
emp
erat
ure
Rat
ios
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Co
rrec
ted
Flo
w
Pressure Ratio @ Maximum Efficiency Temperature Ratio @ Maximum Efficiency
Pressure Ratio @ Surge Temperature Ratio @ Surge
Flow @ Maximum Efficiency Flow @ Surge
Design Line
X Denotes Effective Surge Line - - Denotes Effective Maximum Efficiency Line
Corrected T3/T1= 1.33
Dynamically Compensated Compression System Stability
with Scheme 3 Feedback
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Slo
pe o
f P
ress
ure
Ris
e C
hara
cter
istic
s
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Eff
ectiv
e S
lop
e o
f Pre
ssu
re R
ise
Ch
arac
teri
stic
s
110% 100% 90% 80% 70% Surge Line Effective Surge Line
UNSTABLE
STABLE
78
MIT 1 Scheme 4
Corrected Pressure Ratio (Density Ratio)with Scheme 4 Feedback
94.7%
95.2%
95.7%
96.2%
96.7%
95.6%
95.0%
94.3%
93.7%
93.1%
92.6%
93.3%94.0%
94.6%95.3%
1
1.02
1.04
1.06
1.08
1.1
1.12
0.1 0.15 0.2 0.25 0.3 0.35 0.4
Corrected Flow
Cor
rect
ed P
ress
ure
Rat
io (
Den
sity
Rat
io)
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line
Corrected T2/T1
100.75E-2
101.25E-2
101.75E-2
102.2E-2
143.0E-2
140.0E-2
136.0E-2
132.0E-2
128.0E-2
Corrected Pressure Ratio (Density Ratio)
with Scheme 4 Feedback
96.7%
96.2%
95.7%
95.2%
94.7%
93.1%
93.7%
94.3%
95.0%
95.6%
95.3%94.6%
94.0%
93.3%
92.6%
1
1.02
1.04
1.06
1.08
1.1
1.12
0.1 0.15 0.2 0.25 0.3 0.35 0.4
Corrected Flow
Co
rrec
ted
Pre
ssu
re R
atio
(Den
sity
Rat
io)
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Maximum Efficiency Line
120.0E-2
116.0E-2
112.0E-2
108.0E-2
104.0E-2
Corrected T3/T1
Safe Operating Line
124.0E-2
128.0E-2
132.0E-2140.0E-2148.0E-2166.0E-2 156.0E-2
Efficiency (Propulsive/Thermal) Ratio
with Scheme 4 Feedback
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Eff
icie
ncy
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line Loss (Propulsive/Thermal) Ratio
with Scheme 4 Feedback
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Loss
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Work (Propulsive/Thermal) Ratiowith Scheme 4 Feedback
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
0 0.05 0.1 0.15 0 . 2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Wor
k R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line Head (Propulsive/Thermal) Ratio
with Scheme 4 Feedback
0.9999
1
1.0001
1.0002
1.0003
1.0004
1.0005
1.0006
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Hea
d R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line Pressure-Flow and Pressure-Density Cross-Elasticities
with Scheme 4 Feedback
1.405
1.41
1.415
1.42
1.425
1.43
1.435
1.44
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Co
rrec
ted
Pre
ssu
re-D
ensi
ty E
last
icity
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
Co
rrec
ted
Pre
ssu
re-F
low
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Pressure-Flow
Pressure-
Propulsive (Deviation) Efficiency and Loss
with Scheme 4 Feedback
0.94
0.95
0.96
0.97
0.98
0.99
1
0 0.05 0 . 1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Pro
pu
lsiv
e E
ffic
ien
cy
0
0.01
0.02
0.03
0.04
0.05
0.06
Pro
puls
ive
Loss
110% 100% 90% 80% 70% Surge Line
Propulsive Efficiency
Propulsive Loss
79
Thermal (Dissipation) Efficiency and Losswith Scheme 4 Feedback
0
0.2
0.4
0.6
0.8
1
1.2
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Th
erm
al E
ffic
ien
cy
0
0.1
0.2
0.3
0.4
0.5
0.6
Th
erm
al L
oss
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Thermal Efficiency
Thermal Loss
Overall (Propulsive & Thermal) Efficiency and Loss
with Scheme 4 Feedback
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Ove
rall
Eff
icie
ncy
0
0.1
0.2
0.3
0.4
0.5
0.6
Ove
rall
Lo
ss
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Overall Efficiency
Overall Loss
Compression System Aeroelastic Characteristics
at Maximum Efficiency & Stall
1.41
1.412
1.414
1.416
1.418
1.42
1.422
1.424
1.426
0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1
Corrected Speed
Co
rrec
ted
Pre
ssu
re-D
ensi
ty A
ero
elas
tici
ty
-0.45
-0.35
-0.25
-0.15
-0.05
0.05
0.15
0.25
0.35
0.45
Co
rrec
ted
Pre
ssu
re-F
low
Aer
oel
astic
ity
E_Density @ Stall E_Density @ Maximum EfficiencyE_Flow & Effective E_Flow @ Stall Design Line
E_Flow @ Maximum Efficiency Effective E_Flow @ Maximum Efficiency
Note: Effective E_density= E_density
Corrected T3/T1= 1.66
Corrected T2/T1= 1.30
Compression System Pumping Characteristic
at Maximum Efficiency & Stall
1
1.02
1.04
1.06
1.08
1.1
1.12
0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1
Corrected Speed
Co
rrec
ted
Pre
ssu
re &
T
emp
erat
ure
Rat
ios
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Co
rrec
ted
Flo
w
Pressure Ratio @ Maximum Efficiency Temperature Ratio @ Maximum Efficiency
Pressure Ratio @ Surge Temperature Ratio @ Surge
Flow @ Maximum Efficiency Flow @ Surge
Design Line
X Denotes Effective Surge Line - - Denotes Effective Maximum Efficiency Line
Corrected T3/T1= 1.66
Dynamically Compensated Compression System Stability
with Scheme 4 Feedback
- 2
-1.5
- 1
-0.5
0
0.5
1
1.5
2
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Slo
pe
of
Pre
ssu
re R
ise
Ch
arac
teri
stic
s
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Eff
ectiv
e S
lop
e o
f Pre
ssu
re R
ise
Ch
arac
teri
stic
s
110% 100% 90% 80% 70% Surge Line Effective Surge Line
UNSTABLE
STABLE
80
MIT 1 Scheme 5
Corrected Pressure Ratio (Density Ratio)with Scheme 5 Feedback
96.7%
96.2%
95.7%
95.2%
94.7%
95.3%
94.6%
94.0%
93.3%
92.6%
1
1.01
1.02
1.03
1.04
1.05
1.06
0.1 0.15 0.2 0.25 0.3 0.35 0.4
Corrected Flow
Co
rrec
ted
Pre
ssu
re R
atio
(D
ensi
ty R
atio
)
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line
Corrected T2/T1
102.0E-2
101.5E-2
101.0E-2
100.5E-2
100.75E-2
101.25E-2
101.75E-2
102.2E-2
Corrected Pressure Ratio (Density Ratio)
with Scheme 5 Feedback
94.7%
95.2%
95.7%
96.2%
96.7%
92.6%
93.3%
94.0%
94.6%
95.3%
1
1.01
1.02
1.03
1.04
1.05
1.06
0.1 0.15 0.2 0.25 0.3 0.35 0.4
Corrected Flow
Co
rrec
ted
Pre
ssu
re R
atio
(Den
sity
Rat
io)
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line
118.0E-2 116.0E-2
114.0E-2
112.3E-2
110.0E-2
108.0E-2
106.0E-2
104.0E-2
102.0E-2
Corrected T3/T1
Efficiency (Propulsive/Thermal) Ratio
with Scheme 5 Feedback
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Eff
icie
ncy
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line Loss (Propulsive/Thermal) Ratio
with Scheme 5 Feedback
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Loss
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Work (Propulsive/Thermal) Ratiowith Scheme 5 Feedback
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
0 0.05 0.1 0.15 0 . 2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Wor
k R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line Head (Propulsive/Thermal) Ratio
with Scheme 5 Feedback
0.99995
1
1.00005
1.0001
1.00015
1.0002
1.00025
1.0003
1.00035
1.0004
1.00045
0 0.05 0.1 0.15 0.2 0.25 0 . 3 0.35 0.4 0.45 0.5
Corrected Flow
Hea
d R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line Pressure-Flow and Pressure-Density Cross-Elasticities
with Scheme 5 Feedback
1.405
1.41
1.415
1.42
1.425
1.43
1.435
1.44
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Co
rrec
ted
Pre
ssu
re-D
ensi
ty E
last
icity
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Co
rrec
ted
Pre
ssu
re-F
low
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Pressure-Flow
Pressure-Density
Propulsive (Deviation) Efficiency and Loss
with Scheme 5 Feedback
0.94
0.95
0.96
0.97
0.98
0.99
1
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Pro
pu
lsiv
e E
ffic
ien
cy
0
0.01
0.02
0.03
0.04
0.05
0.06
Pro
puls
ive
Loss
110% 100% 90% 80% 70% Surge Line
Propulsive Efficiency
Propulsive Loss
81
Thermal (Dissipation) Efficiency and Losswith Scheme 5 Feedback
0
0.2
0.4
0.6
0.8
1
1.2
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Th
erm
al E
ffic
ien
cy
0
0.1
0.2
0.3
0.4
0.5
0.6
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Thermal Efficiency
Thermal Loss
Overall (Propulsive & Thermal) Efficiency and Loss
with Scheme 5 Feedback
0
0.2
0.4
0.6
0.8
1
1.2
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Ove
rall
Eff
icie
ncy
0
0.1
0.2
0.3
0.4
0.5
0.6
Ove
rall
Lo
ss
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Overall Efficiency
Overall Loss
Compression System Aeroelastic Characteristics
at Maximum Efficiency & Stall
1.41
1.412
1.414
1.416
1.418
1.42
1.422
1.424
1.426
0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1
Corrected Speed
Co
rrec
ted
Pre
ssu
re-D
ensi
ty A
ero
elas
tici
ty
-0.45
-0.35
-0.25
-0.15
-0.05
0.05
0.15
0.25
0.35
0.45
Co
rrec
ted
Pre
ssu
re-F
low
Aer
oel
astic
ity
E_Density @ Stall E_Density @ Maximum EfficiencyE_Flow & Effective E_Flow @ Stall Design Line
E_Flow @ Maximum Efficiency Effective E_Flow @ Maximum Efficiciency
Note: Effective E_density= E_density
Corrected T3/T1= 1.123
Corrected T2/T1= 1.010
Compression System Pumping Characteristic
at Maximum Efficiency & Stall
1
1.01
1.02
1.03
1.04
1.05
1.06
0.7 0.8 0.9 1 1.1
Corrected Speed
Co
rrec
ted
Pre
ssu
re &
T
emp
erat
ure
Rat
ios
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Co
rrec
ted
Flo
w
Pressure Ratio @ Maximum Efficiency Temperature Ratio @ Maximum Efficiency
Pressure Ratio @ Surge Temperature Ratio @ Surge
Flow @ Maximum Efficiency Flow @ Surge
Design Line
X Denotes Effective Surge Line - - Denotes Effective Maximum Efficiency Line
Corrected T3/T1= 1.123
Dynamically Compensated Compression System Stability
with Scheme 5 Feedback
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Slo
pe o
f P
ress
ure
Ris
e C
hara
cter
istic
s
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Eff
ectiv
e S
lop
e o
f Pre
ssu
re R
ise
Ch
arac
teri
stic
s
110% 100% 90% 80% 70% Surge Line Effective Surge Line
UNSTABLE
STABLE
82
MIT 1 Scheme 6
Corrected Pressure Ratio (Density Ratio)with Scheme 6 Feedback
96.7%
96.2%
95.7%
95.2%
94.7%
95.3%
94.6%
94.0%
93.3%
92.6%
1
1.01
1.02
1.03
1.04
1.05
1.06
0.1 0.15 0.2 0.25 0.3 0.35 0.4
Corrected Flow
Co
rrec
ted
Pre
ssu
re R
atio
(Den
sity
Rat
io)
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line
Corrected T3/T1
118.0E-2 116.0E-2
114.0E-2
112.3E-2
110.0E-2
108.0E-2
106.0E-2
104.0E-2
102.0E-2
Efficiency (Propulsive/Thermal) Ratio
with Scheme 6 Feedback
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Eff
icie
ncy
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line Loss (Propulsive/Thermal) Ratio
with Scheme 6 Feedback
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Loss
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line Work (Propulsive/Thermal) Ratio
with Scheme 6 Feedback
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
0 0.05 0.1 0.15 0 . 2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Wor
k R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Head (Propulsive/Thermal) Ratiowith Scheme 6 Feedback
0.99995
1
1.00005
1.0001
1.00015
1.0002
1.00025
1.0003
1.00035
1.0004
1.00045
0 0.05 0.1 0.15 0.2 0.25 0 . 3 0.35 0.4 0.45 0.5
Corrected Flow
Hea
d R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line Pressure-Flow and Pressure-Density Cross-Elasticities
with Scheme 6 Feedback
1.405
1.41
1.415
1.42
1.425
1.43
1.435
1.44
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Co
rrec
ted
Pre
ssu
re-D
ensi
ty E
last
icity
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Co
rrec
ted
Pre
ssu
re-F
low
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Pressure-Flow
Pressure-Density
Propulsive (Deviation) Efficiency and Loss
with Scheme 6 Feedback
0.94
0.95
0.96
0.97
0.98
0.99
1
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Pro
pu
lsiv
e E
ffic
ien
cy
0
0.01
0.02
0.03
0.04
0.05
0.06
Pro
puls
ive
Loss
110% 100% 90% 80% 70% Surge Line
Propulsive Efficiency
Propulsive Loss
Thermal (Dissipation) Efficiency and Loss
with Scheme 6 Feedback
0
0.2
0.4
0.6
0.8
1
1.2
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Th
erm
al E
ffic
ien
cy
0
0.1
0.2
0.3
0.4
0.5
0.6
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Thermal Efficiency
Thermal Loss
83
Overall (Propulsive & Thermal) Efficiency and Losswith Scheme 6 Feedback
0
0.2
0.4
0.6
0.8
1
1.2
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Ove
rall
Eff
icie
ncy
0
0.1
0.2
0.3
0.4
0.5
0.6
Ove
rall
Lo
ss
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Overall Efficiency
Overall Loss
Compression System Aeroelastic Characteristics
at Maximum Efficiency & Stall
1.41
1.412
1.414
1.416
1.418
1.42
1.422
1.424
1.426
0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1
Corrected Speed
Co
rrec
ted
Pre
ssu
re-D
ensi
ty A
ero
elas
tici
ty
-0.45
-0.35
-0.25
-0.15
-0.05
0.05
0.15
0.25
0.35
0.45
Co
rrec
ted
Pre
ssu
re-F
low
Aer
oel
astic
ity
E_Density @ Stall E_Density @ Maximum EfficiencyE_Flow & Effective E_Flow @ Stall Design Line
E_Flow @ Maximum Efficiency Effective E_Flow @ Maximum Efficiency
Note: Effective E_density= E_density
Corrected T3/T1= 1.123
Corrected T2/T1= 1.010
Compression System Pumping Characteristic
at Maximum Efficiency & Stall
1
1.01
1.02
1.03
1.04
1.05
1.06
0.7 0.8 0.9 1 1.1
Corrected Speed
Co
rrec
ted
Pre
ssu
re &
T
emp
erat
ure
Rat
ios
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Co
rrec
ted
Flo
w
Pressure Ratio @ Maximum Efficiency Temperature Ratio @ Maximum Efficiency
Pressure Ratio @ Surge Temperature Ratio @ Surge
Flow @ Maximum Efficiency Flow @ Surge
Design Line
X Denotes Effective Surge Line - - Denotes Effective Maximum Efficiency Line
Corrected T3/T1= 1.123
Dynamically Compensated Compression System Stability
with Scheme 6 Feedback
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Slo
pe o
f P
ress
ure
Ris
e C
hara
cter
istic
s
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Eff
ectiv
e S
lop
e o
f Pre
ssu
re R
ise
Ch
arac
teri
stic
s
110% 100% 90% 80% 70% Surge Line Effective Surge Line
UNSTABLE
STABLE
84
MIT 1 Scheme 7
Corrected Pressure Ratio (Density Ratio)with Scheme 7 Feedback
96.7%
96.2%
95.7%
95.2%
94.7%
95.3%
94.6%
94.0%
93.3%
92.6%
1
1.01
1.02
1.03
1.04
1.05
1.06
0.1 0.15 0.2 0.25 0.3 0.35 0 . 4
Corrected Flow
Co
rrec
ted
Pre
ssu
re R
atio
(Den
sity
Rat
io)
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line
Corrected T2/T1
102.0E-2
101.5E-2
101.0E-2
100.5E-2
100.75E-2
101.25E-2
101.75E-2
102.2E-2
Corrected Pressure Ratio (Density Ratio)
with Scheme 7 Feedback
96.7%
96.2%
95.7%
95.2%
94.7%
95.3%
94.6%
94.0%
93.3%
92.6%
1
1.01
1.02
1.03
1.04
1.05
1.06
0.1 0.15 0.2 0.25 0.3 0.35 0.4
Corrected Flow
Co
rrec
ted
Pre
ssu
re R
atio
(Den
sity
Rat
io)
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line
118.0E-2 116.0E-2
114.0E-2
112.3E-2
110.0E-2
108.0E-2
106.0E-2
104.0E-2
102.0E-2
Corrected T3/T1
Efficiency (Propulsive/Thermal) Ratio
with Scheme 7 Feedback
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Eff
icie
ncy
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line Loss (Propulsive/Thermal) Ratio
with Scheme 7 Feedback
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Loss
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Work (Propulsive/Thermal) Ratiowith Scheme 7 Feedback
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
0 0.05 0.1 0.15 0 . 2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Wor
k R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line Head (Propulsive/Thermal) Ratio
with Scheme 7 Feedback
0.99995
1
1.00005
1.0001
1.00015
1.0002
1.00025
1.0003
1.00035
1.0004
1.00045
0 0.05 0.1 0.15 0.2 0.25 0 . 3 0.35 0.4 0.45 0.5
Corrected Flow
Hea
d R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line Pressure-Flow and Pressure-Density Cross-Elasticities
with Scheme 7 Feedback
1.405
1.41
1.415
1.42
1.425
1.43
1.435
1.44
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Co
rrec
ted
Pre
ssu
re-D
ensi
ty E
last
icity
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Co
rrec
ted
Pre
ssu
re-F
low
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Pressure-Flow
Pressure-Density
Propulsive (Deviation) Efficiency and Loss
with Scheme 7 Feedback
0.94
0.95
0.96
0.97
0.98
0.99
1
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Pro
pu
lsiv
e E
ffic
ien
cy
0
0.01
0.02
0.03
0.04
0.05
0.06
Pro
puls
ive
Loss
110% 100% 90% 80% 70% Surge Line
Propulsive Efficiency
Propulsive Loss
85
Thermal (Dissipation) Efficiency and Losswith Scheme 7 Feedback
0
0.2
0.4
0.6
0.8
1
1.2
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Th
erm
al E
ffic
ien
cy
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Thermal Efficiency
Thermal Loss
Overall (Propulsive & Thermal) Efficiency and Loss
with Scheme 7 Feedback
0
0.2
0.4
0.6
0.8
1
1.2
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Ove
rall
Eff
icie
ncy
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Ove
rall
Lo
ss
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Overall Efficiency
Overall Loss
Compression System Aeroelastic Characteristics
at Maximum Efficiency & Stall
1.41
1.412
1.414
1.416
1.418
1.42
1.422
1.424
1.426
0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1
Corrected Speed
Co
rrec
ted
Pre
ssu
re-D
ensi
ty A
ero
elas
tici
ty
-0.45
-0.35
-0.25
-0.15
-0.05
0.05
0.15
0.25
0.35
0.45
Co
rrec
ted
Pre
ssu
re-F
low
Aer
oel
astic
ity
E_Density @ Stall E_Density @ Maximum EfficiencyE_Flow & Effective E_Flow @ Stall Design Line
E_Flow @ Maximum Efficiency Effective E_Flow @ Maximum Efficiency
Corrected T3/T1= 1.123
Note: Effective E_density= E_density
Corrected T2/T1= 1.010
Compression System Pumping Characteristic
at Maximum Efficiency & Stall
1
1.01
1.02
1.03
1.04
1.05
1.06
0.7 0.8 0.9 1 1.1
Corrected Speed
Co
rrec
ted
Pre
ssu
re &
T
emp
erat
ure
Rat
ios
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Co
rrec
ted
Flo
w
Pressure Ratio @ Maximum Efficiency Temperature Ratio @ Maximum Efficiency
Pressure Ratio @ Surge Temperature Ratio @ Surge
Flow @ Maximum Efficiency Flow @ Surge
Design Line
X Denotes Effective Surge Line - - Denotes Effective Maximum Efficiency Line
Corrected T3/T1= 1.123
Dynamically Compensated Compression System Stability
with Scheme 7 Feedback
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Slo
pe o
f P
ress
ure
Ris
e C
hara
cter
istic
s
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Eff
ectiv
e S
lop
e o
f Pre
ssu
re R
ise
Ch
arac
teri
stic
s
110% 100% 90% 80% 70% Surge Line Effective Surge Line
UNSTABLE
STABLE
86
MIT 1 Scheme 8
Corrected Pressure Ratio (Density Ratio)with Scheme 8 Feedback
94.7%
95.2%
95.7%
96.2%
96.7%
92.6%
93.3%
94.0%
94.6%
95.3%
1
1.01
1.02
1.03
1.04
1.05
1.06
0.1 0.15 0 . 2 0.25 0.3 0.35 0.4
Corrected Flow
Co
rrec
ted
Pre
ssu
re R
atio
(Den
sity
Rat
io)
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line
Corrected T2/T1
102.0E-2
101.5E-2
101.0E-2
100.5E-2
100.75E-2
101.25E-2
101.75E-2
102.2E-2
Corrected Pressure Ratio (Density Ratio)
with Scheme 8 Feedback
94.7%
95.2%
95.7%
96.2%
96.7%
92.6%
93.3%
94.0%
94.6%
95.3%
1
1.01
1.02
1.03
1.04
1.05
1.06
0.1 0.15 0.2 0.25 0.3 0.35 0.4
Corrected Flow
Co
rrec
ted
Pre
ssu
re R
atio
(Den
sity
Rat
io)
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line
118.0E-2 116.0E-2
114.0E-2
112.3E-2
110.0E-2
108.0E-2
106.0E-2
104.0E-2
102.0E-2
Corrected T3/T1
Efficiency (Propulsive/Thermal) Ratio
with Scheme 8 Feedback
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Eff
icie
ncy
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line Loss (Propulsive/Thermal) Ratio
with Scheme 8 Feedback
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Loss
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Work (Propulsive/Thermal) Ratiowith Scheme 8 Feedback
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
0 0.05 0.1 0.15 0 . 2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Wor
k R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line Head (Propulsive/Thermal) Ratio
with Scheme 8 Feedback
0.99995
1
1.00005
1.0001
1.00015
1.0002
1.00025
1.0003
1.00035
1.0004
1.00045
0 0.05 0.1 0.15 0.2 0.25 0 . 3 0.35 0.4 0.45 0.5
Corrected Flow
Hea
d R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line Pressure-Flow and Pressure-Density Cross-Elasticities
with Scheme 8 Feedback
1.405
1.41
1.415
1.42
1.425
1.43
1.435
1.44
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Co
rrec
ted
Pre
ssu
re-D
ensi
ty E
last
icity
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Co
rrec
ted
Pre
ssu
re-F
low
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Pressure-Flow
Pressure-
Propulsive (Deviation) Efficiency and Loss
with Scheme 8 Feedback
0.94
0.95
0.96
0.97
0.98
0.99
1
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Pro
pu
lsiv
e E
ffic
ien
cy
0
0.01
0.02
0.03
0.04
0.05
0.06
Pro
puls
ive
Loss
110% 100% 90% 80% 70% Surge Line
Propulsive Efficiency
Propulsive Loss
87
Thermal (Dissipation) Efficiency and Losswith Scheme 8 Feedback
0
0.2
0.4
0.6
0.8
1
1.2
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Th
erm
al E
ffic
ien
cy
0
0.1
0.2
0.3
0.4
0.5
0.6
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Thermal Efficiency
Thermal Loss
Overall (Propulsive & Thermal) Efficiency and Loss
with Scheme 8 Feedback
0
0.2
0.4
0.6
0.8
1
1.2
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Ove
rall
Eff
icie
ncy
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Ove
rall
Lo
ss
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Overall Efficiency
Overall Loss
Compression System Aeroelastic Characteristics
at Maximum Efficiency & Stall
1.41
1.412
1.414
1.416
1.418
1.42
1.422
1.424
1.426
0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1
Corrected Speed
Co
rrec
ted
Pre
ssu
re-D
ensi
ty A
ero
elas
tici
ty
-0.45
-0.35
-0.25
-0.15
-0.05
0.05
0.15
0.25
0.35
0.45
Co
rrec
ted
Pre
ssu
re-F
low
Aer
oel
astic
ity
E_Density @ Stall E_Density @ Maximum EfficiencyE_Flow & Effective E_Flow @ Stall Design Line
E_Flow @ Maximum Efficiency Effective E_Flow @ Maximum Efficiency
Corrected T3/T1= 1.123
Note: Effective E_density= E_density
Corrected T2/T1= 1.010
Compression System Pumping Characteristic
at Maximum Efficiency & Stall
1
1.01
1.02
1.03
1.04
1.05
1.06
0.7 0.8 0.9 1 1.1
Corrected Speed
Co
rrec
ted
Pre
ssu
re &
T
emp
erat
ure
Rat
ios
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Co
rrec
ted
Flo
w
Pressure Ratio @ Maximum Efficiency Temperature Ratio @ Maximum Efficiency
Pressure Ratio @ Surge Temperature Ratio @ Surge
Flow @ Maximum Efficiency Flow @ Surge
Design Line
X Denotes Effective Surge Line - - Denotes Effective Maximum Efficiency Line
Corrected T3/T1= 1.123
Dynamically Compensated Compression System Stability
with Scheme 7 Feedback
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Slo
pe o
f P
ress
ure
Ris
e C
hara
cter
istic
s
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Eff
ectiv
e S
lop
e o
f Pre
ssu
re R
ise
Ch
arac
teri
stic
s
110% 100% 90% 80% 70% Surge Line Effective Surge Line
UNSTABLE
STABLE
88
MIT 3 Open Loop
Corrected Pressure Ratio (Density Ratio)
59%
55%
63%
67%
71%
0.98
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
Corrected Flow
Cor
rect
ed P
ress
ure
Rat
io (
Den
sity
Rat
io)
110% 100% 90% 80% 70% Surge Line
Maximum Efficiency Line
70 80% 90% 100% 110%
105.0E-2
104.0E-2
103.0E-2
102.0E-2
101.0E-2
Corrected T2/T1
Corrected Pressure Ratio (Density Ratio)
59%
55%
63%
67%
71%
0.98
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
Corrected Flow
Co
rrec
ted
Pre
ssu
re R
atio
(Den
sity
Rat
io)
110% 100% 90% 80% 70% Surge Line
Maximum Efficiency Line
70%
80% 90% 100% 110%
130.0E-2
135.0E-2139.4E-2145.0E-2
125.0E-2
120.0E-2
115.0E-2
110.0E-2
105.0E-2
Corrected T3/T1
Efficiency (Propulsive/Thermal) Ratio
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Eff
icie
ncy
Rat
io
110% 100% 90% 80% 70% Surge Line
Loss (Propulsive/Thermal) Ratio
0.6
0.8
1
1.2
1.4
1.6
1.8
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Loss
Rat
io
110% 100% 90% 80% 70% Surge Line
Work (Propulsive/Thermal) Ratio
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Wor
k R
atio
110% 100% 90% 80% 70% Surge Line
Head (Propulsive/Thermal) Ratio
0.998
1
1.002
1.004
1.006
1.008
1.01
1.012
1.014
1.016
1.018
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Hea
d R
atio
110% 100% 90% 80% 70% Surge Line Pressure-Density Elasticity vs. Corrected Flow
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Pre
ssu
re-D
ensi
ty E
last
icity
110% 100% 90% 80% 70% Surge Line Pressure-Flow Elasticity vs. Corrected Flow
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Pre
ssu
re-F
low
Ela
stic
ity
110% 100% 90% 80% 70%
89
Propulsive Efficiency
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Pro
pu
lsiv
e E
ffic
ien
cy
110% 100% 90% 80% 70% Surge Line Propulsive (Deviation) Loss
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Pro
pu
lsiv
e L
oss
110% 100% 90% 80% 70% Surge Line Thermal Efficiency
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Ther
mal
Eff
icie
ncy
110% 100% 90% 80% 70% Surge Line Thermal (Viscous) Loss
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Ther
mal
Los
s
110% 100% 90% 80% 70% Surge Line
Overall (Propulsive & Thermal) Efficiency
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Ove
rall
Eff
icie
ncy
110% 100% 90% 80% 70% Surge Line Overall (Viscous+Dissipation) Loss
0
0.2
0.4
0.6
0.8
1
1.2
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Ove
rall
Loss
110% 100% 90% 80% 70% Surge Line Compression System Aeroelastic Characteristics
at Maximum Efficiency & Stall
1.5
1.55
1.6
1.65
1.7
1.75
1.8
1.85
70% 75% 80% 85% 90% 95% 100% 105% 110%
Corrected Speed
Co
rrec
ted
Pre
ssu
re-D
ensi
ty A
ero
elas
tici
ty
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Co
rrec
ted
Pre
ssu
re-F
low
Aer
oel
asti
city
E_Density @ Maximum Efficiency E_Density @ Stall E_Flow @ StallDesign Line E_Flow @ Maximum Efficiency
Corrected T3/T1= 1.394
Note: Effective E_density= E_density
Compressor System Pumping Characteristic
at Maximum Efficiency & Stall
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
70% 75% 80% 85% 90% 95% 100% 105% 110%Corrected Speed
Co
rrec
ted
Pre
ssu
re &
Tem
per
atu
re
Rat
ios
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Co
rrec
ted
Flo
w
Temperature Ratio @ Maximum Efficiency Temperature Ratio @ SurgePressure Ratio @ Maximum Efficiency Pressure Ratio @ SurgeFlow @ Maximum Efficiency Flow @ SurgeDesign Line
Corrected T3/T1= 1.394
90
Temperature Ratio vs. Entropy
0.99
1
1.01
1.02
1.03
1.04
1.05
1.06
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Entropy
Tem
pera
ture
Rat
io
110% 100% 90% 80% 70% Temperature- Propulsive Loss (Ts_d) Elasticity with respect to Propulsive Loss vs.
Corrected Flow
-4-3.5
-3
-2.5
-2
-1.5
-1
-0.50
0.5
1
1.5
0 0.1 0.2 0.3 0.4 0.5
Corrected Flow
Ts_d
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line Temperature- Propulsive Loss (Ts_d) Elasticity with respect to Propulsive Loss vs. Relative Non-Dimensional Corrected Flow
-4-3.5
-3-2.5
-2-1.5
-1-0.5
00.5
11.5
0 0.1 0.2 0.3 0.4 0.5
Relative Non-Dimensional Corrected Flow
Ts_
d E
last
icity
110% 100% 90% 80% 70% Surge Line Temperature-Viscous Loss (Ts_o) Elasticity with respect to Viscous Loss vs.
Corrected Flow
-2
0
2
4
6
8
10
12
14
16
18
20
0 0.1 0.2 0.3 0.4 0.5
Corrected Flow
Ts_
o E
last
icity
110% 100% 90% 80% 70% Surge Line
Temperature-Viscous Loss (Ts_o) Elasticity with respect to Viscous Loss vs. Relative Non-Dimensional Corrected Flow
-2
0
2
4
6
8
10
12
14
16
18
20
0 0.005 0.01 0.015 0.02 0.025 0.03
Relative Non-Dimensional Corrected Flow
Ts_o
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line Corrected Specific Volume Ratio (v2/v1) vs. Entropy
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
1.02
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Entropy
Co
rrec
ted
Sp
ecif
ic V
olu
me
Rat
io (v
2/v1
)
110% 100% 90% 80% 70% Corrected Specific Volume-Propulsive Loss (vs_d) Elasticity with respect to Propulsive Loss vs.
Corrected Flow
-4
-2
0
2
4
6
8
10
0 0.1 0.2 0.3 0.4 0.5
Corrected Flow
vs_d
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line Corrected Specific Volume-Propulsive Loss (vs_d) Elasticity with respect to
Propulsive Loss vs. Relative Non-Dimensional Corrected Flow
-4
-2
0
2
4
6
8
10
0 0.005 0.01 0.015 0.02 0.025 0.03
Relative Non-Dimensional Corrected Flow
vs_d
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line
91
Corrected Specific Volume-Viscous Loss (vs_o) Elasticity with respect to Viscous Loss vs. Corrected Flow
-50
-40
-30
-20
-10
0
10
0 0.1 0.2 0.3 0.4 0.5
Corrected Flow
vs_o
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line Corrected Specific Volume-Viscous Loss (vs_o) Elasticity with respect to
Viscous Loss vs. Relative Non-Dimensional Corrected Flow
-50
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
5
0 0.1 0.2 0.3 0.4 0.5
Relative Non-Dimensional Corrected Flow
vs_o
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line Corrected Specific Volume Ratio (v2/v1) vs. Temperature Ratio (T2/T1)
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
1.02
0.99 1 1.01 1.02 1.03 1.04 1.05 1.06
Temperature Ratio
Co
rrec
ted
Sp
ecif
ic V
olu
me
Rat
io (v
2/v1
)
110% 100% 90% 80% 70% Corrected Specific Volume-Temperature (vT) Elasticity with respect to
Temperature vs. Corrected Flow
-2.9
-2.8
-2.7
-2.6
-2.5
-2.4
-2.3
-2.2
-2.1
-2
0 0.1 0.2 0.3 0.4 0.5
Corrected Flow
vT E
last
icity
110% 100% 90% 80% 70% Surge Line
Corrected Specific Volume-Temperature (vT) Elasticity with respect to Temperature vs. Relative Non-Dimensional Corrected Flow
-2.9
-2.8
-2.7
-2.6
-2.5
-2.4
-2.3
-2.2
-2.1
-20 0.005 0.01 0.015 0.02 0.025 0.03
Relative Non-Dimensional Corrected Flow
vT E
last
icity
110% 100% 90% 80% 70% Surge Line Corrected Pressure Ratio vs. Entropy
0.98
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Entropy
Co
rrec
ted
Pre
ssu
re R
atio
110% 100% 90% 80% 70%
(solid) Denotes thermal Loss (dotted) Denotes propulsive Loss
Pressure-Propusive Loss (Ps_d) Elasticity with respect to Propulsive Loss
vs. Corrected Flow
-10
-8
-6
-4
-2
0
2
4
0 0.1 0.2 0.3 0.4 0.5
Corrected Flow
Ps_
d E
last
icity
110% 100% 90% 80% 70% Surge Line Pressure-Propusive Loss (Ps_d) Elasticity with respect to Propulsive Loss vs.
Relative Non-Dimensional Corrected Flow
-10
-8
-6
-4
-2
0
2
4
0 0.005 0.01 0.015 0.02 0.025 0.03
Relative Non-Dimensional Corrected Flow
Ps_
d E
last
icity
110% 100% 90% 80% 70% Surge Line
92
Pressure-Viscous Loss (Ps_o) Elasticity with respect to Viscous Loss vs. Corrected Flow
-5
0
5
10
15
20
25
30
35
40
45
50
0 0.1 0.2 0.3 0.4 0.5
Corrected Flow
Ps_
o E
last
icity
110% 100% 90% 80% 70% Surge Line Pressure-Viscous Loss (Ps_o) Elasticity with respect to Viscous Loss vs.
Relative Non-Dimensional Corrected Flow
-5
0
5
10
15
20
25
30
35
40
45
50
0 0.005 0.01 0.015 0.02 0.025 0.03
Relative Non-Dimensional Corrected Flow
Ps_
o E
last
icity
110% 100% 90% 80% 70% Surge Line Corrected Pressure vs. Temperature Ratio
0.98
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
0.99 1 1.01 1.02 1.03 1.04 1.05 1.06
Temperature Ratio
Co
rrec
ted
Pre
ssu
re R
atio
110% 100% 90% 80% 70% Corrected Pressure- Temperature (PT) Elasticity with respect to Temperature vs.
Corrected Flow
2.3
2.35
2.4
2.45
2.5
2.55
2.6
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
PT
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line Corrected Pressure- Temperature (PT) Elasticity with respect to Temperature vs.
Relative Non-Dimensional Corrected Flow
2.3
2.35
2.4
2.45
2.5
2.55
2.6
0 0.005 0.01 0.015 0.02 0.025 0.03
Relative Non-Dimensional Corrected Flow
PT
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line
Corrected Pressure Ratio vs. Corrected Specific Volume Ratio (v2/v1)
0.98
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 1.02
Corrected Specific Volume Ratio (v2/v1)
Co
rrec
ted
Pre
ssu
re R
atio
110% 100% 90% 80% 70% Corrected Pressure-Corrected Specific Volume (Pv) Elasiticity with respect to Corrected Specific Volume vs.
Corrected Flow
-1.15
-1.1
-1.05
-1
-0.95
-0.9
-0.85
-0.8
-0.75
-0.70 0.1 0.2 0.3 0.4 0.5
Corrected Flow
Pv
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line Corrected Pressure-Corrected Specific Volume (Pv) Elasiticity with respect to Corrected Specific Volume vs. Relative
Non-Dimensional Corrected Flow
-1.15
-1.1
-1.05
-1
-0.95
-0.9
-0.85
-0.8
-0.75
-0.7
0 0.005 0.01 0.015 0.02 0.025 0.03
Relative Non-Dimensional Corrected Flow
Pv
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line
93
MIT 3 Scheme 1
Corrected Pressure Ratio (Density Ratio)with Scheme 1 Feedback
59%
55%
63%
67%
71%
50%
55%
59%
64%
68%
53%
46%
39%
32%
25%
1
1.02
1.04
1.06
1.08
1 . 1
1.12
1.14
1.16
0 . 1 0.15 0 . 2 0.25 0.3 0.35 0 . 4 0 . 4 5
Corrected Flow
Corr
ecte
d Pr
essu
re R
atio
(De
nsit
y Ra
tio)
1 1 0 % 100% 90% 8 0 % 70% Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line
Corrected T2/T1
105.0E-2
104.0E-2
103.0E-2
102.0E-2
101.0E-2
105.7E-2
104.8E-2
103.9E-2
103.2E-2
102.5E-2
Corrected Pressure Ratio (Density Ratio)
with Scheme 1 Feedback
59%
55%
63%
67%
71%
50%
55%
59%
64%
68%
53%
46%
39%
32%
25%
1
1.02
1.04
1.06
1.08
1 . 1
1.12
1.14
1.16
0 . 1 0.15 0 . 2 0.25 0.3 0.35 0 . 4 0 . 4 5
Corrected Flow
Corr
ecte
d Pr
essu
re R
atio
(Den
sity
Rat
io)
110% 100% 9 0 % 80% 70% Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line
130.0E-2
135.0E-2140.0E-2145.0E-2
125.0E-2
120.0E-2
115.0E-2
110.0E-2
105.0E-2
Corrected T3/T1150.0E-2155.0E-2160.0E-2165.0E-2
Efficiency (Propulsive/Thermal) Ratio
with Scheme 1 Feedback
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Eff
icie
ncy
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line Loss (Propulsive/Thermal) Ratio
with Scheme 1 Feedback
0.6
0.8
1
1.2
1.4
1.6
1.8
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Loss
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Work (Propulsive/Thermal) Ratiowith Scheme 1 Feedback
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Wor
k R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line Head (Propulsive/Thermal) Ratio
with Scheme 1 Feedback
0.998
1
1.002
1.004
1.006
1.008
1.01
1.012
1.014
1.016
1.018
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Hea
d R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line Pressure-Flow and Pressure-Density Cross-Elasticities
with Scheme 1 Feedback
1.4
1.45
1.5
1.55
1.6
1.65
1.7
1.75
1.8
1.85
1.9
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Co
rrec
ted
Pre
ssu
re-D
ensi
ty E
last
icit
y
Co
rrec
ted
Pre
ssu
re-F
low
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Pressure-Density
Pressure-Flow
Propulsive (Deviation) Efficiency and Loss
with Scheme 1 Feedback
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Pro
pu
lsiv
e E
ffic
ien
cy
110% 100% 90% 80% 70% Surge Line
Propulsive Efficiency
Propulsive Loss
94
Thermal (Dissipation) Efficiency and Losswith Scheme 1 Feedback
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Th
erm
al E
ffic
ien
cy
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Thermal Efficiency
Thermal Loss
Overall (Propulsive & Thermal) Efficiency and Loss
with Scheme 1 Feedback
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Ove
rall
Eff
icie
ncy
Ove
rall
Lo
ss
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Overall Efficiency
Overall Loss
Compression System Aeroelastic Characteristics
at Maximum Efficiency & Stall
1.5
1.55
1.6
1.65
1.7
1.75
1.8
1.85
0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1
Corrected Speed
Co
rrec
ted
Pre
ssu
re-D
ensi
ty A
ero
elas
tici
ty
- 1
-0.8
-0.6
-0.4
-0.2
0
0 . 2
0 . 4
0 . 6
Co
rrec
ted
Pre
ssu
re-F
low
Aer
oel
astic
ity
E_Density @ Maximum Efficiency E_Density @ Stall E_Flow & Effective E_Flow @ StallDesign Line E_Flow @ Maximum Efficiency Effective E_Flow @ Maximum Efficiency
Corrected T3/T1= 1.450
Note: Effective E_density= E_density
Corrected T2/T1= 1.025
Compressor System Pumping Characteristic
at Maximum Efficiency & Stall
1
1.05
1.1
1.15
1.2
1.25
0.7 0.8 0.9 1 1.1
Corrected Speed
Co
rrec
ted
Pre
ssu
re &
Tem
per
atu
re
Rat
ios
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Co
rrec
ted
Flo
w
Temperature Ratio @ Maximum Efficiency Temperature Ratio @ SurgePressure Ratio @ Maximum Efficiency Pressure Ratio @ Surge
Flow @ Maximum Efficiency Flow @ Surge
Design Line
X Denotes Effective Surge Line - - Denotes Effective Maximum Efficiency Line
Corrected T3/T1= 1.450
Dynamically Compensated Compression System Stability
with Scheme 1 Feedback
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Slo
pe o
f P
ress
ure
Ris
e C
hara
cter
istic
s
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
Eff
ectiv
e S
lop
e o
f P
ress
ure
Ris
e C
har
acte
rist
ic
110% 100% 90% 80% 70% Surge Line Effective Surge Line
95
MIT 3 Scheme 2
Corrected Pressure Ratio (Density Ratio)with Scheme 2 Feedback
59%
55%
63%
67%
71%
50%
55%
59%
64%
68%
54.1%
47.5%
40.9%
34.4%
27.8%
1
1.02
1.04
1.06
1.08
1 . 1
1.12
1.14
1.16
0.1 0.15 0 . 2 0.25 0 . 3 0.35 0.4 0.45
Corrected Flow
Corr
ecte
d Pr
essu
re R
atio
(Den
sity
Rat
io)
110% 1 0 0 % 9 0 % 8 0 % 7 0 % Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line
Corrected T2/T1
105.0E-2
104.0E-2
103.0E-2
102.0E-2
101.0E-2
106.2E-2
105.3E-2
104.4E-2
103.7E-2
103.0E-2
Corrected Pressure Ratio (Density Ratio)
with Scheme 2 Feedback
59%
55%
63%
67%
71%
50%
55%
59%
64%
68%
54.1%
47.5%
40.9%
34.4%
27.8%
1
1.02
1.04
1.06
1.08
1 . 1
1.12
1.14
1.16
0.1 0.15 0 . 2 0.25 0 . 3 0.35 0.4 0.45Corrected Flow
Corr
ecte
d Pr
essu
re R
atio
(Den
sity
Rat
io)
110% 100% 90% 80% 7 0 % Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line
130.0E-2
135.0E-2
140.0E-2145.0E-2
125.0E-2
120.0E-2
115.0E-2
110.0E-2
105.0E-2
Corrected T3/T1150.0E-2155.0E-2160.0E-2165.0E-2170.0E-2
Efficiency (Propulsive/Thermal) Ratio
with Scheme 2 Feedback
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Eff
icie
ncy
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line Loss (Propulsive/Thermal) Ratio
with Scheme 2 Feedback
0.6
0.8
1
1.2
1.4
1.6
1.8
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Loss
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Work (Propulsive/Thermal) Ratiowith Scheme 2 Feedback
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Wor
k R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line Head (Propulsive/Thermal) Ratio
with Scheme 2 Feedback
0.998
1
1.002
1.004
1.006
1.008
1.01
1.012
1.014
1.016
1.018
1.02
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Hea
d R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line Pressure-Flow and Pressure-Density Cross-Elasticities
with Scheme 2 Feedback
1.4
1.5
1.6
1.7
1.8
1.9
2
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Co
rrec
ted
Pre
ssu
re-D
ensi
ty E
last
icit
y
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
Co
rrec
ted
Pre
ssu
re-F
low
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Pressure-Density
Pressure-Flow
Propulsive (Deviation) Efficiency and Loss
with Scheme 2 Feedback
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Pro
pu
lsiv
e E
ffic
ien
cy
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
110% 100% 90% 80% 70% Surge Line
Propulsive Efficiency
Propulsive Loss
96
Thermal (Dissipation) Efficiency and Losswith Scheme 2 Feedback
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Th
erm
al E
ffic
ien
cy
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Thermal Efficiency
Thermal Loss
Overall (Propulsive & Thermal) Efficiency and Loss
with Scheme 2 Feedback
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Ove
rall
Eff
icie
ncy
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Ove
rall
Lo
ss
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Overall Efficiency
Overall Loss
Compression System Aeroelastic Characteristics
at Maximum Efficiency & Stall
1.5
1.55
1.6
1.65
1.7
1.75
1.8
1.85
0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1
Corrected Speed
Co
rrec
ted
Pre
ssu
re-D
ensi
ty A
ero
elas
tici
ty
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Co
rrec
ted
Pre
ssu
re-F
low
Aer
oel
astic
ity
E_Density @ Maximum Efficiency E_Density @ Stall E_Flow & Effective E_Flow @ StallDesign Line E_Flow @ Maximum Efficiency Effective E_Flow @ Maximum Efficiency
Corrected T3/T1= 1.600
Note: Effective E_density= E_density
Corrected T2/T1= 1.030
Compressor System Pumping Characteristic
at Maximum Efficiency & Stall
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
1.18
0.7 0.8 0.9 1 1.1
Corrected Speed
Co
rrec
ted
Pre
ssu
re &
Tem
per
atu
re
Rat
ios
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Co
rrec
ted
Flo
w
Temperature Ratio @ Maximum Efficiency Temperature Ratio @ SurgePressure Ratio @ Maximum Efficiency Pressure Ratio @ Surge
Flow @ Maximum Efficiency Flow @ Surge
Design Line
X Denotes Effective Surge Line - - Denotes Effective Maximum Efficiency Line
Corrected T3/T1= 1.600
Dynamically Compensated Compression System Stability
with Scheme 2 Feedback
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Slo
pe o
f P
ress
ure
Ris
e C
hara
cter
istic
s
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
Eff
ectiv
e S
lop
e o
f P
ress
ure
Ris
e C
har
acte
rist
ic
110% 100% 90% 80% 70% Surge Line Effective Surge Line
97
MIT 3 Scheme 3
Corrected Pressure Ratio (Density Ratio)with Scheme 3 Feedback
59%
55%
63%
67%
71%
50%
55%
59%
64%
68%
53%
47%
3 9 %
3 4 %
27%
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
0.1 0.15 0.2 0.25 0.3 0.35 0 . 4 0 . 4 5
Corrected Flow
Corr
ecte
d Pr
essu
re R
atio
(De
nsit
y Ra
tio)
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line
Corrected T2/T1
105.0E-2
104.0E-2
103.0E-2
102.0E-2
101.0E-2
105.9E-2
105.0E-2
104.1E-2
103.4E-2
102.7E-2
Corrected Pressure Ratio (Density Ratio)
with Scheme 3 Feedback
71%
67%
63%
55%
59%
68%
64%
59%
55%
50%
27%
3 4 %
3 9 %
47%
53%
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
0.1 0.15 0.2 0.25 0.3 0.35 0 . 4 0 . 4 5
Corrected Flow
Corr
ecte
d Pr
essu
re R
atio
(Den
sity
Rat
io)
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line
130.0E-2
135.0E-2139.4E-2145.0E-2
125.0E-2
120.0E-2
115.0E-2
110.0E-2
105.0E-2
Corrected T3/T1
151.0E-2155.0E-2160.0E-2
Efficiency (Propulsive/Thermal) Ratio
with Scheme 3 Feedback
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Eff
icie
ncy
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line Loss (Propulsive/Thermal) Ratio
with Scheme 3 Feedback
0.6
0.8
1
1.2
1.4
1.6
1.8
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Loss
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Work (Propulsive/Thermal) Ratiowith Scheme 3 Feedback
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Wor
k R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line Head (Propulsive/Thermal) Ratio
with Scheme 3 Feedback
0.998
1
1.002
1.004
1.006
1.008
1.01
1.012
1.014
1.016
1.018
1.02
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Hea
d R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line Pressure-Flow and Pressure-Density Cross-Elasticities
with Scheme 3 Feedback
1.4
1.45
1.5
1.55
1.6
1.65
1.7
1.75
1.8
1.85
1.9
0 0.05 0.1 0.15 0 . 2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Co
rrec
ted
Pre
ssu
re-D
ensi
ty E
last
icit
y
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
Co
rrec
ted
Pre
ssu
re-F
low
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Pressure-Density
Pressure-Flow
Propulsive (Deviation) Efficiency and Loss
with Scheme 3 Feedback
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Pro
pu
lsiv
e E
ffic
ien
cy
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
110% 100% 90% 80% 70% Surge Line
Propulsive Efficiency
Propulsive Loss
98
Thermal (Dissipation) Efficiency and Losswith Scheme 3 Feedback
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Th
erm
al E
ffic
ien
cy
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Thermal Efficiency
Thermal Loss
Overall (Propulsive & Thermal) Efficiency and Loss
with Scheme 3 Feedback
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Ove
rall
Eff
icie
ncy
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Ove
rall
Lo
ss
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Overall Efficiency
Overall Loss
Compression System Aeroelastic Characteristics
at Maximum Efficiency & Stall
1.5
1.55
1.6
1.65
1.7
1.75
1.8
1.85
0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1
Corrected Speed
Co
rrec
ted
Pre
ssu
re-D
ensi
ty A
ero
elas
tici
ty
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Co
rrec
ted
Pre
ssu
re-F
low
Aer
oel
astic
ity
E_Density @ Maximum Efficiency E_Density @ Stall E_Flow & Effective E_Flow @ StallDesign Line E_Flow @ Maximum Efficiency Effective E_Flow @ Maximum Efficiency
Corrected T3/T1= 1.51
Note: Effective E_density= E_density
Corrected T2/T1= 1.027
Compressor System Pumping Characteristic
at Maximum Efficiency & Stall
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
0.7 0.8 0.9 1 1.1
Corrected Speed
Co
rrec
ted
Pre
ssu
re &
Tem
per
atu
re
Rat
ios
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Co
rrec
ted
Flo
w
Temperature Ratio @ Maximum Efficiency Temperature Ratio @ SurgePressure Ratio @ Maximum Efficiency Pressure Ratio @ Surge
Flow @ Maximum Efficiency Flow @ Surge
Design Line
X Denotes Effective Surge Line - - Denotes Effective Maximum Efficiency Line
Corrected T3/T1= 1.51
Dynamically Compensated Compression System Stability
with Scheme 3 Feedback
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Slo
pe o
f P
ress
ure
Ris
e C
hara
cter
istic
s
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
Eff
ectiv
e S
lop
e o
f P
ress
ure
Ris
e C
har
acte
rist
ic
110% 100% 90% 80% 70% Surge Line Effective Surge Line
99
MIT 3 Scheme 4
Corrected Pressure Ratio (Density Ratio)with Scheme 4 Feedback
71%
67%
63%
55%
59%
6 8 %
6 4 %
5 9 %
5 5 %
5 0 %
2 9 %
36%
42%
49%
55%
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
1.18
0.08 0.13 0.18 0 . 2 3 0.28 0.33 0.38 0.43
Corrected Flow
Corr
ecte
d Pr
essu
re R
atio
(Den
sity
Rat
io)
110% 1 0 0 % 90% 80% 70% Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line
Corrected T2/T1
105.0E-2
104.0E-2
103.0E-2
102.0E-2
101.0E-2
106.4E-2
105.5E-2
104.7E-2
103.9E-2
103.3E-2
Corrected Pressure Ratio (Density Ratio)
with Scheme 4 Feedback
71%
67%
63%
55%
59%
68%
64%
59%
55%
50%
29%
36%
42%
49%
55%
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
1.18
0.1 0.15 0.2 0.25 0 . 3 0.35 0 . 4 0.45
Corrected Flow
Corr
ecte
d Pr
essu
re R
atio
(Den
sity
Rat
io)
110% 1 0 0 % 90% 80% 70% Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line
130.0E-2
135.0E-2
140.0E-2145.0E-2
125.0E-2
120.0E-2
115.0E-2
110.0E-2
105.0E-2
Corrected T3/T1
170.0E-2 155.0E-2185.0E-2 160.0E-2
Efficiency (Propulsive/Thermal) Ratio
with Scheme 4 Feedback
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Eff
icie
ncy
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line Loss (Propulsive/Thermal) Ratio
with Scheme 4 Feedback
0.6
0.8
1
1.2
1.4
1.6
1.8
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Loss
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Work (Propulsive/Thermal) Ratiowith Scheme 4 Feedback
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Wor
k R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line Head (Propulsive/Thermal) Ratio
with Scheme 4 Feedback
1
1.002
1.004
1.006
1.008
1.01
1.012
1.014
1.016
1.018
1.02
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Hea
d R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line Pressure-Flow and Pressure-Density Cross-Elasticities
with Scheme 4 Feedback
1.4
1.45
1.5
1.55
1.6
1.65
1.7
1.75
1.8
1.85
1.9
0 0.05 0.1 0.15 0 . 2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Co
rrec
ted
Pre
ssu
re-D
ensi
ty E
last
icit
y
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
Co
rrec
ted
Pre
ssu
re-F
low
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Pressure-Density
Pressure-Flow
Propulsive (Deviation) Efficiency and Loss
with Scheme 4 Feedback
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Pro
pu
lsiv
e E
ffic
ien
cy
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
110% 100% 90% 80% 70% Surge Line
Propulsive Efficiency
Propulsive Loss
100
Thermal (Dissipation) Efficiency and Losswith Scheme 4 Feedback
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.05 0.1 0.15 0.2 0.25 0 . 3 0.35 0.4 0.45 0.5
Corrected Flow
Th
erm
al E
ffic
ien
cy
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Thermal Efficiency
Thermal Loss
Overall (Propulsive & Thermal) Efficiency and Loss
with Scheme 4 Feedback
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Ove
rall
Eff
icie
ncy
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Ove
rall
Lo
ss
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Overall Efficiency
Overall Loss
Compression System Aeroelastic Characteristics
at Maximum Efficiency & Stall
1.5
1.55
1.6
1.65
1.7
1.75
1.8
1.85
0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1
Corrected Speed
Co
rrec
ted
Pre
ssu
re-D
ensi
ty A
ero
elas
tici
ty
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Co
rrec
ted
Pre
ssu
re-F
low
Aer
oel
astic
ity
E_Density @ Maximum Efficiency E_Density @ Stall E_Flow & Effective E_Flow @ StallDesign Line E_Flow @ Maximum Efficiency Effective E_Flow @ Maximum Efficiency
Corrected T3/T1= 1.700
Note: Effective E_density= E_density
Corrected T2/T1= 1.033
Compressor System Pumping Characteristic
at Maximum Efficiency & Stall
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
1.18
0.7 0.8 0.9 1 1.1
Corrected Speed
Co
rrec
ted
Pre
ssu
re &
Tem
per
atu
re
Rat
ios
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Co
rrec
ted
Flo
w
Temperature Ratio @ Maximum Efficiency Temperature Ratio @ SurgePressure Ratio @ Maximum Efficiency Pressure Ratio @ Surge
Flow @ Maximum Efficiency Flow @ Surge
Design Line
X Denotes Effective Surge Line - - Denotes Effective Maximum Efficiency Line
Corrected T3/T1= 1.700
Dynamically Compensated Compression System Stability
with Scheme 4 Feedback
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Slo
pe o
f P
ress
ure
Ris
e C
hara
cter
istic
s
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
Eff
ectiv
e S
lop
e o
f P
ress
ure
Ris
e C
har
acte
rist
ic
110% 100% 90% 80% 70% Surge Line Effective Surge Line
101
MIT 3 Scheme 5
Corrected Pressure Ratio (Density Ratio)with Scheme 5 Feedback
71%
67%
63%
55%
59%
6 8 %
64%
5 9 %
5 5 %
5 0 %
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
0.1 0.15 0.2 0.25 0 . 3 0.35 0 . 4
Corrected Flow
Corr
ecte
d Pr
essu
re R
atio
(De
nsit
y Ra
tio)
110% 1 0 0 % 90% 80% 70% Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line
Corrected T2/T1
105.0E-2
104.0E-2
103.0E-2
102.0E-2
101.0E-2
Corrected Pressure Ratio (Density Ratio)
with Scheme 5 Feedback
71%
67%
63%
55%
59%
6 8 %
64%
5 9 %
5 5 %
5 0 %
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
0.1 0.15 0.2 0.25 0 . 3 0.35 0 . 4
Corrected Flow
Corr
ecte
d Pr
essu
re R
atio
(Den
sity
Rat
io)
110% 1 0 0 % 90% 80% 70% Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line
130.0E-2
135.0E-2139.4E-2145.0E-2
125.0E-2
120.0E-2
115.0E-2
110.0E-2
105.0E-2
Corrected T3/T1
Efficiency (Propulsive/Thermal) Ratio
with Scheme 5 Feedback
0.8
1.3
1.8
2.3
2.8
3.3
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Eff
icie
ncy
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line Loss (Propulsive/Thermal) Ratio
with Scheme 5 Feedback
0.6
0.8
1
1.2
1.4
1.6
1.8
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Loss
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Work (Propulsive/Thermal) Ratiowith Scheme 5 Feedback
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Wor
k R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line Head (Propulsive/Thermal) Ratio
with Scheme 5 Feedback
1
1.002
1.004
1.006
1.008
1.01
1.012
1.014
1.016
1.018
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Hea
d R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line Pressure-Flow and Pressure-Density Cross-Elasticities
with Scheme 5 Feedback
1.4
1.45
1.5
1.55
1.6
1.65
1.7
1.75
1.8
1.85
1.9
0 0.1 0.2 0.3 0.4 0.5
Corrected Flow
Co
rrec
ted
Pre
ssu
re-D
ensi
ty E
last
icit
y
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
Co
rrec
ted
Pre
ssu
re-F
low
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Pressure-Density
Pressure-Flow
Propulsive (Deviation) Efficiency and Loss
with Scheme 5 Feedback
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Pro
pu
lsiv
e E
ffic
ien
cy
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
110% 100% 90% 80% 70% Surge Line
Propulsive Efficiency
Propulsive Loss
102
Thermal (Dissipation) Efficiency and Losswith Scheme 5 Feedback
0
0 . 1
0 . 2
0 . 3
0 . 4
0 . 5
0 . 6
0 . 7
0 . 8
0 . 9
1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Th
erm
al E
ffic
ien
cy
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Thermal Efficiency
Thermal Loss
Overall (Propulsive & Thermal) Efficiency and Loss
with Scheme 5 Feedback
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Ove
rall
Eff
icie
ncy
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Ove
rall
Lo
ss
110% 100% 90% 80% 70% Surge Line
Overall Efficiency
Overall Loss
Compression System Aeroelastic Characteristics
at Maximum Efficiency & Stall
1.5
1.55
1.6
1.65
1.7
1.75
1.8
1.85
0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1
Corrected Speed
Co
rrec
ted
Pre
ssu
re-D
ensi
ty A
ero
elas
tici
ty
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Co
rrec
ted
Pre
ssu
re-F
low
Aer
oel
astic
ity
E_Density @ Maximum Efficiency E_Density @ Stall E_Flow @ StallDesign Line E_Flow @ Maximum Efficiency
Corrected T3/T1= 1.394
Note: Effective E_density= E_density
Corrected T2/T1= 1.022
Compressor System Pumping Characteristic
at Maximum Efficiency & Stall
1
1.05
1.1
1.15
1.2
1.25
0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1
Corrected Speed
Co
rrec
ted
Pre
ssu
re &
Tem
per
atu
re
Ra
tio
s
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Co
rrec
ted
Flo
w
Temperature Ratio @ Maximum Efficiency Temperature Ratio @ SurgePressure Ratio @ Maximum Efficiency Pressure Ratio @ Surge
Flow @ Maximum Efficiency Flow @ Surge
Design Line
Corrected T3/T1= 1.394
X Denotes Effective Surge Line - - Denotes Effective Maximum Efficiency Line
Dynamically Compensated Compression System Stability
with Scheme 5 Feedback
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
0 0 . 2 0.4 0.6 0.8 1 1.2
Corrected Flow
Slo
pe o
f P
ress
ure
Ris
e C
hara
cter
istic
s
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
Eff
ectiv
e S
lop
e o
f P
ress
ure
Ris
e C
har
acte
rist
ic
110% 100% 90% 80% 70% Surge Line Effective Surge Line
103
MIT 3 Scheme 6
Corrected Pressure Ratio (Density Ratio)with Scheme 6 Feedback
59%
55%
63%
67%
71%
50%
55%
59%
64%
68%
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
Corrected Flow
Corr
ecte
d Pr
essu
re R
atio
(De
nsit
y Ra
tio)
110% 1 0 0 % 90% 80% 70% Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line
Corrected T2/T1
105.0E-2
104.0E-2
103.0E-2
102.0E-2
101.0E-2
Corrected Pressure Ratio (Density Ratio)
with Scheme 6 Feedback
59%
55%
63%
67%
71%
50%
55%
59%
64%
68%
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
0.1 0.15 0.2 0.25 0 . 3 0.35 0 . 4 0.45
Corrected Flow
Corr
ecte
d Pr
essu
re R
atio
(Den
sity
Rat
io)
110% 100% 90% 80% 70% Surge Line
Safe Operating Line
Maximum Efficiency Line
130.0E-2
135.0E-2139.4E-2145.0E-2
125.0E-2
120.0E-2
115.0E-2
110.0E-2
105.0E-2
Corrected T3/T1
Efficiency (Propulsive/Thermal) Ratio
with Scheme 6 Feedback
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Eff
icie
ncy
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line Loss (Propulsive/Thermal) Ratio
with Scheme 6 Feedback
0.6
0.8
1
1.2
1.4
1.6
1.8
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Loss
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Work (Propulsive/Thermal) Ratiowith Scheme 6 Feedback
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Wor
k R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line Head (Propulsive/Thermal) Ratio
with Scheme 6 Feedback
1
1.002
1.004
1.006
1.008
1.01
1.012
1.014
1.016
1.018
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Hea
d R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line Pressure-Flow and Pressure-Density Cross-Elasticities
with Scheme 6 Feedback
1.4
1.45
1.5
1.55
1.6
1.65
1.7
1.75
1.8
1.85
1.9
0 0.05 0.1 0.15 0 . 2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Co
rrec
ted
Pre
ssu
re-D
ensi
ty E
last
icit
y
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
Co
rrec
ted
Pre
ssu
re-F
low
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Pressure-Density
Pressure-Flow
Propulsive (Deviation) Efficiency and Loss
with Scheme 6 Feedback
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Pro
pu
lsiv
e E
ffic
ien
cy
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
110% 100% 90% 80% 70% Surge Line
Propulsive Efficiency
Propulsive Loss
104
Thermal (Dissipation) Efficiency and Losswith Scheme 6 Feedback
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Th
erm
al E
ffic
ien
cy
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Thermal Efficiency
Thermal Loss
Overall (Propulsive & Thermal) Efficiency and Loss
with Scheme 6 Feedback
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Ove
rall
Eff
icie
ncy
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Ove
rall
Lo
ss
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Overall Efficiency
Overall Loss
Compression System Aeroelastic Characteristics
at Maximum Efficiency & Stall
1.5
1.55
1.6
1.65
1.7
1.75
1.8
1.85
70% 75% 80% 85% 90% 95% 100% 105% 110%
Corrected Speed
Co
rrec
ted
Pre
ssu
re-D
ensi
ty A
ero
elas
tici
ty
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Co
rrec
ted
Pre
ssu
re-F
low
Aer
oel
astic
ity
E_Density @ Maximum Efficiency E_Density @ Stall E_Flow & Effective E_Flow @ StallDesign Line E_Flow @ Maximum Efficiency Effective E_Flow @ Maximum Efficiency
Corrected T3/T1= 1.394
Note: Effective E_density= E_density
Corrected T2/T1= 1.022
Compressor System Pumping Characteristic
at Maximum Efficiency & Stall
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
70% 80% 90% 100% 110%
Corrected Speed
Co
rrec
ted
Pre
ssu
re &
Tem
per
atu
re
Rat
ios
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Co
rrec
ted
Flo
w
Temperature Ratio @ Maximum Efficiency Temperature Ratio @ SurgePressure Ratio @ Maximum Efficiency Pressure Ratio @ Surge
Flow @ Maximum Efficiency Flow @ Surge
Design Line
X Denotes Effective Surge Line - - Denotes Effective Maximum Efficiency Line
Corrected T3/T1= 1.394
Dynamically Compensated Compression System Stability
with Scheme 6 Feedback
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Slo
pe o
f P
ress
ure
Ris
e C
hara
cter
istic
s
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
Eff
ectiv
e S
lop
e o
f P
ress
ure
Ris
e C
har
acte
rist
ic
110% 100% 90% 80% 70% Surge Line Effective Surge Line
105
MIT 3 Scheme 7
Corrected Pressure Ratio (Density Ratio)with Scheme 7 Feedback
71%
67%
63%
55%
59%
68%
64%
59%
55%
50%
1
1.02
1.04
1.06
1.08
1 . 1
1.12
1.14
1.16
0.1 0.15 0.2 0.25 0.3 0.35 0 . 4 0.45
Corrected Flow
Corr
ecte
d Pr
essu
re R
atio
(De
nsit
y Ra
tio)
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line
Corrected T2/T1105.0E-2
104.0E-2
103.0E-2
102.0E-2
101.0E-2
Corrected Pressure Ratio (Density Ratio)
with Scheme 7 Feedback
71%
67%
63%
55%
59%
68%
64%
59%
55%
50%
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
0.1 0.15 0 . 2 0.25 0 . 3 0.35 0 . 4 0.45
Corrected Flow
Corr
ecte
d Pr
essu
re R
atio
(Den
sity
Rat
io)
1 1 0 % 100% 9 0 % 8 0 % 70% Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line
130.0E-2
135.0E-2139.4E-2145.0E-2
125.0E-2
120.0E-2
115.0E-2
110.0E-2
105.0E-2
Corrected T3/T1
Efficiency (Propulsive/Thermal) Ratio
with Scheme 7 Feedback
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Eff
icie
ncy
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line Loss (Propulsive/Thermal) Ratio
with Scheme 7 Feedback
0.6
0.8
1
1.2
1.4
1.6
1.8
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Loss
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Work (Propulsive/Thermal) Ratiowith Scheme 7 Feedback
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Wor
k R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line Head (Propulsive/Thermal) Ratio
with Scheme 7 Feedback
1
1.002
1.004
1.006
1.008
1.01
1.012
1.014
1.016
1.018
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Hea
d R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Pressure-Flow and Pressure-Density Cross-Elasticitieswith Scheme 7 Feedback
1.4
1.45
1.5
1.55
1.6
1.65
1.7
1.75
1.8
1.85
1.9
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Co
rrec
ted
Pre
ssu
re-D
ensi
ty E
last
icit
y
Co
rrec
ted
Pre
ssu
re-F
low
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Pressure-Density
Pressure-Flow
Propulsive (Deviation) Efficiency and Loss
with Scheme 7 Feedback
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Pro
pu
lsiv
e E
ffic
ien
cy
110% 100% 90% 80% 70% Surge Line
Propulsive Efficiency
Propulsive Loss
106
Thermal (Dissipation) Efficiency and Losswith Scheme 7 Feedback
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Th
erm
al E
ffic
ien
cy
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Thermal Efficiency
Thermal Loss
Overall (Propulsive & Thermal) Efficiency and Loss
with Scheme 7 Feedback
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Ove
rall
Eff
icie
ncy
Ove
rall
Lo
ss
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Overall Efficiency
Overall Loss
Compression System Aeroelastic Characteristics
at Maximum Efficiency & Stall
1.5
1.55
1.6
1.65
1.7
1.75
1.8
1.85
0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1
Corrected Speed
Co
rrec
ted
Pre
ssu
re-D
ensi
ty
Aer
oel
asti
city
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Co
rrec
ted
Pre
ssu
re-F
low
Aer
oel
astic
ity
E_Density @ Maximum Efficiency E_Density @ Stall
E_Flow & Effective E_Flow @ Stall Design LineE_Flow & Effective E_Flow @ Maximum Efficiency
Corrected T3/T1= 1.394
Note: Effective E_density= E_density
Corrected T2/T1= 1.022
Compressor System Pumping Characteristic
at Maximum Efficiency & Stall
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1
Corrected Speed
Co
rrec
ted
Pre
ssu
re &
Tem
per
atu
re
Rat
ios
Co
rrec
ted
Flo
w
Temperature Ratio @ Maximum Efficiency Temperature Ratio @ SurgePressure Ratio @ Maximum Efficiency Pressure Ratio @ Surge
Flow @ Maximum Efficiency Flow @ Surge
Design Line
X Denotes Effective Surge Line - - Denotes Effective Maximum Efficiency Line
Corrected T3/T1= 1.394
Dynamically Compensated Compression System Stability
with Scheme 7 Feedback
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Slo
pe o
f P
ress
ure
Ris
e C
hara
cter
istic
s
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
Eff
ectiv
e S
lop
e o
f P
ress
ure
Ris
e C
har
acte
rist
ic
110% 100% 90% 80% 70% Surge Line Effective Surge Line
107
MIT 3 Scheme 8
Corrected Pressure Ratio (Density Ratio)with Scheme 8 Feedback
71%
67%
63%
55%
59%
68%
6 4 %
5 9 %
5 5 %
50%
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
0.1 0.15 0.2 0.25 0 . 3 0.35 0 . 4 0.45
Corrected Flow
Cor
rect
ed P
ress
ure
Rat
io (D
ensi
ty R
atio
)
110% 1 0 0 % 90% 80% 70% Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line
Corrected T2/T1105.0E-2
104.0E-2
103.0E-2
102.0E-2
101.0E-2
Corrected Pressure Ratio (Density Ratio)
with Scheme 8 Feedback
71%
67%
63%
55%
59%
68%
6 4 %
5 9 %
55%
50%
1
1.02
1.04
1.06
1.08
1 . 1
1.12
1.14
1.16
0.1 0.15 0 . 2 0.25 0 . 3 0.35 0 . 4 0.45
Corrected Flow
Corr
ecte
d Pr
essu
re R
atio
(Den
sity
Rat
io)
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line
130.0E-2
135.0E-2
139.4E-2145.0E-2
125.0E-2
120.0E-2
115.0E-2
110.0E-2
105.0E-2
Corrected T3/T1
Efficiency (Propulsive/Thermal) Ratio
with Scheme 8 Feedback
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Eff
icie
ncy
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line Loss (Propulsive/Thermal) Ratio
with Scheme 8 Feedback
0.6
0.8
1
1.2
1.4
1.6
1.8
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Loss
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Work (Propulsive/Thermal) Ratiowith Scheme 8 Feedback
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Wor
k R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line Head (Propulsive/Thermal) Ratio
with Scheme 8 Feedback
1
1.002
1.004
1.006
1.008
1.01
1.012
1.014
1.016
1.018
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Hea
d R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line Pressure-Flow and Pressure-Density Cross-Elasticities
with Scheme 8 Feedback
1.4
1.45
1.5
1.55
1.6
1.65
1.7
1.75
1.8
1.85
1.9
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Co
rrec
ted
Pre
ssu
re-D
ensi
ty E
last
icit
y
Co
rrec
ted
Pre
ssu
re-F
low
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Pressure-Density
Pressure-Flow
Propulsive (Deviation) Efficiency and Loss
with Scheme 8 Feedback
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Pro
pu
lsiv
e E
ffic
ien
cy
110% 100% 90% 80% 70% Surge Line
Propulsive Efficiency
Propulsive Loss
108
Thermal (Dissipation) Efficiency and Losswith Scheme 8 Feedback
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Th
erm
al E
ffic
ien
cy
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Thermal Efficiency
Thermal Loss
Overall (Propulsive & Thermal) Efficiency and Loss
with Scheme 8 Feedback
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Ove
rall
Eff
icie
ncy
Ove
rall
Lo
ss
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Overall Efficiency
Overall Loss
Compression System Aeroelastic Characteristics
at Maximum Efficiency & Stall
1.5
1.55
1.6
1.65
1.7
1.75
1.8
1.85
70% 75% 80% 85% 90% 95% 100% 105% 110%
Corrected Speed
Co
rrec
ted
Pre
ssu
re-D
ensi
ty
Aer
oel
asti
city
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Co
rrec
ted
Pre
ssu
re-F
low
Aer
oel
astic
ity
E_Density @ Maximum Efficiency E_Density @ Stall
E_Flow & Effective E_Flow @ Stall Design LineE_Flow & Effective E_Flow @ Maximum Efficiency
Corrected T3/T1= 1.394
Note: Effective E_density= E_density
Corrected T2/T1= 1.022
Compressor System Pumping Characteristic
at Maximum Efficiency & Stall
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
70% 75% 80% 85% 90% 95% 100% 105% 110%
Corrected Speed
Co
rrec
ted
Pre
ssu
re &
Tem
per
atu
re
Rat
ios
Co
rrec
ted
Flo
w
Temperature Ratio @ Maximum Efficiency Temperature Ratio @ SurgePressure Ratio @ Maximum Efficiency Pressure Ratio @ Surge
Flow @ Maximum Efficiency Flow @ Surge
Design Line
X Denotes Effective Surge Line - - Denotes Effective Maximum Efficiency Line
Corrected T3/T1= 1.394
Dynamically Compensated Compression System Stability
with Scheme 8 Feedback
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Slo
pe o
f P
ress
ure
Ris
e C
hara
cter
istic
s
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
Eff
ectiv
e S
lop
e o
f P
ress
ure
Ris
e C
har
acte
rist
ic
110% 100% 90% 80% 70% Surge Line Effective Surge Line
109
MIT 3 Scheme 9
Corrected Pressure Ratio (Density Ratio)with Scheme 9 Feedback
59%
55%
63%
67%
71%
50%
55%
59%
64%
68%
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
0 . 1 0.15 0 . 2 0.25 0.3 0.35 0.4 0 . 4 5
Corrected Flow
Corr
ecte
d Pr
essu
re R
atio
(Den
sity
Rat
io)
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line
Corrected T2/T1
105.0E-2
104.0E-2
103.0E-2
102.0E-2
101.0E-2
Corrected Pressure Ratio (Density Ratio)
with Scheme 9 Feedback
59%
55%
63%
67%
71%
50%
55%
59%
64%
68%
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
0 . 1 0.15 0 . 2 0.25 0.3 0.35 0.4 0 . 4 5Corrected Flow
Corr
ecte
d Pr
essu
re R
atio
(Den
sity
Rat
io)
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line
130.0E-2
135.0E-2
139.0E-2145.0E-2
125.0E-2
120.0E-2
115.0E-2
110.0E-2
105.0E-2
Corrected T3/T1
Efficiency (Propulsive/Thermal) Ratio
with Scheme 9 Feedback
0.8
1
1.2
1.4
1.6
1.8
2
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Eff
icie
ncy
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line Loss (Propulsive/Thermal) Ratio
with Scheme 9 Feedback
0.6
0.8
1
1.2
1.4
1.6
1.8
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Loss
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Work (Propulsive/Thermal) Ratiowith Scheme 9 Feedback
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Wor
k R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line Head (Propulsive/Thermal) Ratio
with Scheme 9 Feedback
0.998
1
1.002
1.004
1.006
1.008
1.01
1.012
1.014
1.016
1.018
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Hea
d R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line Pressure-Flow and Pressure-Density Cross-Elasticities
with Scheme 9 Feedback
1.4
1.45
1.5
1.55
1.6
1.65
1.7
1.75
1.8
1.85
1.9
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Co
rrec
ted
Pre
ssu
re-D
ensi
ty E
last
icit
y
Co
rrec
ted
Pre
ssu
re-F
low
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Pressure-Density
Pressure-Flow
Propulsive (Deviation) Efficiency and Loss
with Scheme 9 Feedback
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Pro
pu
lsiv
e E
ffic
ien
cy
110% 100% 90% 80% 70% Surge Line
Propulsive Efficiency
Propulsive Loss
110
Thermal (Dissipation) Efficiency and Losswith Scheme 9 Feedback
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Th
erm
al E
ffic
ien
cy
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Thermal Efficiency
Thermal Loss
Overall (Propulsive & Thermal) Efficiency and Loss
with Scheme 9 Feedback
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Ove
rall
Eff
icie
ncy
Ove
rall
Lo
ss
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Overall Efficiency
Overall Loss
Compression System Aeroelastic Characteristics
at Maximum Efficiency & Stall
1.5
1.55
1.6
1.65
1.7
1.75
1.8
1.85
0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1
Corrected Speed
Co
rrec
ted
Pre
ssu
re-D
ensi
ty A
ero
elas
tici
ty
- 1
-0.8
-0.6
-0.4
-0.2
0
0 . 2
0 . 4
0 . 6
Co
rrec
ted
Pre
ssu
re-F
low
Aer
oel
astic
ity
E_Density @ Maximum Efficiency E_Density @ Stall E_Flow & Effective E_Flow @ StallDesign Line E_Flow @ Maximum Efficiency Effective E_Flow @ Maximum Efficiency
Corrected T3/T1= 1.430
Note: Effective E_density= E_density
Corrected T2/T1= 1.021
Compressor System Pumping Characteristic
at Maximum Efficiency & Stall
1
1.05
1.1
1.15
1.2
1.25
0.7 0.8 0.9 1 1.1
Corrected Speed
Co
rrec
ted
Pre
ssu
re &
Tem
per
atu
re
Rat
ios
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Co
rrec
ted
Flo
w
Temperature Ratio @ Maximum Efficiency Temperature Ratio @ SurgePressure Ratio @ Maximum Efficiency Pressure Ratio @ Surge
Flow @ Maximum Efficiency Flow @ Surge
Design Line
X Denotes Effective Surge Line - - Denotes Effective Maximum Efficiency Line
Corrected T3/T1= 1.430
Dynamically Compensated Compression System Stability
with Scheme 9 Feedback
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Slo
pe o
f P
ress
ure
Ris
e C
hara
cter
istic
s
Eff
ectiv
e S
lop
e o
f P
ress
ure
Ris
e C
har
acte
rist
ic
110% 100% 90% 80% 70% Surge Line Effective Surge Line
111
MIT 3 Scheme 10
Corrected Pressure Ratio (Density Ratio)with Scheme 10 Feedback
71%
67%
63%
55%
59%
68%
64%
59%
55%
50%
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
0.1 0.15 0.2 0.25 0 . 3 0.35 0 . 4 0.45
Corrected Flow
Corr
ecte
d Pr
essu
re R
atio
(Den
sity
Rat
io)
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line
Corrected T2/T1
105.0E-2
104.0E-2
103.0E-2
102.0E-2
101.0E-2
Corrected Pressure Ratio (Density Ratio)
with Scheme 10 Feedback
71%
67%
63%
55%
59%
68%
64%
59%
55%
50%
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
0.1 0.15 0.2 0.25 0 . 3 0.35 0 . 4 0.45
Corrected Flow
Corr
ecte
d Pr
essu
re R
atio
(Den
sity
Rat
io)
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Safe Operating Line
Maximum Efficiency Line
130.0E-2
135.0E-2139.4E-2145.0E-2
125.0E-2
120.0E-2
115.0E-2
110.0E-2
105.0E-2
Corrected T3/T1
Efficiency (Propulsive/Thermal) Ratio
with Scheme 10 Feedback
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Eff
icie
ncy
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line Loss (Propulsive/Thermal) Ratio
with Scheme 10 Feedback
0.6
0.8
1
1.2
1.4
1.6
1.8
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Loss
Rat
io
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Work (Propulsive/Thermal) Ratiowith Scheme 10 Feedback
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Wor
k R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line Head (Propulsive/Thermal) Ratio
with Scheme 10 Feedback
1
1.002
1.004
1.006
1.008
1.01
1.012
1.014
1.016
1.018
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Hea
d R
atio
110% 100% 90% 80% 70% Surge Line Effective Surge Line Pressure-Flow and Pressure-Density Cross-Elasticities
with Scheme 10 Feedback
1.4
1.45
1.5
1.55
1.6
1.65
1.7
1.75
1.8
1.85
1.9
0 0.05 0.1 0.15 0 . 2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Co
rrec
ted
Pre
ssu
re-D
ensi
ty E
last
icit
y
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
Co
rrec
ted
Pre
ssu
re-F
low
Ela
stic
ity
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Pressure-Density
Pressure-Flow
Propulsive (Deviation) Efficiency and Loss
with Scheme 10 Feedback
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Pro
pu
lsiv
e E
ffic
ien
cy
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
110% 100% 90% 80% 70% Surge Line
Propulsive Efficiency
Propulsive Loss
112
Thermal (Dissipation) Efficiency and Losswith Scheme 10 Feedback
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Th
erm
al E
ffic
ien
cy
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Thermal Efficiency
Thermal Loss
Overall (Propulsive & Thermal) Efficiency and Loss
with Scheme 10 Feedback
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Ove
rall
Eff
icie
ncy
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Ove
rall
Lo
ss
110% 100% 90% 80% 70% Surge Line Effective Surge Line
Overall Efficiency
Overall Loss
Compression System Aeroelastic Characteristics
at Maximum Efficiency & Stall
1.5
1.55
1.6
1.65
1.7
1.75
1.8
1.85
0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1
Corrected Speed
Co
rrec
ted
Pre
ssu
re-D
ensi
ty
Aer
oel
asti
city
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Co
rrec
ted
Pre
ssu
re-F
low
Aer
oel
astic
ity
E_Density @ Maximum Efficiency E_Density @ Stall
E_Flow & Effective E_Flow @ Stall Design LineE_Flow & Effective E_Flow @ Maximum Efficiency
Corrected T3/T1= 1.394
Note: Effective E_density= E_density
Corrected T2/T1= 1.022
Compressor System Pumping Characteristic
at Maximum Efficiency & Stall
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
0.7 0.8 0.9 1 1.1
Corrected Speed
Co
rrec
ted
Pre
ssu
re &
Tem
per
atu
re
Rat
ios
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Co
rrec
ted
Flo
w
Temperature Ratio @ Maximum Efficiency Temperature Ratio @ SurgePressure Ratio @ Maximum Efficiency Pressure Ratio @ Surge
Flow @ Maximum Efficiency Flow @ Surge
Design Line
X Denotes Effective Surge Line - - Denotes Effective Maximum Efficiency Line
Corrected T3/T1= 1.394
Dynamically Compensated Compression System Stability
with Scheme 10 Feedback
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Corrected Flow
Slo
pe o
f P
ress
ure
Ris
e C
hara
cter
istic
s
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
Eff
ectiv
e S
lop
e o
f P
ress
ure
Ris
e C
har
acte
rist
ic
110% 100% 90% 80% 70% Surge Line Effective Surge Line