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Aerodynamic Design Study of Advanced Multistage Axial Compressor

Authors:
  • Gas Turbine Engine Research

Abstract

As a direct response to the need for further performance gains from current multistage axial compressors, an investigation of advanced aerodynamic design concepts that will lead to compact, high-efficiency, and wide-operability configurations is being pursued. Part I of this report describes the projected level of technical advancement relative to the state of the art and quantifies it in terms of basic aerodynamic technology elements of current design systems. A rational enhancement of these elements is shown to lead to a substantial expansion of the design and operability space. Aerodynamic design considerations for a four-stage core compressor intended to serve as a vehicle to develop, integrate, and demonstrate aerotechnology advancements are discussed. This design is biased toward high efficiency at high loading. Three-dimensional blading and spanwise tailoring of vector diagrams guided by computational fluid dynamics (CFD) are used to manage the aerodynamics of the high-loaded endwall regions. Certain deleterious flow features, such as leakage-vortex-dominated endwall flow and strong shock-boundary-layer interactions, were identified and targeted for improvement. However, the preliminary results were encouraging and the front two stages were extracted for further aerodynamic trimming using a three-dimensional inverse design method described in part II of this report. The benefits of the inverse design method are illustrated by developing an appropriate pressure-loading strategy for transonic blading and applying it to reblade the rotors in the front two stages of the four-stage configuration. Multistage CFD simulations based on the average passage formulation indicated an overall efficiency potential far exceeding current practice for the front two stages. Results of the CFD simulation at the aerodynamic design point are interrogated to identify areas requiring additional development. In spite of the significantly higher aerodynamic loadings, advanced CFD-based tools were able to effectively guide the design of a very efficient axial compressor under state-of-the-art aeromechanical constraints.
Louis M. Larosiliere
U.S. Army Research Laboratory, Glenn Research Center, Cleveland, Ohio
Jerry R. Wood
Glenn Research Center, Cleveland, Ohio
Michael D. Hathaway
U.S. Army Research Laboratory, Glenn Research Center, Cleveland, Ohio
Adam J. Medd and Thong Q. Dang
Syracuse University, Syracuse, New York
Aerodynamic Design Study of Advanced
Multistage Axial Compressor
NASA/TP—2002-211568
December 2002
ARL–TR–2859
U.S. ARMY
RESEARCH LABORATORY
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Louis M. Larosiliere
U.S. Army Research Laboratory, Glenn Research Center, Cleveland, Ohio
Jerry R. Wood
Glenn Research Center, Cleveland, Ohio
Michael D. Hathaway
U.S. Army Research Laboratory, Glenn Research Center, Cleveland, Ohio
Adam J. Medd and Thong Q. Dang
Syracuse University, Syracuse, New York
Aerodynamic Design Study of Advanced
Multistage Axial Compressor
NASA/TP—2002-211568
December 2002
National Aeronautics and
Space Administration
Glenn Research Center
ARL–TR–2859
U.S. ARMY
RESEARCH LABORATORY
Available from
NASA Center for Aerospace Information
7121 Standard Drive
Hanover, MD 21076
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22100
Available electronically at http://gltrs.grc.nasa.gov
NASA/TP—2002-211568 iii
Table of Contents
Summary .......................................................................................................................................... 1
Introduction ..................................................................................................................................... 1
Symbols ........................................................................................................................................... 3
Part I: Level of Technical Advancement ......................................................................................... 4
Basic Aerodynamic Technology Elements .................................................................................. 4
Aerodynamic loading and loss synthesis ................................................................................. 4
Anticipated technology advancements .................................................................................... 5
Extending the Design Envelope ...................................................................................................6
Four-Stage, High-Pressure-Compressor Aerodynamic Technology Demonstrator ..................... 8
Meanline performance synthesis ............................................................................................. 8
Throughflow .......................................................................................................................... 10
Part II: Three-Dimensional Blading Development ........................................................................ 14
Three-Dimensional Inverse Method........................................................................................... 14
Reblading Using INV3D ............................................................................................................ 15
Multistage Performance Evaluation ........................................................................................... 19
Procedure ............................................................................................................................... 19
APNASA results .................................................................................................................... 20
Conclusions ................................................................................................................................... 25
Appendixes
A—Geometry ............................................................................................................................. 27
B—Computed Axisymmetric Averaged Spanwise Profiles at Design Throttle ........................ 31
References ..................................................................................................................................... 36
NASA/TP—2002-211568 1
Summary
As a direct response to the need for further performance
gains from current multistage axial compressors, an
investigation of advanced aerodynamic design concepts
that will lead to compact, high-efficiency, and wide-
operability configurations is being pursued. Part I of this
report describes the projected level of technical advance-
ment relative to the state of the art and quantifies it in
terms of basic aerodynamic technology elements of
current design systems. A rational enhancement of these
elements is shown to lead to a substantial expansion of the
design and operability space. Aerodynamic design con-
siderations for a four-stage core compressor intended to
serve as a vehicle to develop, integrate, and demonstrate
aerotechnology advancements are discussed. This design
is biased toward high efficiency at high loading. Three-
dimensional blading and spanwise tailoring of vector
diagrams guided by computational fluid dynamics (CFD)
are used to manage the aerodynamics of the high-loaded
endwall regions. Certain deleterious flow features, such
as leakage-vortex-dominated endwall flow and strong
shock-boundary-layer interactions, were identified and
targeted for improvement. However, the preliminary
results were encouraging and the front two stages were
extracted for further aerodynamic trimming using a three-
dimensional inverse design method described in part II
of this report.
The benefits of the inverse design method are illus-
trated by developing an appropriate pressure-loading
strategy for transonic blading and applying it to reblade
the rotors in the front two stages of the four-stage configu-
ration. Multistage CFD simulations based on the average
passage formulation indicated an overall efficiency
potential far exceeding current practice for the front two
stages. Results of the CFD simulation at the aerodynamic
design point are interrogated to identify areas requiring
additional development. In spite of the significantly higher
aerodynamic loadings, advanced CFD-based tools were
able to effectively guide the design of a very efficient
axial compressor under state-of-the-art aeromechanical
constraints.
Introduction
The intensely competitive aeropropulsion sector places
some of the most stringent requirements on turbo-
compressors. A common challenge is aerothermo-
dynamic optimization subject to conflicting economic
Aerodynamic Design Study of Advanced Multistage Axial Compressor
Louis M. Larosiliere
U.S. Army Research Laboratory
Glenn Research Center
Cleveland, Ohio 44135
Jerry R. Wood
National Aeronautics and Space Administration
Glenn Research Center
Cleveland, Ohio 44135
Michael D. Hathaway
U.S. Army Research Laboratory
Glenn Research Center
Cleveland, Ohio 44135
Adam J. Medd and Thong Q. Dang
Syracuse University
Syracuse, New York 13244
2 NASA/TP—2002-211568
and system constraints, such as reduced cost, low environ-
mental emissions, and wide operability under adverse
conditions. An interesting account of the first 50 years of
aeropropulsion gas turbines was offered by Singh (ref. 1),
who clarified the trail taken to improve fuel economy by
way of higher thermal and propulsive efficiencies.
Figure 1 shows the effects of component efficiency,
compressor delivery temperature, and turbine entry tem-
perature on the thermal efficiency of a simple Brayton
cycle using a hydrocarbon fuel and metallic materials.
The implication is that overall polytropic efficiencies of
94 percent with compression ratios in the range of 60:1
and beyond must be realized to arrive at thermal efficien-
cies surpassing 55 percent. Techniques for achieving
low losses at high aerodynamic loadings have therefore
received renewed interest in many recent turbomachinery
studies (refs. 2 and 3).
Turbocompression technology has been advanced
continuously by higher work capacity per stage as a result
of increases in rotor speed, aerodynamic loading, and
throughflow Mach numbers. Using sophisticated diag-
nostic tools involving CFD and measurement tech-
niques, more suitable blade shapes with relatively low
losses at higher diffusion and Mach number levels have
been deployed. Better materials and matured structural
analysis methods have also allowed increases in rotor
speed with significant weight reductions. Improved
mechanical design and fabrication techniques have
raised the quality of current products.
The quest for further aerodynamic performance
advancements is becoming progressively more difficult
because of a dwindling residue of losses. Prohibitive
demands such as performance invariance to various oper-
ating conditions and hardware degradation are imposing
severe aerodynamic limitations. Easing these limitations
requires the application of new technology to manage the
particular flow structures responsible for performance
shortfalls. Effective strategies for achieving this are not at
all clear. A vital issue is whether to advance by refining
and extending well-proven concepts, perhaps in the face
of diminishing returns, or by changing to something
more unpredictable yet inviting.
A research program being conducted at the Glenn
Research Center is investigating advanced design con-
cepts that will lead to compact, high-efficiency, and wide-
operability compressors. This is a direct response to the
need for further performance gains from current
turbomachinery systems. To service these gains, a com-
bination of evolutionary and revolutionary approaches to
technology development was selected. The evolutionary
approach employs advancements in simulation techniques
to refine traditional design concepts in a bid for higher
efficiencies at increased aerodynamic loading levels,
whereas the revolutionary approach attempts to explore
unconventional concepts and paradigms for increased
pressure ratio, higher efficiencies, and wider operability.
94
92
88
65
60
55
50
45
40
Thermal efficiency, percent
600 700650 750 800 900
Takeoff
Typical cruise
850 950 1000
Compressor delivery temperature, K
Figure 1.—Impact of component efficiency on thermal efficiency (Singh, ref. 1)
Turbine entry
temperature,
K
1400
1600
1400
1600
1600
1800
Early 21st
century
Engines in
service 13.7
Second
quarter,
21st century
Polytropic
efficiency,
p
,
percent
NASA/TP—2002-211568 3
Part I of this report depicts the level of technical
advancement being sought, quantifies this advancement
in terms of the basic aerodynamic technology elements of
current design systems, and identifies a four-stage core
compressor configuration for advanced technology
development. A preliminary aerodynamic design of the
four-stage configuration is described in the context of
current practice. Custom-tailored blade contours were
initially developed from mean camber surfaces derived
from axisymmetric stream surfaces generated by an
inverse throughflow calculation. Isolated blade-row
CFD simulations provided some guidance to fine-tune
the blading. A multistage CFD computation using a
mixing plane scheme indicated an efficiency potential for
the four-stage compressor that is within current stan-
dards. In addition, performance-limiting flow features,
such as leakage-vortex-dominated endwall action and/or
reaction and strong shock-boundary-layer interactions,
were identified and targeted for improvement. The possi-
bility of further performance gains requires a design
method that effectively extends the custom-tailored
blading philosophy into the endwall regions and
adequately allows matching of blade rows in the multi-
stage environment.
In part II of the report, an aerodynamic design of the
front two stages of the four-stage configuration is devel-
oped using the best available CFD tools. The three-
dimensional inverse design method of Dang (ref. 4) was
used to define advanced transonic rotor blading. To
illustrate the benefits of this method, the front two stages
of the four-stage configuration were rebladed and the
performance potential evaluated. The multistage aerody-
namic environment was modeled using the substantiated
method of Adamczyk (ref. 5). This modeling permitted a
reliable prediction of the performance potential of the
two-stage group and guided design revisions, including
the facilitation of stage matching. The results show the
critical role of this method and illustrate achievable
performance using an evolutionary approach buttressed
by advanced turbomachinery CFD.
Geometric information for all blade rows is given in
appendix A, and spanwise profiles of axisymmetric aver-
aged flow properties extracted from the multistage CFD
simulation of the front two-stages at the aerodynamic
design point are given in appendix B.
Symbols
Aex passage exit area, in.
Aθtangential projection of blade surface area
Dfactor diffusion factor
Eeffectivity ratio
fblade mean camber surface, f(r,z)
fstack blade stacking line, fstack(r)
Htotal enthalpy change, BTU/lbm
Ldiff equivalent diffusion length
LA
diff
/
ex
ratio of equivalent diffusion length
to effective passage exit width
M1inlet Mach number
˙
m
mass flow rate, lbm/s
Ptotal pressure, psia
PR pressure ratio
pstatic pressure, psia
pstatic-pressure difference between blade
upper and lower surfaces at fixed axial
positions, p = p(r,z)
Recchord Reynolds number
Tblade thickness distribution, T(r,z)
t/gratio of clearance to staggered spacing
Ublade speed, ft/s
Vvelocity, ft/s
V
θ
absolute tangential velocity, ft/s
Wc inlet corrected flow, lbm/s
z/sratio of axial spacing to pitch
αswirl angle from axial direction, deg
ηefficiency, percent
4 NASA/TP—2002-211568
Λblade aspect ratio; ratio of average length to
pitchline chord
σsolidity; ratio of chord to average tangential
spacing
ϕflow coefficient, Vz /Um
ψwork coefficient, H/Um
2
corrected mechanical speed, rpm
Subscripts:
abs absolute
ex exit
in inlet
le leading edge
mmeanline
max maximum
ppolytropic
ref reference
rel relative
ttotal
te trailing edge
tip tip
tt total to total
zaxial
Part I: Level of Technical Advancement
Basic Aerodynamic Technology Elements
Aerodynamic loading and loss synthesis.—Turbo-
compressor aerodynamics comprises a complex array of
intimately linked thermofluid processes that are difficult
to separate into neat compartments. However, simplified
models, which sufficiently incorporate the important
physical phenomena, have been synthesized into design
systems. Three essential aerodynamic technology ele-
ments of such design systems are (1) entropy production
or loss; (2) aerodynamic transport including spanwise
mixing; and (3) aerodynamic stability. The demarcation
of these three elements is sometimes distorted by various
empirical correlations that implicitly account for aerody-
namic transport. Denton (ref. 6) gives a good physical
description of entropy production in turbomachines and
Greitzer (ref. 7) does likewise for aerodynamic stability.
Adamczyk (ref. 5) and Adkins and Smith (ref. 8) discuss
aerodynamic transport phenomena in turbocompressors.
An adaptation of the loss model of Koch and Smith
(ref. 9) and the stage maximum static-pressure-rise pre-
diction method of Koch (ref. 10) was used to estimate
both the efficiency potential and the maximum aerody-
namic loading capability for the present study. The losses
are grouped according to source: (1) viscous dissipation
along the blade-surface profile and the resultant wake
mixing; (2) endwall viscous shear including interactions
with secondary and leakage flows; and (3) shocks on the
blading. Blade-surface-profile losses are linked to
suction-surface diffusion (V
max/V
te), blade trailing-edge
thickness, Reynolds number, and surface roughness.
Endwall losses that have been determined from hub and
casing viscous layer measurements are related to aspect
ratio, solidity, blade stagger, endwall clearance, blade-
row axial spacing, and aerodynamic loading level. The
shock loss model relates passage shock losses to inlet and
exit Mach numbers. A leading-edge bow shock loss is
calculated based on the inlet Mach number and leading-
edge thickness.
The stage maximum static-pressure-rise potential is
linked to stage geometric parameters (e.g., solidity,
aspect ratio, stagger, etc.) by a correlation based on an
analogy between compressor blade passages and straight
diffusers. There are also corrections for Reynolds num-
ber, endwall leakage, and blade-row axial spacing. The
blading is averaged over a stage without separating the
rotor and stator performance. This is a simple yet effec-
tive method to complement conceptual design calcula-
tions made at a representative section of a machine (i.e.,
meanline with implicit accounting of aerotransport). A
relative aerodynamic loading parameter is defined by the
ratio of the actual stage pressure-rise coefficient to that
predicted by the correlation (the effectivity ratio E).
Hence, an effectivity of 1 (E = 1.0) indicates limit loading.
It can be argued that this is a more appropriate indicator
of aerodynamic loading from the point of view of insta-
bility initiated by the endwall flow. Measurements
(ref. 11) have indicated that for well-designed blading
with adequate circulation capacity, aerodynamic instabil-
ity is likely to occur when endwall viscous layers increase
to a limiting value dependent on effectivity and clearance.
NASA/TP—2002-211568 5
The loss and aerodynamic loading models are unified in
the sense that endwall loss and aerodynamic blockage are
interrelated through aerodynamic loading. Thus, it is
possible to determine the maximum pressure rise that can
be obtained with moderate losses but not necessarily to
determine the point of instability.
Anticipated technology advancements.—Changes to
the loss and peak pressure-rise models were made to
reflect anticipated aerodynamic technology advancements.
It was surmised that low blade profile losses could
be extended to higher diffusion levels by employing
boundary-layer control techniques. Cascade tests and
boundary-layer analysis have shown the potential for
effecting this through diffusion control using tailored
contours, staged diffusion (e.g., tandem and/or splittered
architectures), or active diffusion control (e.g., surface
transpiration or surface morphing). Figure 2 shows the
postulated improvement in the ratio of the blade trailing-
edge momentum thickness to the chord (i.e., viscous
dissipation) relative to the state of the practice for a fixed-
chord Reynolds number Rec, an inlet Mach number M1,
and an axial velocity-density ratio (AVDR). Note that
the reference is the state of the practice extracted from
the method of Koch and Smith rather than state of the art
because there are some uncertainties as to what the
latter is. Also indicated is a data point assembled from
measurements (ref. 12) on a compressor stator equipped
with bleed slots for boundary-layer control. Research
currently underway should provide the knowledge
required for practically achieving this control.
The stage maximum static-pressure-rise capability was
postulated to increase relative to the state of the practice
as shown in figure 3 for a fixed Reynolds number Re, the
ratio of clearance to staggered spacing t/g, and the ratio of
axial spacing to pitch z/s. The abscissa,
LA
diff
/
ex
, is
the ratio of an equivalent diffusion length Ldiff to an
effective passage exit width (square root of passage exit
area Aex). This ratio can be expressed in terms of concep-
tual design parameters (solidity, aspect ratio, stagger) at
a representative section of the machine. Shown on the
ordinate is the stage maximum effective static-pressure-
rise coefficient averaged over the rotor and stator (see
ref. 10 for details). Also indicated in the figure is a data
point from a low-speed rig with high-stagger, forward-
swept blading. This data point is clearly above the state-
of-the-practice level and reasons for this are under
investigation using a simple physical model developed
by Khalid et al. (ref. 13) for clearance-related blockage.
The results from this model provide a quantification of
aerodynamic blockage and a framework for screening
endwall flow-management strategies based on casing
treatment, vector diagrams, or pressure-loading distribu-
tion. The model corroborates the experiments of Lee and
Greitzer (ref. 14), who demonstrated significant enhance-
ments to the peak static-pressure rise of a blade row by the
downstream removal of low-momentum flow and the
0.040
0.035
0.030
0.025
0.020
0.015
0.010
0.005
0.000
Ratio of trailing-edge momentum
thickness to chord
1.0 1.5 2.0 2.5 3.0 3.5
Suction-surface diffusion ratio, V
max
/V
te
Aspirated
cascade
demonstrator
Projections with advanced
aerodynamic concepts
State-of-the-practice
technology (Koch and
Smith, ref. 10)
Figure 2.Enhancements to profile loss model. Fixed-
chord Reynolds number, Re
c
, 10
6
; inlet Mach number,
M
1
, 0.05; axial velocity-density ratio, AVDR, 1.0.
Figure 3.Enhancements to stage maximum static-
pressure rise. Fixed Reynolds number, Re, 130 000;
ratio of clearance to staggered spacing, t/g, 0.055;
ratio of axial spacing to pitch, z/s, 0.38.
1.0
0.8
0.9
0.6
0.7
0.4
0.3
0.5
0.2
Maximum effective static-pressure-rise
coefficient
012345
Equivalent conical diffusion angle parameter,
L
diff
/(A
ex
)
0.5
Rig demonstrator
Projections with
advanced aerodynamic
concepts
State-of-the-practice
technology (Koch's
correlation, ref. 11)
6 NASA/TP—2002-211568
upstream injection of flow with sufficient streamwise
momentum.
It was judged that managing the endwall flow (e.g.,
secondary and leakage flow control) would also allow the
blading to be more effective in that region, thereby
reducing the required torque supplied to the rotor. This is
accounted for in the endwall loss model by a 17-percent
increase in the so-called tangential force thickness as
described by Smith (ref. 11). All other loss sources,
including direct shock losses, remained unmodified. The
loss and aerodynamic loading models were integrated in
a computerized preliminary design and analysis proce-
dure, which allowed perturbations to specific aerody-
namic technology elements to be readily appraised.
Extending the Design Envelope
The consequences of the aerodynamic advancements
previously discussed were evaluated by comparing the
design space of a prototypical stage with and without
these advancements. A so-called Smith chart is used to
represent the design and operational space of a
turbocompressor stage with a given geometric form and
flow type. This space is spanned by a suitably averaged
flow coefficient (ϕ = Vz/Um) and work coefficient
(ψ = H/Um
2). A relative aerodynamic loading para-
meter E (ψ, ϕ, geometric form, flow type) and an
efficiency η (ψ, ϕ, geometric form, flow type) can be
superimposed on this chart. It should be noted that the
work coefficient is generally not a direct measure of
aerodynamic loading as defined herein because it has no
explicit link to mean static-pressure rise. This is reflected
in the additional functional dependence of loading on
flow coefficient and geometric form. The basic design
challenge is to generate geometry that establishes a flow
satisfying the ψ-ϕ requirements at high efficiency with-
out exceeding the relative aerodynamic loading limit.
Geometric parameters for a prototypical single-
stage axial compressor with a 21-in. maximum diameter
were selected to illustrate the expanded design envelope
and enhanced performance trends. A Smith chart for
these parameters is shown in figure 4(a) using state-of-
the-practice aerodynamic technology and in figure 4(b)
with the postulated technology advancements. These
plots are based on the following design choices: (1) zero
swirl at stage inlet; (2) 60-percent-rotor-area contraction;
(3) constant radius casing; and (4) axial velocity ratio of
1.0 across the stage. Since the rotor inlet specific flow
(40.0 lbm/s-ft2) is fixed, varying the flow coefficient
1.00
.95
.85
.75
.65
Effectivity
ratio,
E
1.0
1.1
1.2
1.3
0.8
0.9
0.7
0.6
0.5
0.4
2
Work coefficient, = H/U
m
0.2 0.4 0.6 0.8 1.0 1.2
Flow coefficient, = V
z
/U
m
(a)
Lines of constant
polytropic efficiency
1.00
.95
.85
.75
.65
Effectivity
ratio,
E
1.0
1.1
1.2
1.3
0.8
0.9
0.7
0.6
0.5
0.4
2
Work coefficient, = H/U
m
0.2 0.4 0.6 0.8 1.0 1.2
Flow coefficient, = V
z
/U
m
(b)
Lines of constant
polytropic efficiency
Figure 4.Expanded design envelope and enhanced
performance trends for prototypical single-stage axial
compressor with 21-in. maximum diameter. Geometric
parameters: rotor aspect ratio, 0.940; stator aspect
ratio, 1.250; rotor solidity, 1.800; stator solidity, 1.700;
Reynolds number, 3.2610
6
; ratio of clearance to
staggered spacing, 0.0122. (a) Aerodynamic design
space for state-of-the-practice technology. (b) Ex-
tended design envelope with advanced technology.
sweeps through both subsonic and transonic stages. In
addition, fixing the inlet swirl and rotor area contraction
generates a range of stage reactions as the flow coefficient
is varied. The design point for individual stages of this
particular type may be placed anywhere below the bound-
NASA/TP—2002-211568 7
specific performance trends, figure 5 presents the effect
of rotor tip speed and stage aerodynamic loading on stage
total-pressure ratio and polytropic efficiency for the pro-
totypical stage. Figure 5(a) is based on state-of-the-
practice technology whereas figure 5(b) used the postulated
aerodynamic technology advancements. The curves indi-
cate that higher stage pressure ratios can be obtained by
either increased tip speed or increased stage loading.
Maximum dividends occur when both high loading and
high tip speed are selected. The attainment of gains in
pressure ratio is complicated by the need for high
efficiency and wide operability. As loading is increased,
losses tend to increase, and the potential for flow break-
down and aerodynamic instability is much greater. For
the range of blade speeds shown in figure 5, the rotor tip
relative Mach numbers vary from subsonic to high super-
sonic (i.e., greater than 1.6) values that can result in severe
shock-related viscous losses.
For a fixed geometric envelope, the anticipated aerody-
namic technology advancements suggest the potential for
substantial expansion of the design space in the direction
of higher work coefficients and stage total-pressure ratio.
In addition, high efficiencies are extended to more el-
evated loadings. An increased pressure ratio per stage has
traditionally been realized partly because of higher rotor
speeds and primarily because of a lower aspect ratio,
increased solidity, and higher stagger blading. These
design choices, as can be inferred from figure 3, are often
made to increase stage maximum static-pressure rise,
thereby insuring adequate aerodynamic stability, which
can often be accompanied by increased losses. A report
by Wisler, Koch, and Smith (ref. 15) illustrates the
interactions between different design choices and offers
guidance for selecting multistage core compressor
design parameters that have a high-efficiency potential.
Based upon these results and some vector diagram con-
siderations, figure 6 was constructed using information
from actual compressor rig tests of machines having a
certain degree of similarity in terms of tip clearance,
stability requirement, specific flow, and blading. The
abscissa is the Skoch parameter (SP), which is defined as
SP =+
σϕ
ψϕαΛ112
12
tan in
/
where σ is the solidity (the ratio of chord to average
tangential spacing); Λ is the blade aspect ratio (the ratio
of average length to pitchline chord); and αin is the stage
(a)
3.5
3.0
2.5
2.0
5.5
6.0
5.0
4.5
4.0
1.5
1.0
Total-pressure ratio, PR
tt
600 800 140012001000 1600 1800
Rotor tip speed, U
tip
, ft/s
Lines of constant
polytropic efficiency
.65
.75
.85
.95
1.00
Effectivity
ratio,
E
Figure 5.Performance trends for prototypical stage.
(a) State-of-the-practice technology. (b) Postulated
advanced technology.
3.5
3.0
2.5
2.0
5.5
6.0
5.0
4.5
4.0
1.5
1.0
Total-pressure ratio, PR
tt
600 800 140012001000 1600 1800
Rotor tip speed, U
tip
, ft/s
(b)
Lines of constant
polytropic efficiency
.65
.75
.85
.95
1.00
Effectivity
ratio,
E
ary E = 1.0. For a given relative aerodynamic loading
level E, flow and work coefficients can be selected to
maximize efficiency.
Evident from figure 4 is a significant extension of the
design space in the direction of higher work coefficients
made possible by the postulated aerodynamic technology
advancements. A potential increase of three points in
peak polytropic efficiency is depicted along with the
availability of more options for high-efficiency designs.
Although the operability space, including flow range, is
not directly addressed herein, the choice of how far and in
which direction to extend the design space is greatly
influenced by operability considerations. To illustrate
8 NASA/TP—2002-211568
inlet swirl angle. This parameter, averaged over all
stages, is analogous to a specific speed. The figure indi-
cates the existence of judicious combinations of geomet-
ric form and vector diagram, which lead to high
efficiencies. This is discussed by Wisler, Koch, and
Smith, who showed the competition amongst various loss
sources as aspect ratio and solidity are varied. Thus, the
Skoch parameter provides a basis for trading geometric
form and vector diagram (e.g., compactness and oper-
ability) to optimize efficiency.
To achieve the low parts count and high efficiency
required of modern turbocompression systems, advanced
technology concepts have been driven to high-work-
coefficient and moderate-flow-coefficient designs. This
trend is illustrated in figure 6 with the projected advanced
technology goal for the chosen Skoch parameter. The
advanced technology goal is a result of design choices
orchestrated using the anticipated aerodynamic technol-
ogy advancements. A discussion of these design choices
follows.
Four-Stage, High-Pressure-Compressor Aerody-
namic Technology Demonstrator
So far, no definitive path has been identified for achiev-
ing the assumed technology advancements. A research
configuration was conceived with the intent of evaluating
how far the use of advanced turbomachinery CFD and
three-dimensional design concepts might permit one to
progress in realizing high efficiency at increased loading
levels. The objective was to configure a technology
demonstrator compatible with current multistage core
compressors for high-bypass-ratio turbofans. Although
a specific application was not defined, a four-stage
configuration under current aeromechanical constraints
was selected. The execution of the aerodynamic design
consists of an iterative loop between several computer
programs as illustrated in figure 7. This methodology is
essentially the same as that currently employed in most
design offices with perhaps the exception of the three-
dimensional inverse design method. The steps of the
so-called preliminary design phase of this process and
their interactions are outlined below; the more detailed
design phase, including three-dimensional inverse design
and multistage CFD, is described in part II.
Meanline performance synthesis.—Four parameters
were established at the outset. The corrected specific flow
(flow per unit annulus area) at the first rotor inlet was
40.0 lbm/s-ft2 corresponding to an average axial inlet
Mach number of 0.6, which is consistent with advanced
core compressors. A maximum rotor corrected tip speed
of 1500 ft/s was assumed based on turbine stress consid-
erations for a high-bypass-ratio turbofan. An average
Skoch parameter in the range of 1.5 to 2.0 was selected for
high efficiency and compactness as suggested from
figure 6. With a casing diameter of 21.08 in. and a radius
ratio of 0.528 at the first rotor inlet, the mass flow
corresponding to the prescribed specific flow was
70.0 lbm/s. The design can be scaled to different mass
0.88
0.90
0.92
0.94
0.86
0.84
0.82
0.80
Polytropic efficiency,
p
, percent
1.2 1.4 1.6 1.8 2.0 2.2 2.4
Skoch parameter, SP
Advanced
technology
goal
TESCOM
stage one
NASA-Allison
two stage
NASA
two-stage
fan
General Electric
Energy Efficient Engine
HPC
Figure 6.Peak efficiency trends with various design
choices for geometric form and vector diagram.
Systems
evaluation
Throughflow
UD0300M
Meanline
performance
synthesis
COMPS
Geometry
editor
Maestro
CFD tools
ADPAC
APNASA
SWIFT
TURBO
Inverse
design
INV3D
MISES
Mechanics
Figure 7.Aerodynamic design system.
NASA/TP—2002-211568 9
flow rates if required. Most of the remaining characteris-
tics resulted from the objective of designing a multi-
stage compressor with a high-efficiency potential at an
elevated loading level.
The initial step in the preliminary design of the four-
stage, high-pressure compressor (HPC) was taken by
using a meanline program incorporating the loss and peak
pressure-rise models previously presented. This program
also includes estimates of hub and casing vector diagrams
assuming an isentropic simple radial equilibrium. A
conceptual design using state-of-the-practice technology
and current design practices was executed first. Then,
assuming the postulated technology advancements, an
assessment of the performance potential of this design
was made.
The meanline program provided the average loss, aero-
dynamic blockage, and peak pressure-rise capability of
each stage of the four-stage configuration. A stagewise
distribution of effectivity was prescribed based on the
philosophy that the operating points of the front and back
stages would primarily pivot about the two middle stages
as the compressor is throttled along a typical engine
operating line. In addition, the averaged effectivity of the
compressor was selected to be consistent with a positive
stability margin of about 5 percent at the aerodynamic
design speed. The required stability margin depends on
the intended application and availability of practical
stability-management technologies. Stage effectivity
distributions are given in table I, which shows the
two middle stages to be the set near their peak loading
capabilities.
Of the several flow-path shapes (constant casing,
constant meanline, and constant hub) investigated, a
constant-diameter casing provided the best balance
between high pressure ratio and good efficiency. Because
of the need to limit the exit rim speed, the casing diameter
was reduced at the aft end of the compressor. A discharge
Mach number of about 0.35 was assumed based on
considerations of matching with an additional down-
stream stage. Stage efficiency was refined by balancing
stage reaction, inlet swirl, solidity, aspect ratio, and axial
velocity diffusion. Orchestrating all these parameters
resulted in an overall total-pressure ratio of 12:1 at a rotor
1 (R1) corrected tip speed of 1477 ft/s. The average aspect
ratio of the rotors was 0.8 and that of the stators was 1.0.
Aspect ratios for the rotors were governed primarily by
aeroelastic stability considerations. The rotor and stator
average solidities were about 2.0. The predicted stage-by-
stage distribution of polytropic efficiency and com-
pressor overall efficiency is given in table I. Reflected
in these efficiencies are the following rotor tip clearance
levels: 0.020 in. for R1, 0.018 in. for R2, 0.016 in. for R3,
and 0.014 in. for R4. An evaluation of current and near-
term core compressor clearance trends supported the
assumed clearance levels. The first three stators are
cantilevered from the casing with an average hub clear-
ance of 0.018 in. These hub clearances and other clear-
ances for anticipated variable stators were factored into
the efficiency predictions. The overall performance quoted
for the four-stage HPC extends from the guide-vane
leading edge to the compressor discharge.
The flow path displayed in figure 8 was biased towards
high work and high efficiency. A variable-stagger inlet
guide vane (IGV) provides part-speed operability. The
guide vane is intended to deliver a nominal swirl distribu-
tion of 9° counterswirl at the hub, 2° counterswirl at
midheight, and 0° at the casing. This choice was made to
control the rotor 1 hub reaction and to reduce the absolute
Mach number at the inlet to the stator 1 hub. Note that the
stator leading edges are swept forward near the endwalls
to tailor the loading in those regions. There are 32 inlet
guide vanes, 54 first stators (S1), 74 second stators (S2),
132 third stators (S3), and 104 fourth stators (S4). The
rotor blade counts are 26 R1’s, 56 R2’s, 76 R3’s, and
80 R4’s. Preliminary estimates of off-design perfor-
mance, assuming current technology, indicate a potential
TABLE I.COMPARISON OF STAGE LOADING AND
POLYTROPIC EFFICIENCY
Stage Cumulative State of the practice Advanced technology
total-pressure Effectivity Polytropic Effectivity Polytropic
ratio, ratio, efficiency, ratio, efficiency,
PR
tt
E
η
p
, E η
p
,
percent percent
1 2.372 0.894 0.890 0.755 0.923
2 4.645 .935 .883 .779 .920
3 8.213 .982 .864 .820 .919
4 12.00 .883 .899 .730 .927
Overall 12.00 ----- 0.883 ----- 0.920
10 NASA/TP2002-211568
need for variable S1, variable S2, and interstage bleed
between the second and third stages.
The ultimate performance potential of the previously
described state-of-the-practice design was evaluated by
incorporating the anticipated advanced aerodynamic tech-
nologies in the meanline program. The results shown in
table I indicate a significant increase in overall efficiency
in addition to a higher stability margin for the same duty.
Thus, the advanced technology goal displayed in figure 6
was set.
Throughflow.After selecting the aerodynamic
design point and verifying that the basic geometric
parameters derived from the meanline analysis had the
potential to be developed into a viable configuration
which satisfied the prescribed technical goals, the spanwise
tailoring of the vector diagrams was begun by using an
adaptation of the inverse throughflow computer program
described in reference 16. The tailoring involves an
iterative loop between an intrablade mean-stream surface
analysis and a blade geometry generator. The computa-
tions are based on the streamline curvature method with
the inclusion of an axisymmetric body force field
assumed to act normal to the surface formed by the
stacked camber lines of each blade row. Custom-tailored
airfoils were employed for all blade rows. The airfoil
customization technique used consists of assuming the
meridional distributions of total pressure through the
rotors and of angular momentum through the stators.
Then, after correcting for departures from the mean
camber line, airfoils are fitted to the calculated relative
flow angles and a two-part, quarter-sine-wave thickness
distribution. The stream surface sections are stacked
along a specified backbone or stacking axis to obtain
three-dimensional blade surfaces.
A process of successive refinement guided by CFD
results determined the incidence and deviation angles
used to generate the airfoil sections. Initial values were
estimated using the quasi-three-dimensional, viscous code
RVCQ3D (ref. 17). RVCQ3D was also used to direct
the initial selection (meridional distributions of angular
momentum or total pressure within blades) of airfoil
contours. These contours were updated by conducting
isolated blade-row viscous analysis using ADPAC
(ref. 18) with inflow and outflow boundary conditions
extracted from the throughflow analysis. The results from
the ADPAC analysis were also used to tailor the stacking
axis and to modify vector diagrams to control spanwise
static-pressure gradients. Spanwise distributions of blade-
row losses were also revised using the CFD results as a
guide. Aerodynamic blockages were initially taken from
the meanline program and were successively adjusted
based on CFD results.
Setting the compressor discharge Mach number and
total-pressure ratio fixes the overall static-pressure rise.
With the flow path fixed, the meridional static-pressure
gradient is primarily determined by the stage effectivity
distributions derived from the meanline analysis. The
wall static-pressure distributions established with the
throughflow analysis at the aerodynamic design point
are displayed in figure 9. To achieve low loss and to
ensure aerodynamic stability, it is generally desirable to
minimize static-pressure gradients along the endwalls.
16
14
12
10
8
6
4
2
0
Radius, in.
010
Axial location, z, in.
IGV R1
S1
S3
R4
R2 S2
R3
S4
Figure 8.High-pressure compressor flow path.
NASA/TP2002-211568 11
Figure 9 shows that the meridional gradients of static
pressure are approximately constant through most of the
rotor blade rows (see fig. 8 for blade locations) and then
taper off toward the trailing edge. The static-pressure rise
is more rapid in the front half of the stator blade rows and
quickly tapers off in the remaining half of the blade. For
all blade rows, preferential radial forces were introduced
through the tangential leaning of the mean camber surface
to control spanwise gradients of static pressure.
Spanwise variations of the rotor inlet relative Mach
number are shown in figure 10 for all four rotors at the
aerodynamic design point. For rotor 1, the relative Mach
numbers vary from high subsonic near the hub to 1.6 near
the casing. The two middle rotors (R2 and R3) have
supersonic inlet Mach numbers across the span, which
makes stage matching exceptionally difficult. The rotor 4
inlet Mach numbers are approximately sonic across the
span. The inlet absolute Mach number distributions for
the stators are displayed in figure 11. The stator 1 hub
Mach number is slightly above sonic with all remaining
stators having subsonic inlet Mach numbers.
15
10
12
8
6
4
2
0
Wall static pressure, p/P
ref
0510
Axial location, z, in.
Figure 9.Wall static-pressure distribution at aerodynamic design point.
Hub
Casing
100
90
80
70
60
50
40
30
20
10
0
Percent of span from hub
0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7
Relative Mach number, M
1,rel
Rotor
1
2
3
4
Figure 10.Rotor inlet relative Mach number.
100
90
80
70
60
50
40
30
20
10
Percent of span from hub
0
0.3 0.4 0.5 0.6
2
1
3
4
Stator
0.7 0.8 0.9 1.0 1.1
Absolute Mach number, M
abs
Figure 11.Stator inlet absolute Mach number.
12 NASA/TP2002-211568
100
90
80
70
60
50
40
30
20
10
Percent of span from hub
0
0.2 0.3 0.4 0.5
2
1
3
4
Rotor
0.6 0.7
Diffusion factor, Dfactor
Figure 12.Rotor diffusion factors.
100
90
80
70
60
50
40
30
20
10
Percent of span from hub
0
0.2 0.3 0.4 0.5
2
1
3
4
Stator
0.6 0.7
Diffusion factor, D
factor
Figure 13.Stator diffusion factors.
100
90
80
70
60
50
40
30
20
10
Percent of span from hub
0
20 10 0 10 20 30
Exit
Inlet
40 6050
Absolute flow angle,
abs
, deg
Figure 14.Stator inlet and exit absolute flow angles.
Exit
Inlet
2
1
3
4
Stator
100
90
80
70
60
50
40
30
20
10
Percent of span from hub
024 6
23 4
Rotor
1
81012
Cummulative total-pressure ratio, PR
tt
Figure 15.Rotor exit cumulative total-pressure ratio.
NASA/TP2002-211568 13
The spanwise distributions of the diffusion factor Dfactor
for rotors and stators at the aerodynamic design point are
shown in figures 12 and 13, respectively. These diffusion
factors are locally high, reflecting the increased stage
aerodynamic loadings. The maximum diffusion factors
are in excess of 0.65 and occur near the endwalls. How-
ever, the average values are not far from levels for which
acceptable performance has been demonstrated. The
stator inlet and exit absolute flow angles are plotted in
figure 14. On the average, approximately 50° of turning
was achieved in the stators. The intent was to overturn
near the endwalls to accommodate secondary flows.
Counterswirl (swirl opposite the direction of rotor
rotation) was prescribed for S2 and S3 to control the
spanwise distributions of rotor (R3 and R4) aerodynamic
loading, as defined by the diffusion factor. This
counterswirl also increases the stage reaction, which may
have a favorable impact on stage performance. Spanwise
distributions of cumulative rotor exit total-pressure ratios
are displayed in figure 15. These distributions are com-
patible with the prescribed stator exit swirl profiles. The
intent was to propagate a hub-strong, total-pressure
profile within the multistage. Such a profile was thought
to be favorable with respect to aerodynamic stability as
the machine is throttled. Overall, the vector diagrams
were tailored under the guidance of CFD results to pro-
vide a beneficial relief to the high-loss and high-loading
endwall regions.
Figure 16.Axisymmetric averaged throughflow velocity distribution at aerodynamic design
point.
Velocity
1.02
0.26
The initial blading was generated and refined using
isolated blade-row CFD analysis. The axisymmetric
averaged throughflow velocity distribution at the aerody-
namic design point is presented in figure 16. This was
processed from the results of a three-dimensional multi-
stage simulation employing a mixing plane approach
within the ADPAC code. The results serve to identify in
the design potential weak points that are in need of further
refinements. Evident from the figure is that in the hub
region of R3, there is weak flow caused by the high
aerodynamic loading being requested and by aerody-
namic mismatching between blade rows. In addition, the
rotor tips show flow weaknesses associated with leakage
flow development in a high-loading region with shocks.
Based on the results from the multistage ADPAC simula-
tion, the overall performance potential of this preliminary
design configuration was predicted to be a pressure
ratio of 12:1 at a polytropic efficiency of 89 percent. To
further appreciate the level of technical advancement
being sought, figure 17 shows the fully developed com-
pressor goal relative to established performance trends.
This design sits at an average work factor of 0.44. It can
be observed that the preliminary design results are in line
with current trends and that achievement of the goal
would indicate a substantial advancement over the state of
the practice if not over the state of the art. What is not
explicitly stated is the suitability of such a design for a
practical engine product. Further research and develop-
ment are required to ascertain the postulated aerodynamic
technology advancements.
14 NASA/TP2002-211568
Part II: Three-Dimensional Blading
Development
Three-Dimensional Inverse Method
The primary prescribed quantities in the three-dimen-
sional inverse method are the blade stacking line fstack =
fstack(r), the blade thickness distribution T = T(r,z), and
the blade pressure-loading distribution p = p(r,z).
Herein, blade pressure loading is defined as the pressure
difference between the blade upper and lower surfaces at
fixed axial positions. For a given set of inputs, the three-
dimensional inverse method computes the corresponding
blade mean camber surface f = f(r,z). Clearly, the
blade geometry corresponding to prescribed values for
[fstack, T, p] is not guaranteed to have the optimum
performance or to be aeromechanically acceptable. The
challenge is to pick these quantities to arrive at a satisfac-
tory blade.
The three-dimensional inverse method is based on the
solution of the Navier-Stokes equations using the robust,
finite-volume, time-marching scheme of Jameson,
Schmidt, and Turkel (ref. 19). Viscous effects are mod-
eled using the method proposed by Denton (ref. 20) for
turbulent flows as adapted by Damle (ref. 21). During the
time-marching process, fluid is allowed to cross the blade
surfaces, and a pressure-jump condition (blade pressure
loading) is imposed across the blade surfaces. The flow-
tangency condition along the blade surfaces is then used
to update the blade geometry. Endwall clearances are
modeled by assuming periodicity within the clearance
gap. The INV3D computer code employed in this study
can run in either the standard analysis mode or the inverse
mode.
The successful strategy employed in the previously
published work on this three-dimensional inverse method
(ref. 22) was used to pick the prescribed quantities
[fstack, T, p] that would improve the present transonic
rotor blade designs. The strategy is as follows:
1. Start with blade geometry obtained with the tradi-
tional design tools (e.g., meanline and/or throughflow
method). This geometry is termed the original design.
Then switch to the three-dimensional inverse method to
improve the geometry, using the original design as the
initial guess.
2. Input to the three-dimensional inverse method the
blade tangential thickness distribution, which has been
kept the same as the original design to satisfy some
structural constraints and to reduce the number of degrees
of freedom.
3. Adjust the blade pressure loading p(r,z) to intro-
duce geometric features that enable the control of local
flow structures (shock, secondary flows, boundary lay-
ers, etc.) linked to a performance index. The choice of the
blade pressure loading is a three-dimensional approach.
At a given spanwise station, the blade pressure-loading
distribution is used to manage the local aerodynamics and
to tailor the spanwise vector diagrams:
r p A m rV rV
le
te
te le
d˙()
θθθ
(
)
(
)
[]
1
94
92
90
88
86
Polytropic efficiency,
p
, percent
84
0.10 0.20 0.30 0.40 0.50 0.60 0.70
2
Average work coefficient, = H
avg
/U
tip
Figure 17.Core compressor technology assessment in terms of work factor and
polytropic efficiency. UHBR, ultra-high bypass ratio; EIS, entry into service.
NASA UHBR turbofan contract (2016 EIS)
State of the art
NASA study
(2020 EIS)
Predicted for two stage
Advanced technology goal
Preliminary four stage
NASA/TP2002-211568 15
where the subscripts te and le are trailing edge and leading
edge; Aθ is the tangential projection of the blade surface
area;
˙
m
is the mass flow rate; and
V
θ
is the mass-averaged
tangential velocity. For a rotor, specifying the blade
pressure loading at every spanwise station is the same as
prescribing the spanwise distribution of total temperature
rise across the rotor. This is the usual two-dimensional
thinking when a two-dimensional inverse method is used.
With a three-dimensional method, an additional control is
the spanwise variation of the blade pressure loading. As
will be described shortly, this is used to adjust the orien-
tation of the passage shock as seen in a meridional plane.
4. Modify as needed the prescribed blade stacking line
so as to restrain potential endwall corner separations and
to limit excessive blade twisting.
The blade design procedure proposed herein is very
compatible with the inverse throughflow method used in
part I to generate the original blades. In particular, the
design intents, as described by the spanwise profiles of
axisymmetric averaged pressure, temperature, and angles,
are fed into the inverse method as inflow and outflow
boundary conditions. One of the main advantages of
using a three-dimensional inverse method is that the
critical physics of the complex aerodynamic interactions
are directly accounted for rather than being patched in a
somewhat convoluted fashion.
Reblading Using INV3D
The front two stages, including the inlet guide vane, of
the four-stage configuration were extracted for a more
refined aerodynamic design. A meridional cross section
of the flow path is shown in figure 18. The following are
the aerodynamic design requirements for the two stage: a
corrected flow of 70 lbm/s, an overall total-pressure ratio
of 4.645:1, and a rotor 1 corrected tip speed of
1477 ft/sec. From part I, the state-of-the-practice
efficiency potential of this configuration was estimated to
be 89 percent polytropic. The intended axisymmetric
profiles and design considerations for the original blades
are found in part I.
In this section, the redesign of the second rotor (R2) is
discussed in detail for three important reasons. First, the
second rotor is the most challenging because the incom-
ing relative Mach number is supersonic from hub to tip.
Second, the relative aerodynamic loading based on the
effectivity parameter E is the highest. Third, this rotor is
also critical in terms of proper stage matching because of
possible strong interactions with the upstream stator.
The design intents are obtained from the throughflow
model, which is updated based on information supplied
by the multistage CFD simulations to be described in the
section Multistage Performance Evaluation. It is not
possible to get an exact match between the present
throughflow and the axisymmetric average of the CFD
solution because of inconsistencies in formulation.
Nevertheless, an acceptable match was achieved. At the
inlet, the spanwise distributions of total pressure, total
temperature, and flow angles are specified. The design
intent spanwise distribution of static pressure is pre-
scribed downstream. Since the present formulation of the
inverse problem called for the specification of the blade
pressure loading, which is directly related to the spanwise
distribution of total temperature rather than to the total
pressure, adjustments to the magnitude of the blade
pressure loading were sometimes required to match the
design intent exit total-pressure distribution and the mass
flow rate.
For this reblading exercise, the meridional envelopes of
the blade were fixed. The blade pressure loading was
carefully constructed with the following scheme. Figure
19 shows the contour of the pressure loading of the
Figure 18.Flow path for two-stage high-pressure
compressor.
6
12
Radius, in.
10
8
6
4
6
Axial location, z, in.
4202410812
S1
R1 R2 S2
IGV
0.93 0.75 0.56 0.38 0.20 0.02
Figure 19.Blade pressure loading.
Original New design
16 NASA/TP2002-211568
original blade at the design intent backpressure (left
contour plot). Two distinct discontinuities spanning from
hub to tip are clearly indicated. The axial distribution of
the blade pressure loading superimposed on the Mach
number contours in the blade-to-blade plane at the same
span location (near tip region) is shown in figure 20. Note
that the two near discontinuities in the blade loading
distribution conform to the location of the passage shock.
The front discontinuity corresponds to the passage shock
impinging on the pressure surface of the blade above it,
whereas the back discontinuity corresponds to the pas-
sage shock impinging on the suction surface of the blade
below it. Looking back to figure 19, note that the passage
shock is rather strong at the upper half of the blade and
hence there exists a potential for tailoring the pressure-
loading distribution to weaken it, as has been demon-
strated in previous work (ref. 23).
Another important consideration is the placement and
orientation of the passage shock as seen in the meridional
plane. At the design point, the passage shock should
reside inside the blade passage, and its orientation should
be such that it has maximum obliquity relative to the
incoming flow to minimize shock loss (shock sweep).
This suggests that the passage shock near the tip region
should be placed as far back as possible (i.e., the passage
shock impinging on the suction surface near the trailing
edge), whereas it should be as far forward as possible at
the other end (the passage shock impinging on the pres-
sure surface near the leading edge). After the desired
shock position in the blade passage is selected, it is
possible to estimate where the passage shock intersects
the blade surfaces based on the geometry of the blade
passage (the blade stagger angle and the blade spacing).
There are a number of different aspects to the selection
of pressure loading for transonic blades. First, the selec-
tion of loading shape and magnitude in the entrance
region of the blade translates into tailoring the aerody-
Figure 20.Axial loading
distribution.
namic surfaces for the proper supersonic wave pattern
and throat area. This tailoring is a means for achieving the
required mass flow rate with a started shock configura-
tion. Additionally, the selection of shock position on
suction and pressure surfaces as well as its strength must
be carefully crafted to obtain low losses. After the shock
position in the meridional plane has been selected, one of
the loading discontinuities is fixed at that span position
(points A and B in fig. 21). The other discontinuity can be
placed to introduce some obliquity of the shock in the
blade-to-blade plane. As part of the selection of the
meridional shock position, the region encompassing the
passage shock must also be determined. The tip of the
blade sets the first spanwise location and the second is
chosen to be where the inlet relative Mach number is
slightly above unity. This positioning divides the blade
into the low supersonic-subsonic region where smooth
loading shapes can be used without producing
discontinuities in the blade and the supersonic flow
portion where the discontinuities in loading must be
prescribed to obtain smooth blade shapes (fig. 21).
The strength of the shock can be controlled somewhat
through the specification of the severity of the pressure-
loading gradient. A steep gradient will produce a strong
shock with a greater shock loss and a potentially greater
risk of shock-induced, boundary-layer separation. How-
ever, there are limits as to how much the shock can be
weakened and how much obliquity can be introduced in
the blade-to-blade plane. If the shock is weakened past a
certain point, the resulting blade will have a kink that
may lead to poor performance at off-design conditions.
The second limit, blade-to-blade shock obliquity, is
Point A
Point A
Point B
Low supersonic-
subsonic region
Figure 21.Passage shock positioning in meridional
plane.
Back
Front
Supersonic
region
Point B
NASA/TP2002-211568 17
observed when the two discontinuities have been placed
too far from one another (dashed line in fig. 21). In such
a case, the shock will occur at the specified location on the
pressure surface (front discontinuity, see fig. 21) but will
impinge on the suction surface at a location upstream of
the specified back discontinuity, resulting in too much
loading in the subsonic diffusion portion of the blade and
therefore overcambering the blade in that region. This
manual adjustment of the blade pressure loading is a
delicate process and does require some experience to
achieve success.
Figure 19 (right contour plot) shows the blade pressure
loading of the redesigned rotor 2. Compared with the
original design (left contour plot), the figure clearly
illustrates the weakening of the passage shock and an
increase in its obliquity. Figure 22 compares the detailed
blade pressure loading (bottom) and pressure distribu-
tions on the blade surfaces (top) of the original design and
the new design at several spanwise stations. Two impor-
tant differences between the two designs are worth point-
ing out. First, the passage shock is weakened at all
spanwise stations. Second, the passage shock moves a
little forward below the 50-percent-span location while
being displaced farther aft above the 50-percent-span
location. Recall that the reorientation of the passage
shock was purposely created in the specification of the
blade pressure loading to increase its obliquity relative to
the meridional flow.
Figure 22.Blade-surface pressure and loading distributions for several span sections. (a) Near the hub. (b) Below
50-percent span. (c) Above 50-percent span. (d) Near the tip.
1.5
1.0
0.5
0.0
0.5
Pressure loading Static pressure
0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38
Axial location, z
Original
New design
(d)
1.5
1.0
0.5
0.0
0.5
Pressure loading Static pressure
0.31 0.32
(b)
0.33 0.34 0.35 0.36 0.37 0.38 0.39
Axial location, z
Original
New design
1.5
1.0
0.5
0.0
0.5
Pressure loading Static pressure
0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38
Axial location, z
Original
New design
(c)
1.5
1.0
0.5
0.0
0.5
Pressure loading Static pressure
0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40
Axial location, z
Original
New design
(a)
18 NASA/TP2002-211568
Figure 23 shows the flow field in a crossflow (r,θ) plane
behind the blade trailing edge. The tip clearance-to-chord
ratio is approximately 1 percent. For the new design, there
is a clear indication of a cleaner endwall flow that is
attributed to the weakened passage shock and possibly a
modulation of secondary and leakage flows. Note that the
new blade geometry is twisted differently near the casing
endwall, whereas the original blade was stacked so that
its leading edge is swept forward relative to the flow. This
new twist introduces a component of blade force that
restricts unfavorable spanwise flow migrations. The fig-
ure also shows that the blade wake for the new design is
slightly thinner over the entire span. The Navier-Stokes
solver ADPAC (ref. 18) was used to independently con-
firm the improved flow field and performance of the new
design. The calculation used a mesh size of 904840 (a
total of 172 800 cells) that included 4 cells in the tip
clearance region. At the design intent backpressure, the
ADPAC solution predicted an overall adiabatic effi-
ciency improvement of 2 percent over the original design
running at the same backpressure with approximately the
same flow rate. Figure 24 shows the spanwise distribution
of adiabatic efficiency as predicted by ADPAC. It can be
observed that efficiency improvements are found over the
Original
Suction
surface Pressure
surface
New design
0.2 0.3 0.3 0.5
Relative Mach number, M
rel
0.50.4 0.4 0.6 0.6 0.7 0.8
Figure 23.Relative Mach number contours at blade
trailing-edge plane.
100
90
80
70
60
50
40
30
20
10
Spanwise location, percent
of span
0
0.6 0.7 0.8
46
48
50
52
54
1.5 percent
0.960.94
0.9 1.0
Adiabatic efficiency, tt
Figure 24.Comparison of spanwise distribution of
adiabatic efficiency at design point.
Original
New design
Casing
Hub
Figure 25.Comparison of pressure loading.
1.0 0.9 0.8 0.7 0.6 0.5 0.2 0.10.4 0.3 0.0
Original New design
Original New design
x
z
Figure 26.Cascade flow near casing.
0.2 0.3 0.5 0.6 0.8 0.9 1.21.0 1.3 1.5 1.6
Mach number
Rotation
NASA/TP2002-211568 19
entire span, with about 1.5 percent over the core flow and
over 10 percent in the casing endwall.
The first rotor (R1) was also revised using the same
pressure-loading scheme. Figure 25 compares the blade
pressure loading of the original design (left contour
plot) with that of the new design (right contour plot), and
figure 26 presents the blade-to-blade flow field near the
tip. As in the second rotor (R2), the passage shock was
weakened and slightly reoriented to increase shock obliq-
uity. The performance of R1 (as predicted by ADPAC)
showed an improvement of 1.5 percent in adiabatic
efficiency over the original design.
In summary, the transonic rotor blades generated by
INV3D using the present pressure-loading strategy indi-
cated a relatively higher efficiency potential than the
original blades. Stacking and thickness distributions were
fixed according to the original blades. Perhaps a combi-
nation inverse direct method can be used to explore other
degrees of freedom. Preliminary mechanical and struc-
tural assessments of the inverse-designed blades thus far
appear promising. The blades are curvier than usual,
having forward-swept leading edges (fig. 27). Implica-
tions for this design freedom, from the perspective of
product development and total cost, are beyond our
scope. Similar to the rotors, a pressure-loading strategy
can be developed for subsonic stators, but this is reserved
for future work. The stators were designed as described
in part I and were matched to the rotors solely based on
CFD simulations. Additional geometric information for
all blade rows is given in appendix A.
Multistage Performance Evaluation
Procedure.To verify the improved performance
potential of the rebladed two stage and to facilitate stage
matching, the multistage CFD code APNASA, based on
the formulation of Adamczyk (ref. 5), was employed. The
APNASA code computes the time-mean flow as seen by
an average passage of a blade row imbedded in a multi-
stage environment. Details of the numerics, turbulence
model, and deterministic stress closure are given by
Adamczyk et al. (ref. 24). This code has undergone
extensive validation and/or calibration (refs. 25 and 26)
and has been found to be a reliable predictive tool for
multistage aerodynamics. In executing the design,
APNASA, ADPAC, and INV3D were integrated in the
iterative design loop. The procedure is as follows:
1. From the throughflow model, extract the inflow and
outflow boundary conditions for INV3D. Rotor blades
are designed using INV3D with the pressure-loading
strategy previously described; the stators are designed
according to the inverse throughflow method outlined in
part I.
2. ADPAC is used to fine-tune the individual blade-row
designs while holding the inflow conditions extracted
from the throughflow model. The exit profiles from the
individual blades are checked against the design intent
and the blades are redesigned as in step 1 should the exit
profiles or losses be far too different from those of the
throughflow.
Figure 27.Visualization of rotor blades generated with INV3D.
R1
R2
20 NASA/TP2002-211568
3. The multistage aerodynamics of all the blade rows
are predicted with APNASA. An interrogation of the
APNASA solution is made to arrive at appropriate revi-
sions for the throughflow (i.e., aerodynamic blockage,
loss and turning distributions) model and the blade design
strategies (incidence, trailing-edge loading distribution,
and stacking).
The above steps usually converge after two to three
design iterations. Note that step 3, involving mainly
APNASA, is more like a development stage rather than a
design stage. The throughflow model is still at the center
of the overall process and allows all the blade rows to be
designed simultaneously. Additional work is needed to
streamline this procedure and make it more direct.
Perhaps a totally different process with a well-founded
formalism is warranted. In addition, the entire process or
parts of it may be very amenable to various optimization
schemes that can directly accommodate aeromechanical
and manufacturing constraints.
APNASA results.A sheared H-mesh was constructed
for the two-stage configuration that included the inlet
guide vane. The mesh consisted of 61 streamwise points
on each of the 5 blade rows, 61 spanwise points, and 51
blade-to-blade points for a total dimension of 6266151.
There are four cells in the rotor tip clearances and stator
hub clearances. The clearance gaps were modeled with a
periodic boundary condition rather than with direct
discretization. Different mesh sizes were investigated to
ascertain the sensitivity of the results and to determine the
adequacy of the selected mesh size. Simulations were
conducted at several operating speeds and backpressures.
The results for the simulation closest to the aerodynamic
design point will be presented followed by the overall
characteristics at other operating conditions.
The predicted performance potential at the aerody-
namic design point is presented in table II. The perfor-
mance is determined from computed circumferentially
mass-averaged total pressures and temperatures at recti-
fying planes situated midway between the individual
blade rows. The overall performance quoted in the table
TABLE II.PREDICTED PERFORMANCE POTENTIAL
AT AERODYNAMIC DESIGN POINT
Inlet correct flow, Wc, lbm/s ..........................................71.2
Overall total-pressure ratio, PR
tt
.................................4.65:1
Corrected mechanical speed, , rpm .........................16 060
Overall efficiency, percent
Adiabatic,
η
tt
............................................................90.36
Polytropic,
η
p
...........................................................92.19
Figure 28.Predicted spanwise variations in adiabatic
efficiency at aerodynamic design point. (a) Overall.
(b) Rotor 1. (c) Rotor 2.
1.0
0.8
0.6
0.4
0.2
0.0
Fraction of span
60 70 80 90 100
Efficiency,
tt
, percent
1.0
0.8
0.6
0.4
0.2
0.0
Fraction of span
60 70 80 90 100
Efficiency,
tt
, percent
1.0
0.8
0.6
0.4
0.2
0.0
Fraction of span
60 70 80 90 100
Efficiency,
tt
, percent
(a)
(b)
(c)
Area averaged
Mass averaged
TABLE III.DESIGN POINT STAGE
PERFORMANCE POTENTIAL
PREDICTEDBYAPNASA
Stage Rotor Stator
Total-pressure Polytropic Total
ratio, efficiency, pressure
PRtt ηp,loss,
percent Pt/Pt,
percent
1 2.423 95.100 1.636
2 1.995 94.420 1.725
NASA/TP2002-211568 21
extends from the IGV inlet to one meridional chord
downstream of S2. The total pressure loss across the
IGV is Pt/Pt = 0.476 percent. A summary of the stage-
by-stage performance potential is given in table III.
At the design corrected speed and pressure ratio, the
predicted mass flow rate is approximately 1.7 percent
higher than the design intent. The polytropic efficiency
significantly exceeds the state-of-the-practice value indi-
cated in part I and is, in fact, at a level consistent with
the four-stage advanced technology goal. The design-
point overall performance potential for the rotors is
exceptionally good in terms of efficiency. The spanwise
variations of adiabatic efficiency for R1, R2, and the
overall two stages are plotted in figure 28. It is evident
that the efficiency of R1 is relatively high over the lower
80-percent span and rapidly drops off in the remaining
10-percent span near the casing. A similar trend is
observed for R2, except that the efficiency levels are
somewhat lower between 20- to 50-percent span. The
distribution of efficiency for the overall two stages, ex-
tracted one meridional chord aft of S2, indicates a good
distribution across most of the span with a gradual dropoff
near the casing. Additional spanwise profiles of
axisymmetric averaged flow properties are given in
appendix B.
The APNASA results at the aerodynamic design point
were interrogated to identify the major flow features
responsible for the aerodynamic character of the blading
and to synthesize their relative impact on performance.
The cascade plane relative Mach number distributions for
R1 at near hub (9-percent span), midspan, and near tip
(95-percent span) are shown in figure 29. Near the hub,
a rapid diffusion from about 40-percent chord without
any shock is observed within the passage, which is
consistent with the intended pressure loading shown in
figure 25 and does not appear to adversely impact the
viscous layers because of the favorable spanwise sweep-
ing of low-momentum fluid near the hub. At midspan,
an oblique shock exists in the passage at about 40-percent
chord, and the subsonic diffusion in the aft section thick-
ens the suction-surface boundary layer near the trailing
edge. The low-momentum fluid in this region centrifuges
outward and accumulates near the tip. A cesspool, fed
by this process and augmented by the leakage flow, is
observed at the blade tip near the pressure side corner.
Further evidence of this cesspool is shown in figure 30,
which corresponds to the entropy distribution at the
0.7
0.7
1.5
1.4
0.9
0.7
1
0.7
0.7
0.9
1
1
(a)
(b)
Figure 29.Relative Mach number distributions at design point for rotor 1. (a) 9-percent
span. (b) 50-percent span. (c) 95-percent span.
0.9
0.8
1.2
1.6
1.6
1.3
(c)
Pressure surface
Suction
surface
Leakage vortex core
Entropy
.4
2.3
1.6
1.0
Figure 30.Entropy distribution at trailing-edge plane of
rotor 1.
22 NASA/TP2002-211568
trailing-edge plane of R1. Near the tip, note the existence
of a double shock (evident in fig. 29) that is inconsistent
with the intent shown in figure 25. This double shock is
perhaps an indication of a deficiency in the viscous
treatment of the inverse method and is under investiga-
tion. Nevertheless, the flow structure indicates a rela-
tively clean flow conducive to a high-efficiency potential.
The absolute Mach number distribution at the trailing
edge of S1 is shown in figure 31. Note the low-momentum
region at the hub resulting from the interaction of the hub
leakage with the endwall flow. There is indication of a
thin wake in the core region. Because of the hub clearance
and the local orientation (e.g., sweep and dihedral) of the
blading near the endwalls, there is a tendency for low-
momentum fluid on the blade surfaces to migrate into the
core region, hence the appearance of a relatively thinner
wake near the endwalls.
Figure 32 shows the distribution of the relative total
pressure at several cross-passage planes from the leading
edge to the trailing edge of R2. Evident is the develop-
ment of the boundary layer on the suction surface along
with the evolution of a low-energy cesspool associated
with shock-endwall viscous interaction and tip clearance
leakage in the casing endwall region. A band of low
relative total pressure can be observed at the hub, indicat-
ing a weak flow due to excessive diffusion imposed by
the blading. Although not explicitly shown here, a strong
interaction exists between the bow shock emanating at the
leading edge of R2 and the suction-surface boundary
layer at the trailing edge of S1. This interaction leads to a
local underturning of the stator core flow. However, there
does not seem to be any adverse effect on the swallowing
capacity of R2 or on the overall matching of the two
stages.
Figure 31.Absolute Mach number distribution at
trailing-edge plane of stator 1.
Pressure
surface Hub
leakage
Suction
surface
0.8
.6
.3
.0
Absolute
Mach
number,
M
abs
Figure 32.Relative total-pressure distribution on several cross-
passage planes for rotor 2 (courtesy of ASE Technologies, ref. 27).
Leading
edge
Tip
Trailing-edge
wake
Trailing edge
Relative
total
pressure,
P
t,rel
,
psia
65
60
55
80
85
75
70
50
45
40
35
30
25
20
15
y
z
x
Suction surface
Hub
Losses from
oblique shock
Accumulation of
low-momentum fluid
NASA/TP2002-211568 23
The distribution of absolute total pressure at several
cross-passage planes from the leading edge to the trailing
edge of S2 is presented in figure 33. Clearly evident is the
development of the hub leakage flow and its interaction
with the endwall blading. A hub-strong, total-pressure
profile exists at the inlet to S2 and is rapidly degraded by
this process.
A loss audit was performed on R1 to identify sources of
entropy generation and their relative contribution to the
rotor overall inefficiency. The approach selected for
the loss audit was to create the postprocessing tool
DISECT-N (ref. 27) that can decompose the spatial
domain of a blade passage into zones encompassing
selected flow features and entropy generation mecha-
nisms. Entropy fluxes are summed over the boundaries of
each zone and the results used as a direct measure of the
entropy production within that zone. Note that this tacitly
assumes a negligible thermal entropy production. Nine
zones (figs. 34 and 35) were selected based on interroga-
tions of the APNASA results; the targeted entropy
generation mechanisms are cursorily described as
Zone 01: Casing endwall regionfocus on clearance
leakage and shock-endwall boundary-layer interactions
Zone 02: Casing endwall region, low-momentum
region, including shock interaction effectsfocus on
pressure surface
Zone 03: Hub endwall region, low-momentum
regionfocus on pressure surface
Zone 04: Suction-surface, low-momentum region
encompassing passage shock-boundary-layer inter-
actionfocus on endwall region
Zone 05: Suction-surface, low-momentum region
encompassing shock-boundary-layer interactionfocus
on core flow region
Zone 06: Downstream region, mixing losses
Zone 07: Outer region, passage shockfocus on
suction side
Figure 33.Absolute total-pressure distribution on
cross-passage planes through stator 2 (courtesy
of ASE Technologies, ref. 27).
Leading
edge
Sator 2,
1.1-percent span
Hub
Pressure
surface Tip
Trailing
edge
x
y
z
Absolute
total
pressure,
P
t,abs
,
psia
66
64
70
68
72
76
74
62
60
58
56
Figure 34.Zonal decomposition of rotor 1
flow domain for assessment of entropy
production.
01 Purple
02 Red
03 Green
04 Blue
05 Teal
06 Orange
Zone
07 Red
08 Green
09 Blue
11 Orange
Zone
Figure 35.Additional zones for
assessment of rotor 1 entropy
production.
24 NASA/TP2002-211568
Zone 08: Outer region, passage shockfocus on
pressure side
Zone 09: Inner region, passage shockfocus on core
The loss audit results are given in figure 36, where the
entropy production from each zone is indicated in terms
of its relative contribution to the overall entropy produc-
tion. Also shown for comparison is a similar loss audit for
the initial R1 designed using an inverse throughflow
method. As expected, the endwall zone 01 has the largest
loss contribution with approximately 30 percent of the
total. Zone 02 accounts for a significant 20 percent of the
total losses by capturing the transport of low-momentum
fluid and its interaction with the passage shock near the
pressure surface. The processes within these two endwall
zones account for a little over 50 percent of the overall
losses. A significant 44 percent of the total loss is attrib-
uted to the suction-surface viscous dissipation within
zones 04 and 05 and the combined outboard shock loss
from zones 07 and 08. The downstream mixing losses are
on the order of 1 percent of the total but do not cover full
mixing of the downstream flow field. Note that relative to
the inverse throughflow design, the prescribed pressure-
loading design has significantly lower shock and shock-
boundary-layer-related losses.
Further information about the entropy production
mechanisms in the casing endwall region (zone 01,
15-percent immersion from the casing) was gained by
subdividing this region into seven smaller zones encom-
passing flow features thought to be critical and then
performing a loss audit for the region. This audit indicated
that tip clearance leakage and viscous dissipation along
the endwall suction-surface corner contribute to approxi-
mately 40 percent of the total casing endwall entropy
production. The passage shock and its interaction with the
viscous endwall flow under the influence of the leakage
vortex accounts for about 30 percent of the endwall
entropy production. Although the spanwise transport of
low-momentum fluid feeding the cesspool near the pres-
sure surface corner directly contributes a relatively small
amount to the endwall entropy production, its indirect
impact on performance is linked to the downstream
30
25
20
15
10
5
Net entropy flux, percent
02468
Zone
Prescribed pressure-loading
blading (INV3D)
Figure 36.Relative distribution of entropy production
for rotor 1.
Custom-tailored blading
(inverse throughflow method)
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
Total-pressure ratio, PR
tt
1.020 30 40 50 60 70 80
Symbols denote APNASA
predictions at nominal IGV
and S1 Percent
speed
/IGV reset/
S1 reset
100
/0/0/
95
/5/1.2/
90
/10/2.3/
80
/20/4.7/
70
/30/7/
Corrected mass flow, m, lbm/s
(a)
Figure 37.Predicted overall performance characteristics.
(a) Total-pressure ratio. (b) Adiabatic efficiency.
Adiabatic efficiency,
tt
, percent
0.900
0.875
0.850
0.825
0.800
0.750
0.775
Symbols denote APNASA
predictions at nominal IGV
and S1
Percent
speed
/IGV reset/
S1 reset
100
/0/0/
95
/5/1.2/
90
/10/2.3/
80
/20/4.7/
70
/30/7/
20 30 40
(b)
50 60 70 80
Corrected mass flow, m, lbm/s
NASA/TP2002-211568 25
mixing loss and the increased aerodynamic blockage.
Thus, with this audit, various redesign strategies can be
conceived and tested via numerical simulation to assess
their relative benefits.
APNASA was used to simulate the off-design perfor-
mance of the two-stage configuration at 100-, 95-, and
90-percent rotational speeds with nominal IGV and vane
settings. The geometry was frozen as designed without
accounting for structural deformation effects with vary-
ing operating conditions. The results of the simulation
were used to construct stage characteristics for each of the
two stages and these were subsequently stacked to predict
the overall performance characteristics with various
IGV and vane resets. The overall adiabatic efficiency
predicted by APNASA was degraded by 1.46 percent,
based on engineering judgment reflective of hardware
quality shortfalls and other X-factors that may compro-
mise the CFD predictive capability. Figure 37 shows the
overall characteristics (total-pressure ratio and adiabatic
efficiency) derived from the stage-stacking procedure at
the indicated resets and compares them with APNASA
predictions. Since there is no definitive application for
this two-stage group, the adequacy of the characteristic
map cannot be absolutely assessed. Nevertheless, a
potentially adequate operating range seems to be avail-
able for further aerodynamic development.
Conclusions
In part I, very aggressive performance goals were
defined by a rational perturbation of basic aerodynamic
technology elements of current design systems. A poten-
tial for a substantial expansion of the aerodynamic design
and operability space was shown. The research at NASA
Glenn on practical means to effect these aerodynamic
advancements is, in reality, still in its infancy. The chal-
lenge of discovering and developing new technology in
a multistage turbocompressor environment requires a
well-conceived plan of attack. Nevertheless, achieve-
ment of these advancements would give the design engi-
neer the freedom to innovate.
A preliminary design of a four-stage compressor con-
figuration was established for advanced technology
development. This design was biased toward high effi-
ciency at high loading. Three-dimensional blading and
spanwise tailoring of vector diagrams were employed
under the guidance of computational fluid dynamics
(CFD) to control the aerodynamics of the high-loaded
endwall regions. The preliminary results were encourag-
ing and the front two stages were extracted for further
aerodynamic trimming using a three-dimensional inverse
design method.
In part II, the design principles for constructing blade-
surface, pressure-loading distributions to be applied in a
three-dimensional inverse design method were presented.
This method produced blading having a high-efficiency
potential relative to current practice. In addition, the
inverse-designed blades were successfully adapted to the
multistage environment using the APNASA code. An
overall efficiency potential far exceeding current practice
was demonstrated with the APNASA CFD.
In spite of the significantly higher aerodynamic load-
ings, advanced CFD-based tools were able to effectively
guide the design of a very efficient two-stage compressor
under state-of-the-art aeromechanical constraints.
Adequate operability for aerodynamic research and devel-
opment was predicted. This two-stage configuration can
be used for further aerodynamic technology research and
development to meet the goals established in part I.
26 NASA/TP2002-211568
NASA/TP2002-211568 27
Appendix A
Geometry
TABLE IV.FLOW-PATH COORDINATES: DESIGN AERODYNAMIC INTENT
Hub Casing Hub Casing
z,
in.
r,
in.
z,
in.
r,
in.
z,
in.
r,
in.
z,
in.
r,
in.
10.000 4.993 10.00 10.540 8.439 8.958 8.071 10.540
9.000 4.993 9.000 10.540 8.628 8.987 8.347 10.540
8.000 4.993 8.000 10.540 8.919 9.021 8.695 10.540
7.044 4.993 7.017 10.540 9.211 9.039 9.043 10.540
6.090 4.993 6.040 10.540 9.504 9.051 9.392 10.540
5.136 4.993 5.082 10.540 9.796 9.064 9.740 10.540
4.181 4.993 4.169 10.540 10.088 9.085 10.088 10.540
3.225 4.993 3.262 10.540 10.224 9.099 10.250 10.521
2.717 5.015 2.766 10.540 10.356 9.116 10.408 10.497
2.417 5.039 2.400 10.540 10.546 9.145 10.579 10.470
2.118 5.071 2.031 10.540 10.736 9.177 10.749 10.439
1.820 5.112 1.660 10.540 10.927 9.206 10.919 10.406
1.523 5.162 1.287 10.540 11.118 9.224 11.089 10.371
1.228 5.221 .913 10.540 11.311 9.221 11.258 10.334
.605 5.377 .412 10.540 11.604 9.182 11.604 10.253
.000 5.569 .000 10.540 11.815 9.133 11.813 10.202
.734 5.886 .518 10.540 12.023 9.071 12.021 10.149
1.420 6.294 1.039 10.540 12.229 9.004 12.230 10.096
2.094 6.721 1.559 10.540 12.437 8.940 12.439 10.043
2.777 7.134 2.080 10.540 12.647 8.886 12.647 9.991
3.489 7.495 2.601 10.540 12.842 8.850 12.887 9.932
3.869 7.645 3.072 10.540 12.981 8.834 13.008 9.903
4.258 7.766 3.551 10.540 13.120 8.826 13.129 9.875
4.677 7.873 4.052 10.540 13.259 8.824 13.251 9.848
5.100 7.964 4.553 10.540 13.399 8.822 13.372 9.822
5.524 8.052 5.054 10.540 13.538 8.819 13.494 9.797
5.947 8.146 5.555 10.540 13.785 8.806 13.786 9.741
6.367 8.252 6.057 10.540 13.979 8.790 13.978 9.707
6.561 8.310 6.359 10.540 14.172 8.771 14.170 9.678
6.754 8.374 6.662 10.540 14.365 8.749 14.363 9.651
7.052 8.485 6.889 10.540 14.557 8.727 14.557 9.629
7.347 8.603 7.116 10.540 14.751 8.713 14.751 9.610
7.642 8.719 7.342 10.540 14.962 8.710 14.962 9.594
7.940 8.828 7.569 10.540 15.466 8.709 15.466 9.575
8.245 8.918 7.796 10.540 15.970 8.709 15.970 9.575
28 NASA/TP2002-211568
Figure 38.Inlet guide vane, aft
looking forward. Aspect ratio,
3.150; number of blades, 32.
Figure 39.Rotor 1. Aspect ratio, 0.837; number of
blades, 26.
Figure 40.Stator 1. Aspect ratio, 1.128; number of
blades, 54.
Figure 41.Rotor 2. Aspect ratio, 0.888; number
of blades, 56.
NASA/TP2002-211568 29
Figure 42.Stator 2. Aspect ratio, 0.923; number of
blades, 74.
Figure 43.Four-stage flow path with first two stages
extracted for further aerodynamic development.
NASA/TP2002-211568 31
Appendix B
Computed Axisymmetric Averaged Spanwise Profiles at Design Throttle
1.0
0.8
0.6
0.4
0.2
Fraction of span
0.0
0.90 1.00 1.10 1.20
Total pressure, Pt
1.0
0.8
0.6
0.4
0.2
Fraction of span
0.0 0.92 0.96 1.00
Total temperature
1.0
0.8
0.6
0.4
0.2
Fraction of span
0.060 61 62 63 6564
Relative flow angle,
rel
, deg Relative Mach number, M
rel
1.0
0.8
0.6
0.4
0.2
Fraction of span
0.0 1.61.41.21.00.8
1.0
0.8
0.6
0.4
0.2
Fraction of span
0.0 04812
Absolute flow angle,
abs
, deg Absolute Mach number, M
abs
1.0
0.8
0.6
0.4
0.2
Fraction of span
0.0 0.4 0.6 0.8
Figure 44.Rectifying plane of inlet guide vane exit and rotor 1 inlet.
32 NASA/TP2002-211568
1.0
0.8
0.6
0.4
0.2
Fraction of span
0.0
1.8 2.22.0 2.4 2.6
Total pressure, Pt
1.0
0.8
0.6
0.4
0.2
Fraction of span
0.0 1.28 1.32 1.401.36
Total temperature
1.0
0.8
0.6
0.4
0.2
Fraction of span
0.0 20 40 8060
Relative flow angle,
rel
, deg Relative Mach number, M
rel
1.0
0.8
0.6
0.4
0.2
Fraction of span
0.0 2.01.51.00.50.0
1.0
0.8
0.6
0.4
0.2
Fraction of span
0.0 70 60 50
Absolute flow angle,
abs
, deg Absolute Mach number, M
abs
1.0
0.8
0.6
0.4
0.2
Fraction of span
0.0 0.6 0.8 1.0
Figure 45.Rectifying plane of rotor 1 exit and stator 1 inlet.
NASA/TP2002-211568 33
1.0
0.8
0.6
0.4
0.2
Fraction of span
0.0
1.8 2.0 2.2 2.62.4
Total pressure, Pt
1.0
0.8
0.6
0.4
0.2
Fraction of span
0.0 1.28 1.32 1.36 1.40
Total temperature
1.0
0.8
0.6
0.4
0.2
Fraction of span
0.0 56 60 64 68 72
Relative flow angle,
rel
, deg Relative Mach number, M
rel
1.0
0.8
0.6
0.4
0.2
Fraction of span
0.0 1.401.301.201.101.00
1.0
0.8
0.6
0.4
0.2
Fraction of span
0.0
10 0 10 20
Absolute flow angle,
abs
, deg Absolute Mach number, M
abs
1.0
0.8
0.6
0.4
0.2
Fraction of span
0.00.2 0.4 0.6
Figure 46.Rectifying plane of stator 1 exit and rotor 2 inlet.
34 NASA/TP2002-211568
1.0
0.8
0.6
0.4
0.2
Fraction of span
0.04.0 4.4 4.8 5.2
Total pressure, P
t
1.0
0.8
0.6
0.4
0.2
Fraction of span
0.0 1.601.50 1.70 1.80
Total temperature
1.0
0.8
0.6
0.4
0.2
Fraction of span
0.020 40 60 80
Relative flow angle,
rel
, deg Relative Mach number, M
rel
1.0
0.8
0.6
0.4
0.2
Fraction of span
0.0 0.800.700.600.50
1.0
0.8
0.6
0.4
0.2
Fraction of span
0.0
70 60 50 40
Absolute flow angle,
abs
, deg Absolute Mach number, M
abs
1.0
0.8
0.6
0.4
0.2
Fraction of span
0.0
0.4 0.6 0.8
Figure 47.Rectifying plane of rotor 2 exit and stator 2 inlet.
NASA/TP2002-211568 35
1.0
0.8
0.6
0.4
0.2
Fraction of span
0.0
4.0 4.4 4.8 5.2
Total pressure, P
t
1.0
0.8
0.6
0.4
0.2
Fraction of span
0.0
1.6 1.8 2.0
Total temperature
1.0
0.8
0.6
0.4
0.2
Fraction of span
0.0 56 60 64 68 72
Relative flow angle,
rel
, deg Relative Mach number, M
rel
1.0
0.8
0.6
0.4
0.2
Fraction of span
0.0 1.301.201.101.000.90
1.0
0.8
0.6
0.4
0.2
Fraction of span
0.0 05 5 10 15 20
Absolute flow angle,
abs
, deg Absolute Mach number, M
abs
1.0
0.8
0.6
0.4
0.2
Fraction of span
0.0
0.30 0.40 0.50 0.60
Figure 48.Rectifying plane of stator 2 exit.
36 NASA/TP2002-211568
References
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This publication is available from the NASA Center for AeroSpace Information, 301–621–0390.
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ARL–TR–2859
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1L161102AF20
41
Aerodynamic Design Study of Advanced Multistage Axial Compressor
Louis M. Larosiliere, Jerry R. Wood, Michael D. Hathaway, Adam J. Medd,
and Thong Q. Dang
Machines for compressing air or other fluids; Compressors
Unclassified - Unlimited
Subject Category: 07 Distribution: Standard
Louis M. Larosiliere and Michael D. Hathaway, U.S. Army Research Laboratory, NASA Glenn Research Center;
Jerry R. Wood, NASA Glenn Research Center; and Adam J. Medd and Thong Q. Dang, Syracuse University,
Syracuse, New York 13244. Responsible person, Louis M. Larosiliere, organization code 5810, 216–433–3403.
As a direct response to the need for further performance gains from current multistage axial compressors, an investigation of advanced aerodynamic
design concepts that will lead to compact, high-efficiency, and wide-operability configurations is being pursued. Part I of this report describes the
projected level of technical advancement relative to the state of the art and quantifies it in terms of basic aerodynamic technology elements of current
design systems. A rational enhancement of these elements is shown to lead to a substantial expansion of the design and operability space. Aerodynamic
design considerations for a four-stage core compressor intended to serve as a vehicle to develop, integrate, and demonstrate aerotechnology advance-
ments are discussed. This design is biased toward high efficiency at high loading. Three-dimensional blading and spanwise tailoring of vector diagrams
guided by computational fluid dynamics (CFD) are used to manage the aerodynamics of the high-loaded endwall regions. Certain deleterious flow
features, such as leakage-vortex-dominated endwall flow and strong shock-boundary-layer interactions, were identified and targeted for improvement.
However, the preliminary results were encouraging and the front two stages were extracted for further aerodynamic trimming using a three-dimensional
inverse design method described in part II of this report. The benefits of the inverse design method are illustrated by developing an appropriate pressure-
loading strategy for transonic blading and applying it to reblade the rotors in the front two stages of the four-stage configuration. Multistage CFD
simulations based on the average passage formulation indicated an overall efficiency potential far exceeding current practice for the front two stages.
Results of the CFD simulation at the aerodynamic design point are interrogated to identify areas requiring additional development. In spite of the
significantly higher aerodynamic loadings, advanced CFD-based tools were able to effectively guide the design of a very efficient axial compressor
under state-of-the-art aeromechanical constraints.
... An increase of solidity could achieve high flow turning, but increases the number of blades and profile loss (Sans et al., 2014). To meet the needs of empirical solidity inputs in mean-line and through-flow design, performance prediction models including solidity which can be used in multistage axial flow compressor are needed (Larosiliere et al., 2002;Horlock and Denton, 2005;Burberi et al., 2020). Sans et al. (2014) updated the correlations for controlled diffusion blades and extended their application to the high Mach number flow regimes. ...
Article
Full-text available
Solidity and camber angle are key parameters with a primary effect on airfoil diffusion. Maximum thickness location has a considerable impact on blade loading distribution. This paper investigates correlations of maximum thickness location, solidity, and camber angle with airfoil performance to choose maximum thickness location quickly for compressor airfoils with different diffusion. The effects of maximum thickness location, solidity, and camber angle on incidence characteristics are discussed based on abundant two-dimensional cascade cases computed through numerical methods. Models of minimum loss incidence, total pressure loss coefficient, diffusion factor, and static pressure rise coefficient are established to describe correlations quantitatively. Based on models, dependence maps of total pressure loss coefficient, diffusion factor, and static pressure rise coefficient are drawn and total loss variation brought by maximum thickness location is analyzed. The study shows that the preferred selection of maximum thickness location can be the most forward one with no serious shock loss. Then, the choice maps of optimal maximum thickness location on different design conditions are presented. The optimal maximum thickness locates at 20–35% chord length. Finally, a database of optimal cases which can meet different loading requirements is provided as a tool for designers to choose geometrical parameters.
... The model was targeted to predict breakdown of the flow physics in the four stage compressor at different speeds and inlet mass flow. Louis et al [15] pursued aerodynamic design of advanced multistage axial compressor to achieve high efficiency with high loading, compact size and wide operating range which was carried out in two phases. First phase was oriented to develop confidence in design methodology through CFD and inverse design technique, the second phase as an outcome of the first led to development of a four stage advance axial compressor with stated objectives. ...
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Modern day gas-turbine engines are exploited to have better fuel economy, thrust to weight ratio, operational stability and overall efficiency. Achieving all these parameters is largely dependent on compressor/fan being used within. Therefore, most of the engine design efforts are drawn into the compressor/fan design. Present study is intended to build understanding about the design methodology and flow field behavior of multi stage axial flow compressor. A three stage axial flow compressor, suitable for Small Gas Turbine (SGT) application, has been designed. The designed compressor stage is intended to deliver mass flow rate of 3.85 kg/s, pressure ratio of 2.36, with stage efficiency of 82% at design speed of 3500 rpm. Steady RANS 3D CFD simulations are carried out at design and off design speeds to study the interaction among stages and behavior of various flow parameters at chock point (CP), design point (DP) and numerical stall (NS) conditions. Compressor performance is presented in terms of compressor maps consisting of pressure ratio (PR) and efficiency variation with respect to mass flow. Targeted aerodynamic performance is achieved with 1% lower efficiency.
... NASA (National Aeronautics and Space Administration) has designed a new four-stage compressor with a pressure ratio of 6. In this new design system, variable inlet guide vane is used to broaden the compressor margin [10]. Linder and Jones have conducted an experimental study on a single stage compressor in order to analyze the effect of VG on the compressor in off-design condition by comparing preswirl and non-preswirl [11]. ...
Article
Full-text available
Hub corner is a high-loss area located within in the blade passages of turbomachinery. It is well known that flow separation and vortex development in this area directly affects, not only energy loss and efficiency, but also the stability of axial compressors. In this paper, a high diffusion factor cascade is used in order to analyze the vortex structure which causes the hub-corner stall in cascade. The trailing edge clearance method is proposed for controlling the hub-boundary layer and this is compared with full uniform clearance. Our research highlights that the trailing edge clearance suppress the radial development of the suction separation vortex (SSV) in the hub corner and restrains the concentrated separation vortex (CSV). The influence of trailing edge clearance parameters and its effect on control of hub-corner stall is discussed in detail. It is revealed that clearance height avoids flow separation and suppresses radial vortex development, while the clearance length resists the overturning that is caused by transverse pressure gradient and controls the development of CSV. As the radial vortex plays a dominant role in hub-corner stall, clearance height has a better effect in controlling hub-corner stall in comparison to length at the constant flow area.
... However, expectations of greater mass flow proved to be wrong, and real manufactured compressor provided very close to computed value of the mass flow. Similar sort of calculations and its discussion were presented in [8], [9]. ...
Conference Paper
Full-text available
In this paper redesign process of an axial compressor of a Gas Turbine for mechanical drive is discussed together with computational results and experimental data. The goal of the project was to reduce compressor mass flow by 30% and at the same time to increase compressor specific work by about 10%. This could not be achieved by conventional methods such as re-staggering of Inlet Guide Vanes. Throughflow and CFD calculations were performed for redesigned versions. As a result an updated compressor was produced for the real engine and achieved design objectives. This paper shows how the swept area distribution along the compressor affects stage loading distribution and surge limits.
... The use of the streamline curvature method for calculations on multistage axial compressors was utilized by Jansen and Moffat [5], Novak [6], Howard and Gallimore [7] and Aungier [8]. The application of the streamline curvature approach to the design of axial compressors was demonstrated in older work such as [9] and in more recent studies such as [10]. Certain contemporary design tendencies can be found in papers such as [11]. ...
Conference Paper
Full-text available
Part I of this paper presents a method and a computer program for the mean design of multistage axial compressors. This second part describes a method and an additional computer routine that use the basic mean line design to create a fully two-dimensional flow solution and a compressor design. The two-dimensional solution according to a selected swirl vortex function is calculated using streamline curvature throughflow equations and spanwise distribution of losses. An iterative calculation procedure slightly reshapes the initial flow path in order to retain the desired input flow coefficients. Other variables such as stage loading parameters are changed in order to obtain the desired overall pressure ratio. A spanwise distribution of certain stage parameters can then be adjusted to achieve desired radial flow field variations. The basic one-dimensional input data can be varied at any moment to obtain a new one-dimensional result and the corresponding two-dimensional solution. A new output is created instantaneously and can be used for further CFD analysis, external throughflow, blade-to-blade flow computations or mechanical and vibration analysis.
... That means the active flow control method is necessary to improve the performance and to avoid the shortcomings when using the passive flow control of the compressors. So, MIT and NASA presented the researches of the aspirated compressors, which control the flow separation by steady suction if needs to work [14,15]. But, the steady active control methods need external energy and devices, such as: steady suction and blowing. ...
Article
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To control the flow separation in the compressors, a novel pulsed jet concept without external energy injection is proposed. The new concept designs a slot in the middle of the blade and sets a micro device to switch the slot periodically. Such a structure is expected to generate a pulsed jet by the pressure difference between the pressure side and the suction side of the blade. In order to analyze the interaction between the pulsed jet and unsteady separated flow, our numerical and experimental study is based on a specific cascade (with a flow separation inside) and a pulsed jet (one of the unsteady flow control method). The experimental and numerical results both show that when the frequency of pulsed jet is approximate to that of the separation vortex, then the control tends to be more effective. Based on the numerical simulations, the proper orthogonal decomposition (POD) is then used to reveal the control mechanism, extracting the different time-space structures from the original field. The results with the aid of POD show that the pulsed jet can redistribute the kinetic energy of each mode, and strengthen or weaken certain modes, particularly, while the steady jet reduces the kinetic energy of high-order modes in whole. Also, pulsed jet with proper parameters can transfer the energy from higher modes to the first flow mode (averaged flow), which is due to the conversion of the spatial vortical structures and the time evolution of the modes.
... Axial blade stacking is carried out by adding axial gaps between rotor and stators to generated axial coordinates at leading and trailing edges of the blades at hub, mean and tip. Using axial and radial coordinates preliminary flow path is generated [11]. Details of meanline design process are as below. ...
... There are theoretical indications that each g c and g t could be improved a further 1%. [64][65][66][67] C. Heat exchangers ...
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Full-text available
A thermal heat-pump grid storage technology is described based on closed-cycle Brayton engine transfers of heat from a cryogenic storage fluid to molten solar salt. Round-trip efficiency, computed as a function of turbomachinery polytropic efficiency and total heat exchanger steel mass, is found to be competitive with that of pumped hydroelectric storage. The cost per engine watt and cost per stored joule based are estimated based on the present-day prices of power gas turbines and market prices of steel and nitrate salt. Comparison is made with electrochemical and mechanical grid storage technologies.
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In order to improve the performance of high-loaded compressor stator with large camber turning angle, a stator cascade blade with tubercle leading edge was designed based on the wavy leading edge of humpback’s flipper, and computational fluid dynamics simulation was carried out. The results show that the tubercle leading edge can effectively improve the aerodynamic performance of the stator cascade at high attack angles, and the total pressure loss coefficient can be reduced by 26.46%. The main reason why the tubercle structure improves the performance is that it makes the radial displacement of airflow appear as a butterfly-like structure at the leading edge of the blade, which restrains the occurrence and development of airflow separation. By comparing the performance of the blades with full-span and part-span tubercle leading edges, it is considered that the tubercle leading edge of 80% blade height in the mainstream region can improve the aerodynamic performance of cascade better, while the one of 50% blade height has the worst effect.
Conference Paper
The performance of compressors can be enhanced by the judicious removal of the viscous boundary layer fluid from the flow path. Removal of the boundary layer fluid just prior to or in a region of rapid pressure rise, either at shock impingement or more generally at the point of rapid pressure rise on the suction surface of the blade, can give significant increases in the diffusion and therefore increase the work done per stage for a given blade speed. It also provides a thermodynamic benefit by removing the high-entropy fluid from the flow path. Design studies have been done using quasi 3-D viscous and 3-D Euler computational tools on a family of fan stages of varying tip speed that lake advantage of such viscous fluid removal. One stage in this family is a low tip speed fan stage designed to produce a pressure ratio of 1.5 at a tip speed of 700 ft/sec. Fan noise reductions resulting from the decrease in tangential Mach number, without sacrificing total pressure ratio, could make this design attractive for the fan of medium-bypass ratio engines. Another stage in the family would produce a total pressure ratio of 2.0 at a tip speed of 1000 ft/sec and could be very attractive as a fan stage on a lower bypass ratio engine or as a first stage of a low speed core compressor. The final stage in the family would achieve a pressure ratio of more than 3.0 at a tip speed of 1500 ft/sec and could be very attractive as a first stage of a core compressor, or as a fan for a military engine. A design for the suction passages to deal with the fluid removal has been completed for an experimental version of the 1.5 pressure ratio design. A tip shroud allows bleeding of the tip surface boundary layer from the rotor, and carries the fluid removed from the blade surfaces through the tip. One of these stages will be tested in the MIT Blowdown Compressor, serving a dual purpose: as a validation of the computational design process and as a test of the concept of aspirated compressors.
Conference Paper
A nine stage industrial axial flow compressor with a pressure ratio of 9.1:1 was designed, built and rig tested. The modern technology and design tools developed by government/aircraft engine compressor technologists were used for an industrial gas turbine application. The compressor was designed with “arbitrary” airfoil blading including CFD analysis in all blade rows. Flowpath contouring in the hub region of the rotors was used to decrease losses. The compressor rig was tested at the Compressor Research Facility at Wright Patterson Air Force Base in Dayton, Ohio. Extensive testing included determining the impact of stator leading edge instrumentation on performance. The compressor demonstrated excellent efficiency and stall margin in its first build. This paper describes the aerodynamic design, test instrumentation and test results. Copyright © 1998 by ASME Country-Specific Mortality and Growth Failure in Infancy and Yound Children and Association With Material Stature Use interactive graphics and maps to view and sort country-specific infant and early dhildhood mortality and growth failure data and their association with maternal
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A procedure for estimating the maximum pressure rise potential of axial flow compressor stages is presented. A simplified stage average pitchline approach is employed so that the procedure can be used during a preliminary design effort before detailed radial distributions of blading geometry and fluid parameters are established. Semi-empirical correlations of low speed experimental data are presented that relate the stalling static-pressure-rise coefficient of a compressor stage to cascade passage geometry, tip clearance, bladerow axial spacing and Reynolds number. Blading aspect ratio is accounted for through its effect on normalized clearances, Reynolds number and wall boundary layer blockage. An unexpectedly strong effect of airfoil stagger and of the resulting flow coefficient of the stage’s vector triangle is observed in the experimental data. This is shown to be caused by the differing ability of different types of stage vector triangles to re-energize incoming low-momentum fluid. Use of a suitable “effective” dynamic head in the pressure rise coefficient gives a good correlation of this effect. Stalling pressure rise data from a wide range of both low speed and high speed compressor stages are shown to be in good agreement with these correlations.
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An experimental investigation was carried out to examine the effects on stall margin of flow injection into, and flow removal out of, the endwall region of an axial compressor blade row. A primary objective of the investigation was clarification of the mechanism by which casing treatment (which involves both removal and injection) suppresses stall in turbomachines. To simulate the relative motion between blade and treatment, the injection and removal took place through a slotted hub rotating beneath a cantilevered stator row. Overall performance data and detailed (time-averaged) flowfield measurements were obtained. Flow injection and removal both increased the stalling pressure rise, but neither was as effective as the wall treatment. Removal of high blockage flow is thus not the sole reason for the observed stall margin improvement in casing or hub treatment, as injection can also contribute significantly to stall suppression. The results also indicate that the increase in stall pressure rise with injection is linked to the streamwise momentum of the injected flow, and it is suggested that this should be the focus of further studies.
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This paper summarizes the state of 3D CFD based models of the time-averaged flow field within axial flow multistage turbomachines. Emphasis is placed on models that are compatible with the industrial design environment and those models that offer the potential of providing credible results at both design and off-design operating conditions. The need to develop models free of aerodynamic input from semiempirical design systems is stressed. The accuracy of such models is shown to be dependent upon their ability to account for the unsteady flow environment in multistage turbomachinery. The relevant flow physics associated with some of the unsteady flow processes present in axial pow multistage machinery are presented along with procedures that can be used to account for them in 3D CFD simulations. Sample results are presented for both axial flow compressors and axial flow turbines that help to illustrate the enhanced predictive capabilities afforded by including these procedures in 3D CFD simulations. Finally, suggestions are given for future work on the development of time-averaged flow models. [S0889-504X(00)02002-X].