Two Investigations of Compressor Stability: Spike
Stall Inception and Transient Heat Transfer Effects
by
Andras Laszlo Andor Kiss
S.B, Massachusetts Institute of Technology (2013)
Submitted to the Department of Aeronautics and Astronautics
in partial fulfillment of the requirements for the degree of
Masters of Science in Aerospace Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
September 2015
c Massachusetts Institute of Technology 2015. All rights reserved.
Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Department of Aeronautics and Astronautics
August 19, 2015
Certified by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Zoltán S. Spakovszky
Professor of Aeronautics and Astronautics
Thesis Supervisor
Accepted by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Paulo C. Lozano
Associate Professor of Aeronautics and Astronautics
Chair, Graduate Program Committee
2
Two Investigations of Compressor Stability: Spike Stall
Inception and Transient Heat Transfer Effects
by
Andras Laszlo Andor Kiss
Submitted to the Department of Aeronautics and Astronautics on August 19, 2015,
in partial fulfillment of the requirements for the degree of
Masters of Science in Aerospace Engineering
Abstract
Two investigations of current problems in the field of compressor stability are presented. The first is of the formation of spike-type rotating stall precursors. Recently,
high fidelity computations have attributed pre-cursor formation to a leading-edge separation and consequent shedding of vorticity near the rotor tip due to high incidence.
This hypothesis is assessed via experiments in a low-speed compressor and a linear
cascade, supported by unsteady computations. Fast-response pressure measurements
at the blade tip show spike pre-cursors propagating in the cascade environment at
a rate consistent with the low-speed compressor. The cascade design produces high
incidence at the mid-span and fast-response velocity measurements show pre-cursor
formation away from the tip region.
Unsteady computations confirm leading-edge
separation and vortex shedding in both the compressor and cascade. A single blade
was instrumented with smoke injection at the leading-edge to visualize the separation
and the effect of Reynolds number on pre-cursor formation was quantified to facilitate
smoke visualization. The resultant visualizations confirm the leading-edge separation
and propagation of shed vorticity.
The second investigation is of the effects of heat transfer between the compressor
structure and gas path during transient operation. A mean line model of an advanced,
high pressure ratio compressor is extended to include the effects of heat transfer.
Diabatic, transient calculations show a 9.9 point reduction in stall margin from the
adiabatic case. 2.5 points are attributed to the effect of heat transfer on blade row
deviation and the remainder is attributed to stage rematching. Heat transfer increases
loading in the front stages and the stalling pressure ratio is set by front stage stall,
suggesting heat transfer effects are greater for compressors with highly loaded front
stages. Sensitivity studies of heat flow rate and deviation show a linear dependence
of stall margin loss for ratios of heat flow rate to inlet stagnation enthalpy flux much
less than unity.
Thesis Supervisor: Zoltán S. Spakovszky
Title: Professor of Aeronautics and Astronautics
3
4
per aspera ad astra...
5
6
Acknowledgments
I would first and foremost like to thank my advisor Professor Zoltán Spakovszky. It
is hard to believe that it’s already been six years since I began working with him; the
time has simply flown by. He has always pushed me to improve as a researcher and his
passion, enthusiasm, and perpetual optimism have served as a source of inspiration.
This research was supported and made possible by Pratt & Whitney, under the
guidance of Gavin Hendricks. Also at Pratt & Whitney, I would like to thank Ding
Li for his assistance with the many computations in this thesis and Brian Schuler for
his support in developing the mean line model. Thanks also to Scott Jones at NASA
Glenn Research Center for providing OTAC and aiding me (through countless emails)
in its implementation.
I have made many new friends during my time at the Gas Turbine Lab. Vincent,
Derek, Georgi, and Andrew you guys kept me laughing the entire time. Thanks to
Jinwook for making the endless quals study sessions as fun as they could be; we did
it! Special thanks to Vincent for taking over the administration of the GTL cluster
while I sequestered myself in the library to write this thesis.
Outside the GTL I
would like to thank Matt and Taylor for the friendships of a lifetime, Steven for his
boundless positivity and encouragement, and, of course, my partner Jeff; his love and
unwavering support kept me going even when I thought I could not.
I would like to thank all of my family for their love and encouragement. To my
father, Gabor, thank you for inspiring me in the world of engineering and instilling
in me a love of aviation, as well as so many other things. To my mother, Eva, your
limitless love and support has made all of this possible.
7
8
Contents
1 Introduction
23
1.1
Background
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2
Thesis Contributions
. . . . . . . . . . . . . . . . . . . . . . . . . . .
24
1.3
Summary of Thesis Chapters . . . . . . . . . . . . . . . . . . . . . . .
25
2 Spike-Type Rotating Stall Inception
23
29
2.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
2.2
Previous Work
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
2.3
Motivation and Objectives . . . . . . . . . . . . . . . . . . . . . . . .
35
2.4
Technical Roadmap . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
3 Experimental and Computational Setup
3.1
3.2
3.3
39
Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
3.1.1
Test Compressor
. . . . . . . . . . . . . . . . . . . . . . . . .
39
3.1.2
Linear Cascade Design . . . . . . . . . . . . . . . . . . . . . .
41
3.1.3
Smoke Generation and Injection . . . . . . . . . . . . . . . . .
45
3.1.4
Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . .
46
Computational Setup . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
3.2.1
CFD Solver Description
. . . . . . . . . . . . . . . . . . . . .
49
3.2.2
Mesh Generation and Validation . . . . . . . . . . . . . . . . .
52
3.2.3
Computational Procedure
. . . . . . . . . . . . . . . . . . . .
54
3.2.4
Numerical Challenges . . . . . . . . . . . . . . . . . . . . . . .
54
Rotor-Only Axial Compressor Computations . . . . . . . . . . . . . .
55
9
3.4
3.3.1
Validation with Experimental Data . . . . . . . . . . . . . . .
55
3.3.2
Simulation of Stall Pre-cursors . . . . . . . . . . . . . . . . . .
56
Summary
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4 Experimental Assessment of Formation Mechanism
60
61
4.1
Demonstration of Spike Pre-cursor in the Cascade Experiment . . . .
62
4.2
Reynolds Number Effects on Pre-cursor Formation . . . . . . . . . . .
65
4.3
Visualization of Pre-cursor Formation . . . . . . . . . . . . . . . . . .
69
4.4
Major Findings
78
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 Transient Heat Transfer Effects on Compressor Stability
79
5.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
79
5.2
Previous Work
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
5.3
Motivation and Objectives . . . . . . . . . . . . . . . . . . . . . . . .
84
5.4
Technical Roadmap . . . . . . . . . . . . . . . . . . . . . . . . . . . .
86
6 Development and Validation of a Diabatic Mean Line Model
87
6.1
Object-Oriented Turbomachinery Analysis Code (OTAC) . . . . . . .
87
6.2
Mean Line Model Input Parameters . . . . . . . . . . . . . . . . . . .
91
6.3
Simulation Setup of an Acceleration Transient
. . . . . . . . . . . . .
96
6.4
Adiabatic Validation of the Mean Line Model
. . . . . . . . . . . . .
98
6.5
Implementation of Heat Transfer Effects
. . . . . . . . . . . . . . . .
102
Diabatic Loss and Deviation Correlations . . . . . . . . . . . .
103
6.5.1
6.6
Summary
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7 Assessment of Diabatic Stall Margin Loss
105
107
7.1
Quantifying the Impact of Deviation Effects
. . . . . . . . . . . . . .
107
7.2
Heat Transfer Effects on Stage Rematching . . . . . . . . . . . . . . .
112
7.3
Quantifying Stall Margin Loss Sensitivity to Model Inputs
. . . . . .
119
7.4
Limitations and Expansion of Current Capability
. . . . . . . . . . .
123
7.5
Major Findings
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
126
10
8 Conclusions
8.1
8.2
129
Spike-type Rotating Stall Inception . . . . . . . . . . . . . . . . . . .
129
8.1.1
. . . . . . . . . . . . . . .
130
. . . . . . . . . . . . . . . . . . . . .
131
Recommendations for Future Work
Transient Heat Transfer Effects
8.2.1
Recommendations for Future Work
. . . . . . . . . . . . . . .
132
A Guidelines for OTAC Implementation and Usage
135
B Guidelines for Smoke Visualization
137
11
12
List of Figures
2-1
Modal and spike pre-cursors in pressure traces . . . . . . . . . . . . .
30
2-2
Criteria for stall inception type
31
2-3
Tip-clearance flow as a mechanism for spike-type stall inception
2-4
Spike pre-cursor formation process proposed by Pullan et al.
. . . . . . . . . . . . . . . . . . . . .
. . .
33
. . . . .
34
2-5
Technical roadmap for spike-type stall inception investigation . . . . .
36
3-1
MIT research compressor performance and pre-stall behavior . . . . .
40
3-2
Cascade design schematics . . . . . . . . . . . . . . . . . . . . . . . .
42
3-3
Compressor and cascade parameters . . . . . . . . . . . . . . . . . . .
42
3-4
Velocity profile of compressor endwall boundary layer . . . . . . . . .
44
3-5
Smoke generator schematic . . . . . . . . . . . . . . . . . . . . . . . .
46
3-6
Dual cascade top casings facilitate instrumentation and flow visualization 47
3-7
Relationship of compressor operating point and outlet boundary condition
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
3-8
Blade mesh at 90% span . . . . . . . . . . . . . . . . . . . . . . . . .
53
3-9
Computational domain size
. . . . . . . . . . . . . . . . . . . . . . .
53
3-10 Limiting streamlines showing large hub separation . . . . . . . . . . .
55
3-11 Shape of time-averaged pressure rise characteristic in good agreement
with experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
3-12 Pressure traces for compressor computation and experiment at stall in
good agreement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
3-13 Compressor computation captures spike pre-cursor formation . . . . .
58
13
3-14 Pre-cursor formation mechanism in compressor computations agree
with that of Pullan et al. . . . . . . . . . . . . . . . . . . . . . . . . .
4-1
Spike pre-cursor behavior with change in reference frame:
59
up-spike
leads down-spike in compressor, down-spike leads up-spike in cascade
62
4-2
Spike pre-cursor demonstrated in cascade experiment
. . . . . . . . .
63
4-3
Spike pre-cursor formation captured at lower spans
. . . . . . . . . .
64
4-4
Spike pre-cursor formation at 50% span for 15,000 Reynolds number .
68
4-5
Cascade computation show same pre-cursor formation mechanism at
50% span as in compressor computations . . . . . . . . . . . . . . . .
70
4-6
Flow visualization prior to pre-cursor formation
. . . . . . . . . . . .
71
4-7
Flow visualization at
t1 :
partial leading-edge separation at blade 2 . .
72
4-8
Flow visualization at
t1 + 1.2τ :
4-9
Flow visualization at t1 +2.4τ : propagation of shed vorticity to adjacent
blade 2 leading-edge fully separated .
passage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4-10 Flow visualization at
5-1
t1 + 3.6τ :
blade 2 boundary layer re-attached
.
73
74
75
Unsteady component temperatures for typical acceleration transient.
Differing time scales of component and main gas path temperatures
drive transient heat transfer
5-2
. . . . . . . . . . . . . . . . . . . . . . .
Stage pressure ratio as functions of inlet and outlet corrected flow.
Stage outflow sensitive to excursions in inflow
5-3
Demonstration of stage stacking behavior.
stages bring rear stages close to stall
5-4
. . . . . . . . . . . . .
81
Small excursions in front
. . . . . . . . . . . . . . . . . .
82
Stall line reduction due to heat transfer as predicted by Maccallum
and Grant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5-5
80
83
Results of Shah indicate impact of heat extraction on loss and deviation
approximately uniform across incidence range
. . . . . . . . . . . . .
84
5-6
Technical roadmap for transient heat transfer investigation . . . . . .
86
6-1
BladeRow
89
element structure
. . . . . . . . . . . . . . . . . . . . . . .
14
6-2
Compressor model execution sequence
. . . . . . . . . . . . . . . . .
6-3
Representative loss and deviation buckets derived from reference mean
90
line data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
92
6-4
Combined loss parameter polynomial surface . . . . . . . . . . . . . .
94
6-5
Operating points for blockage calculation . . . . . . . . . . . . . . . .
95
6-6
Blockage distribution at design corrected speed
95
6-7
Schematic of transient calculation showing use of engine system model
. . . . . . . . . . . .
(ESM) data and choked HPT assumption . . . . . . . . . . . . . . . .
6-8
Mean line model captures adiabatic compressor performance and agrees
with reference mean line model data
6-9
97
. . . . . . . . . . . . . . . . . .
99
Stall line from diffusion factor stall criterion in agreement with reference mean line data . . . . . . . . . . . . . . . . . . . . . . . . . . . .
101
6-10 Mean line model produces representative transient operating line, with
some discrepancy due to choking assumption . . . . . . . . . . . . . .
6-11 Schematic of
101
BladeRow element modifications for heat transfer capability102
6-12 Heat transfer element reproduces Rayleigh line . . . . . . . . . . . . .
104
7-1
Heat transfer increases excursion of transient operating lines
109
7-2
Net heat flux as a function of non-dimensional time. Maximum heat
. . . . .
addition at 95.3% corrected speed . . . . . . . . . . . . . . . . . . . .
7-3
Composite compressor maps for diabatic transient. 9.9 point reduction
in stall margin between 93% and 100% corrected speed
7-4
. . . . . . . .
Percentage of stalling events per blade row.
111
Heat transfer increases
stall frequency in front blade rows . . . . . . . . . . . . . . . . . . . .
7-6
110
Stall margin as a function of corrected speed for adiabatic and diabatic
calculations. Heat transfer results in a stall margin loss of 9.9 points .
7-5
109
Diffusion factors at stall point for select blade rows.
114
Heat transfer
increases loading for front blade rows and reduces loading for rear blade
rows. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
114
7-7
Loss buckets showing compressor matching at stall for 95.3% corrected
speed. Incidence increases in front stages and decreases in rear stages
with maximum change in incidence of
7-8
3◦
. . . . . . . . . . . . . . . .
Impact of heat transfer at different axial locations. Heat addition backpressures upstream blade rows . . . . . . . . . . . . . . . . . . . . . .
7-9
115
Stall margin as a function of corrected speed for modified values of
stall margin loss is proportional to
7-10 Sensitivity coefficient
Sζ
ζ
117
ζ.
. . . . . . . . . . . . . . . . . .
120
for deviation correlation. Stall margin loss is
approximately linear with
ζ
. . . . . . . . . . . . . . . . . . . . . . .
120
7-11 Stall margin loss as a function of corrected speed for modified values
∗
of heat flux (qcomp,net ). Stall margin loss is proportional to
7-12 Sensitivity coefficient
mately linear with
Sq ∗
∗
qcomp,net
. .
122
for heat flow. Stall margin loss is approxi-
∗
qcomp,net
. . . . . . . . . . . . . . . . . . . . . . .
122
7-13 Transient operating lines from diabatic mean line model and current
NPSS capability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
124
7-14 Stall margin from diabatic mean line model and current NPSS capability. Current capability understimates stall margin loss
. . . . . . .
124
. . . . . . . . . . . . . . . . . .
125
7-16 Uniform heat flow distribution captures 80% of stall margin loss . . .
126
7-15 Time averaged heat flux distribution
16
List of Tables
2.1
Characteristic differences of spike and modal stall pre-cursors . . . . .
31
3.1
Design parameters of MIT research compressor . . . . . . . . . . . . .
41
4.1
Reynolds number study:
Pre-cursor topology and propagation rate
unchanged for Reynolds number range of 30,000 - 60,000. Pre-cursors
not observed near blade tip for 15,000 Reynolds number
. . . . . . .
66
6.1
Heat transfer element independents and dependents . . . . . . . . . .
103
7.1
Compressor block definition
116
. . . . . . . . . . . . . . . . . . . . . . .
17
18
Nomenclature
Abbreviation & Acronym
AG5
AutoGrid 5
DF
Diffusion factor
ESM
Engine system model
NPSS Numerical Propulsion System Simulation
OTAC Object-oriented Turbomachinery Analysis Code
PR
Pressure ratio
Re
Reynolds number
SM
Stall margin
Greek
α
Absolute frame flow angle
β
Relative frame flow angle
δ
Deviation
γ
Ratio of specific heats
κ
Metal angle
λ
Stagger angle
19
ν
Kinematic viscosity
Ω
Rotor angular velocity
Φ, φ
Flow coefficient
Ψ, ψ
Total-to-static pressure rise coefficient
ρ
Density
σ
Solidity
τ
Blade passing period
θ
Circumferential position
ω
Blade loss parameter
ω
Vorticity, specific rate of dissipation of turbulent kinetic energy,
ω̃r
Non-dimensional radial vorticity
ζ
Deviation correlation sensitivity
Vx
Ut
po −Pt,i
1
ρUt2
2
Pt,o −Pt,i
Pt,i −pi
ωr
Ut /rt
Roman
A
Area
cp
Specific heat at constant pressure
cs
Pre-cursor velocity in absolute frame
Cdq
Heat flux distribution control parameter
h, ht
Static, total enthalpy
I
Rothalpy
i
Incidence angle
k
Turbulent kinetic energy
20
ṁ, ṁc
Physical, corrected mass flow
M
Mach number
N, Nc
Physical, corrected rotor speed
p, Pt
Static, total pressure
∆p̃
Pressure coefficient
Q̇
Heat flow rate
q∗
Non-dimensional heat flux
R
Gas constant
r
Radius
S
Blade pitch
Sζ , Sq∗
p− Pt,i
1
ρUt2
2
Q̇
ṁht,i
Stall margin sensitivity coefficients to deviation correlation, net heat flux
s
Specific entropy
T, Tt
Static, total temperature
t
Time
tacc
Acceleration time constant
t∗
Non-dimensional time
t
τ
t̃
Non-dimensional time
t
tacc
Ut
Blade tip velocity
U∞
Cascade free-stream velocity
V
Absolute frame velocity
W
Relative frame velocity
21
Subscript
25
High pressure compressor inlet
3
Combustor inlet
4
High pressure turbine inlet
design
At design point
i, in
Inlet quantity
LE
Leading-edge
m
Meridional component
o, out
Outlet quantity
rel
Relative frame quantity
θ
Tangential component
TE
Trailing-edge
x
Axial component
22
Chapter 1
Introduction
1.1 Background
With the rise of fuel prices and environmental regulation in the past two decades, the
focus on the fuel efficiency of gas turbine engines has grown enormously. To improve
efficiency, engine manufacturers have sought higher pressure ratios in their designs,
with overall pressure ratios of 40 common today and 60 on the horizon.
Rising
pressure, and hence temperature, ratios increases the opportunity for compressor
instability from heat transfer throughout the compressor. To enable lower fan pressure
ratios, gas turbine cores have shrunk considerably in size. Such small cores present
challenges in maintaining tight tip clearances, the lack of which is known to promote
compressor instability. This thesis presents two investigations of current problems in
the area of compressor instability: 1) the onset of spike-type rotating stall and 2) the
impact of heat transfer during compressor transients on stall margin.
The first investigation is of the growth and development of so-called spike stall
pre-cursors. Spike stall pre-cursors are one of two forms of rotating stall inception,
the other being modal stall pre-cursors. Unlike modal-type stall, which is relatively
well understood and captured by existing models, the fluid mechanical mechanisms
of the formation and growth of spike stall pre-cursors are still not well characterized.
Recently, leading-edge vortex shedding has been hypothesized as a mechanism for the
formation of spike stall pre-cursors. In this thesis, this hypothesis is further assessed
23
using an experimental and numerical test program.
The second problem relates to heat transfer between the main gas path and the
compressor blades and endwall surface during transient operation. While the detrimental effects of transient heat transfer are well known, estimation of the stall margin
loss is left largely to empirical models. The heat transfer results in stall margin loss
via two mechanisms: changes in the blade row performance and an alteration of the
stage matching. A first-principles based model is developed to quantify the stall margin loss, as well as to characterize the mechanisms that drive stall margin loss and
assess the sensitivity of the stall margin loss to heat transfer.
1.2 Thesis Contributions
The contributions of this thesis can be summarized as follows:
1. First demonstration of spike pre-cursors in a non-rotating, cascade experiment
2. Identification and quantification of Reynolds number effects on the formation
of spike pre-cursors
3. Visualization of spike stall pre-cursor formation and evidence of leading-edge
vortex shedding as the formation mechanism
4. First-principles based quantification of transient stall margin loss due to heat
transfer in a compressor of technological interest
5. Characterization of the dominant mechanisms of transient stall margin loss
6. Quantification of transient stall margin loss sensitivity to heat transfer magnitude and blade row deviation
24
1.3 Summary of Thesis Chapters
Chapter 2 presents an introduction into compressor instability and the differences
between modal-type and spike-type rotating stall inception. A literature review indicates that while tip-leakage flow has historically been considered necessary for spike
stall pre-cursor formation, recent experiments have shown spike-type stall inception
in the absence of tip-leakage flows. Based on an extensive numerical investigation,
leading-edge separation and vortex shedding has been previously proposed as a formation mechanism for spike pre-cursors. An experimental and numerical test program
is outlined to evaluate this hypothesis, utilizing smoke flow visualization in a linear
rotor blade cascade and corresponding computations.
Chapter 3 details the development of the elements necessary to assess the leadingedge vortex shedding hypothesis. The rotor of the MIT single-stage, low-speed compressor serves as a test geometry and details of the compressor performance are presented.
The design of a linear rotor blade cascade capable of capturing the spike
pre-cursor and a smoke injection mechanism to visualize pre-cursor formation are
given in detail. Computations, of both the compressor and cascade, are used to support the experimental assessment. The computational setup of both calculations is
discussed in detail. The chapter ends with the validation of the compressor computations with experimental data from the MIT single-stage compressor, demonstrating
that the computational methodology is capable of capturing the formation of spike
pre-cursors.
Chapter 4 presents the experimental assessment of the leading-edge vortex shedding hypothesis. The linear cascade demonstrates pre-cursor formation at the blade
tip and the propagation rate is in reasonable agreement with stall experiments in the
single-stage compressor. Pre-cursor formation is demonstrated at lower spans, lending
evidence to the incidence driven, leading-edge vortex shedding hypothesis. Cascade
computations are performed and show the same formation mechanism is present in
the cascade as in the compressor.
Reynolds number is found to impact pre-cursor
formation. These effects are quantified in a systematic investigation, and boundary
25
layer transition is hypothesized as a mechanism for the observed behavior. Informed
by the Reynolds number investigation, spike pre-cursor formation and propagation is
visualized using smoke flow visualization and the visualization is found to be in good
agreement with both the cascade computations and the published literature.
Chapter 5 introduces the investigation of transient heat transfer effects. It starts
with a brief overview of the mechanisms that drive transient heat transfer and stage
matching in multi-stage compressors. A literature review indicates that stall margin
loss due to heat transfer is as great as 12 points, with effects of heat transfer on the
blade boundary layer and stage matching of the same order of magnitude. The limited agreement of the literature with experiment, however, motivates a re-assessment
of this result using higher fidelity tools and data from compressors of current technological interest. The development of a diabatic mean line model capable of capturing
the effects of heat transfer is outlined.
Chapter 6 details the development of the diabatic mean line model. A recently
developed mean line solver for the widely used NPSS framework is utilized and a
brief overview of its capabilities and design is provided. Loss, deviation, and blockage
models are developed utilizing data for an advanced, high pressure ratio compressor.
A procedure for the simulation of transient operation is developed and the adiabatic
steady state and transient performance of the model are validated with compressor
data. A stall criterion based on the Lieblein diffusion factor is developed such that
the effects of heat transfer on the stall line can be assessed. The mean line model is
then expanded to include heat transfer capability and correlations for the effects of
heat transfer on blade loss and deviation are implemented. The heat transfer capability of the mean line model is validated with analytical results for one dimensional,
compressible channel flow with heat addition.
Chapter 7 presents the assessment of transient stall margin loss due to heat transfer. Heat transfer is found to reduce transient stall margin by as much as as 10 points,
with 75% of the stall margin loss due to stage rematching effects. While it is found
that heat transfer does increase transient operating line excursion, the majority of the
stall margin loss is due to reductions in the stall line. The changes in stage match-
26
ing are examined and it is found that heat transfer acts to increase loading in the
front stages, resulting in the stalling of the front blade rows. The sensitivity of the
predicted stall margin loss to heat transfer magnitude and the deviation correlation
used is assessed and the dependence of stall margin loss on both of these quantities is
found to be approximately linear. Simulations representative of the current modeling
capability in NPSS demonstrate that only 7% of the total stall margin loss is captured in the current capability. The chapter ends with the presentation of simplifying
assumptions that can be utilized to form a first approximation of the transient stall
margin loss.
Chapter 8 summarizes the significant findings from both investigations and provides recommendations for future work.
27
28
Chapter 2
Spike-Type Rotating Stall Inception
2.1 Introduction
Stable compressor operation is limited by surge and rotating stall. Surge is an instability of the entire compression system resulting from interactions of the compressor and
a downstream volume and throttle. During surge, the mass flow and compressor pressure rise exhibit large amplitude (relative to the mean), one-dimensional oscillations
and even periods of reversed flow are possible. The onset of surge, and subsequent
compressor behavior, has been well captured by one-dimensional, lumped parameter
models [1, 2].
In contrast, rotating stall is a phenomenon isolated to the compressor. Similar to
traditional wing stall, rotating stall is the result of a separation of the airfoil boundary
layer along all or part of the span. This separation reduces the achievable pressure rise
and mass flow through the passage. The re-distribution of flow around the blocked
passage results in the separation propagating along the circumference in one or more
“stall cells” at 20-70% of the rotor rotational speed [3].
During rotating stall, the
compressor pressure rise and annulus-averaged mass flow are quasi-steady, however,
the local flow through the blade row passages is highly unsteady. The unsteadiness
of the passage flow, as well as the often three-dimensional nature of the separation,
present challenges in modeling and characterizing the onset of rotating stall.
Two distinct forms of rotating stall inception have been identified: modal waves
29
(a) Modal stall pre-cursor
(b) Spike stall pre-cursor
Figure 2-1: Modal and spike pre-cursors in pressure traces (reproduced from [6])
and spike-type stall pre-cursors. In both forms, small disturbances grow in magnitude to the point where the bulk flow through several blade passages breaks down,
separation occurs, and the stall cell is formed. Modal pre-cursors are long-wavelength
(on the order of the annulus circumference), oscillations in pressure and mass flow
throughout the length of the compressor. They are typically observable 100-200 revolutions prior to the onset of rotating stall and travel around the circumference at a
rate between 20% and 40% of rotor speed [3, 4]. Figure 2-1a shows a typical modal
pre-cursor as captured by pressure transducers distributed circumferentially on the
compressor casing.
The growth of the modal pre-cursor is only possible when the
slope of the total-to-static pressure rise characteristic is positive and the compressor
damping is negative [5].
Spike pre-cursors are short-wavelength disturbances (on the order of two to three
blade pitches) that travel around the annulus at approximately 70% rotor speed [7].
The term “spike pre-cursor” is given to these disturbances after the sharp waveforms
they produce in pressure or velocity measurements. The spike pre-cursor is a three
dimensional phenomena producing a local breakdown of the flow within a blade passage. Figure 2-1b shows typical pressure traces of spike stall pre-cursors and Table
2.1 summarizes the characteristic differences between modal and spike pre-cursors.
Camp and Day [8] proposed a criterion, shown schematically in Figure 2-2, for
30
Length Scale
Propagation Speed
Spike
Modal
Blade Pitch
Annulus Circumference
60-90
20-40
2-5
100-200
(% Rotor Speed)
Time Prior to Stall
(Rotor Revolutions)
Table 2.1: Characteristic differences of spike and modal stall pre-cursors
determining which form of stall inception will arise. If a critical rotor incidence angle
is achieved prior to the peak of the compressor characteristic, where the characteristic
is negatively sloped, then the compressor will exhibit spike-type stall inception. The
damping of the compressor is positive and modal waves cannot develop. If, however,
the critical rotor incidence is reached after the peak, the compressor experiences a
region of negative damping, allowing modal pre-cursors to form and grow into a mature stall cell prior to the possible formation of a spike pre-cursor. From this criterion
a general observation can be made: spike-type inception is likely if the compressor
stalls while the characteristic is negatively sloped and modal-type inception is likely
if it stalls while the characteristic is positively sloped or at the peak.
Figure 2-2: Criteria for stall inception type (reproduced from [8])
31
2.2 Previous Work
While the work of Camp and Day provided a criterion to determine the form of
stall inception, it did not identify the underlying fluid mechanisms responsible for the
formation of the spike pre-cursor. This mechanism has been the subject of much study
in the past decades. It has been reported that the spike pre-cursor is confined to the
rotor tip region [7, 8], and as such, the tip-leakage flow was examined as a candidate
mechanism. Early computational studies by Hoying [9] captured the formation of the
spike pre-cursor and provided evidence that its formation was linked to the trajectory
of the tip-clearance vortex. The computations showed the tip-clearance vortex grew
increasingly perpendicular to the main flow as the compressor was throttled into stall
(as shown in Figure 2-3a) and, at the stall point, the tip-clearance vortex moved
axially upstream of the blade row.
Hoying attributed the spike pre-cursor to the
propagation of tip-clearance vortex upstream of the blade row. The spillage of tipclearance flow upstream of the leading edge, as well as backflow of tip-clearance flow
near the trailing edge (see Figure 2-3b), were later established as a criteria for the
formation of spike pre-cursors by Vo et al. [10]. The criteria of Vo et al. was later
supported by full-annulus URANS computations [11].
Recent studies, however, have indicated that spike-type stall inception is possible
in the absence of tip-leakage flow. Spakovszky and Rodunner [12] reported spike-type
stall inception in the vaned diffuser of a centrifugal compressor. The vaned diffuser
has no tip clearance (as there are no rotating components) and thus no tip-leakage
flow. The spike pre-cursor propagated circumferentially at 20% of the impeller speed,
however, this speed was measured in the same reference frame as the stalling blade
row (the absolute frame). In a typical axial rotor, the spike pre-cursor propagates at
60%-90% of rotor speed in the absolute frame, corresponding to 40%-10% with respect
to the rotor (the stalling blade row), in the relative frame. The propagation speed of
20% in the vaned diffuser is thus consistent with the behavior of spike pre-cursors in
axial rotors. Brand and Kottapalli [6] reported spike-type stall inception in a shrouded
axial rotor. A low-speed research compressor was re-staggered such that it exhibited
32
(a) Tip-clearance vortex
trajectories for decreasing
flow-coefficient [9]
(b) Criteria for formation of spike-type stall inception by Vo et
al. [10]
Figure 2-3: Tip-clearance flow as a mechanism for spike-type stall inception
spike-type stall inception and a metallic shroud installed to prevent tip-leakage flow.
Even in the absence of tip-leakage flow, the compressor dynamic behavior was not
altered and the machine still exhibited spike-type stall inception.
The spike pre-
cursors observed with and without the presence of tip-leakage flow appeared identical
in the pressure traces and propagated circumferentially at the same rate, indicating
they had similar topologies and that similar fluid dynamic mechanisms were present.
The work by Spakovszky and Rodunner and by Brand and Kottapalli suggest
tip-leakage flow is not necessary for the formation of spike pre-cursors.
Pullan et
al. [13] proposed that spike pre-cursor formation is the result of a leading-edge flow
separation, and consequent vortex shedding, near the blade tip. Close to stall, a single
blade experiences an increase in incidence, resulting in a separation at the leading
edge (Figure 2-4a). The vorticity once bound in the suction side boundary layer is
shed and rolls up into a vortex tube (Figure 2-4b) which connects the casing and blade
1
suction surface.
The casing “end” of the vortex tube propagates circumferentially
along the leading-edge plane while the blade surface end continues downstream of the
blade row. The blockage associated with the leading-edge separation results in the
up-spike observed in the pressure traces, while the low-pressure core of the vortex
1 Vortex
lines cannot in the fluid, and as such, the vortex tube does not end at the blade or casing
surface. The vortex lines that comprise the vortex tube instead spread out along the surface and
there is no longer a coherent structure
33
(a) Leading-edge separation due to
increased incidence
(b) Vortex tube structure
Figure 2-4: Spike pre-cursor formation process proposed by Pullan et al.
(reproduced from [13])
tube is responsible for the down-spike. The topology of the vortex tube proposed by
Pullan et al. agrees well with the structures seen in the simulations of both Inoue
[14] and Yamada [15].
Pullan et al. presented results from full-wheel 2D and 3D simulations that support this hypothesis. In all three simulations (2D, 3D without tip-clearance, and 3D
with tip-clearance), the same mechanism of increased incidence, leading-edge separation, and shedding of vorticity was found to be responsible for the formation of
the spike pre-cursor. The fluid dynamical process responsible for the increased incidence, however, was dependent on the simulation. In the case of the 2D simulation,
a trailing-edge separation of the adjacent blade resulted in blockage and increased incidence on the stalling blade, whereas in the 3D case without tip-clearance it was the
blockage of a growing hub-corner separation. Regardless of the cause of the increased
incidence, however, it was the consequent leading-edge separation and shed vorticity
that was responsible for the development of the spike pre-cursor.
34
2.3 Motivation and Objectives
Recent experiments have shown the tip-leakage vortex is not necessary for the formation of spike pre-cursors. To explain this development, a mechanism was proposed
by Pullan et al.
which attributes the formation of the pre-cursor to leading-edge
separation and vortex shedding, resulting from a critical incidence being exceeded.
Through several computations, it was shown that this mechanism is responsible for
the formation of spike pre-cursors in the absence of the tip-leakage vortex. The work
of Pullan et al., however, is numerical in nature, as is much of the published literature.
To date there has been limited experimental characterization of the spike pre-cursor
formation and topology, likely owing to the challenges of flow characterization in the
rotating environment of the compressor.
Furthermore, the majority of experimen-
tal investigations have been conducted at low Reynolds numbers, typically an order
of magnitude below those found in gas turbines.
The impact of Reynolds number
on pre-cursor formation, however, has not been characterized.
This work seeks to
address these limitations with the following objectives:
1. Demonstrate the formation of spike pre-cursors in a non-rotating environment
2. Experimentally assess the previously proposed incidence driven, leading-edge
vortex shedding mechanism for the formation of spike pre-cursors
3. Characterize the impact of Reynolds number on pre-cursor formation
4. Visualize the pre-cursor formation process
35
2.4 Technical Roadmap
Single-Stage
Compressor
Test
Stall Inception
Assessment in
Cascade
Reynolds
Number
Study
Cascade
Flow
Visualization
Compressor
Computation
Cascade
Computation
Figure 2-5: Technical roadmap for spike-type stall inception investigation
The technical roadmap is shown in Figure 2-5. The rotor of the MIT single-stage
compressor serves as the basis for this investigation. Stall ramps are used to identify
the critical incidence for the rotor blade geometry.
A linear cascade of the same
geometry is used to capture the spike pre-cursor in a non-rotating environment.
At the core of the previously proposed formation mechanism is the idea of a
critical incidence resulting in a leading-edge separation.
The mechanism does not,
however, require this incidence be achieved at the blade tip.
In theory, pre-cursor
formation should be possible at any spanwise location where the critical incidence is
met.
To assess the incidence driven mechanism, the cascade is designed to enable
large incidence changes away from the blade tip. Specifically, the blades used in the
cascade are twisted, with incidence increasing from the tip to the hub.
Pre-cursor
formation in the cascade is first assessed at the blade tip using a combination of fastresponse pressure and velocity measurements. Velocity measurements are conducted
along the span to determine if pre-cursor formation occurs at lower spans, away from
the tip.
Smoke flow is used to visualize pre-cursor formation. Smoke flow visualization requires low Reynolds numbers to avoid rapid diffusion of the smoke. These Reynolds
numbers are typically an order of magnitude below those achieved in low speed research compressors [16]. To assess the feasibility of using smoke flow, a systematic
36
investigation of pre-cursor formation at lower Reynolds number is conducted. Smoke
flow visualization is then performed at the lowest possible Reynolds number.
The
smoke flow visualization is correlated with velocity measurements to identify the
structures responsible for the characteristic waveform in compressor pressure traces.
The cascade experiment is supported by 3D URANS calculations.
Compressor
calculations are first used to develop the numerical simulation framework and focused
on capturing the pre-cursor formation. The same methodology is used to assess the
formation of the spike pre-cursor in the cascade. The cascade flow visualization and
velocity measurements are compared with the cascade computations and the results
of Pullan et al.
37
38
Chapter 3
Experimental and Computational
Setup
3.1 Experimental Setup
In this section the setup of the single-stage compressor and linear rotor blade cascade
tests are outlined. The cascade design, instrumentation, and smoke generation and
injection are also discussed in detail.
3.1.1 Test Compressor
All work in this investigation was done using the MIT single-stage, low-speed research compressor. This compressor was previously used by Brand and Kottapalli [6]
to investigate spike-type stall inception in a shrouded rotor, but for all studies in this
thesis the rotor was un-shrouded. Design parameters of the MIT research compressor are given in Table 3.1.
The compressor was run without the stator to prevent
losses in the stator from producing a positive slope of the pressure rise characteristic
and promoting the growth of modal stall pre-cursors.
characteristic is shown in Figure 3-1a.
The measured pressure rise
Six fast-response pressure transducers were
installed around the circumference at 25% chord upstream of the rotor leading edge
to investigate the pre-stall behavior. The resultant pressure traces are given in Figure
39
0.35
420
0.3
360
77% Ω
300
0.25
1
ρU 2
2 t
240
Ψ
θ location
0.2
Φ
0.15
stall
= 0.3626
180
120
0.1
60
0.05
0
0
0.3
0.35
0.4
0.45
0.5
0.55
−60
0.6
−7
−6
−5
−4
−3
−2
−1
0
Rotor revolutions
Φ
(a) Pressure rise characteristic
(b) Pre-stall behavior
Figure 3-1: MIT research compressor performance and pre-stall behavior
3-1b and demonstrate that the compressor exhibits spike-type stall inception.
The rotor blade geometry of the compressor is a legacy design and is known to be
more heavily loaded at the hub than the tip [17]. As a result, the hub separates at
even high flow coefficients, the extent of the which is shown in Section 3.2.4. While
the hub separation reduces the negative slope of the measured characteristic, the
slope of the “local” characteristic at the tip can be more negative.
Ultimately the
compressor exhibits spike-type stall inception, making it an appropriate test vehicle
for this study.
The rotor blade geometry was used for all computational studies and for the
linear cascade investigation.
For the computations, the rotor blade geometry was
re-constructed using the information reported by Gopalakrishnan [18].
The mean
cross-section is a NACA 6409 airfoil with varying leading-edge and trailing-edge metal
angles along the span. The maximum camber magnitude and position,
m
and
p
in
the NACA centerline polynomial respectively [19], were varied to match the metal
angles, resulting in several airfoil cross-sections along the span.
The cross-sections
were linearly lofted to define the 3D blade geometry for computation.
40
Table 3.1: Design parameters of MIT research compressor
0.59
Tip Stagger Angle
60◦
0.66
Mean Radius
259 mm
Hub to Tip Ratio
0.75
Chord
38 mm
Solidity
1.03
Blade Count
44
Aspect Ratio
1.90
Reynolds Numbers
75,000-150,000
Design Flow Coefficient
φ
Design Pressure Rise Coefficient
ψ
3.1.2 Linear Cascade Design
One objective of this work is to generate a spike pre-cursor in a non-rotating cascade
experiment so as facilitate visualization of the formation process. This results in the
following design requirements for the cascade:
1. Re-create rotor tip flow field at stall and capture spike pre-cursor
2. Facilitate smoke injection near the leading edge
3. Permit instrumentation with pressure transducers and a hotwire anemometer
Figure 3-2 presents two schematics of the cascade design. This section discusses
the design decisions to meet the first requirement. Smoke generation and instrumentation are discussed in the next two sections.
The key feature of the formation mechanism proposed by Pullan et al. is a leadingedge separation resulting from a critical incidence being reached. As such, reproducing
the rotor tip incidence
α
at stall in the cascade is of great importance. Figure 3-3
shows the relevant parameters in both the compressor and cascade.
41
(a) Design features
(b) Top view
Figure 3-2: Cascade design schematics
S
λ
Tunnel
Airflow
U∞ = W
λ
i
β
i
Ωr
W
S
β
Vx
Compressor
Cascade
Figure 3-3: Compressor and cascade parameters
42
While the blade stagger angle is a function of the compressor geometry only, the
flow angle in the compressor is a function of the flow coefficient at stall,
1
,
β = arctan
φ
φ=
Vx
Ut
As the incidence angle at the blade tip is under consideration, the flow coefficient
is defined using the blade speed at the tip.
In the cascade, the flow angle is set
by the angle between the tunnel axis (the direction of the free-stream flow) and the
leading-edge plane.
The pressure rise characteristic in Figure 3-1a shows that the compressor stalled at
a flow coefficient of 0.3626, corresponding to a blade tip flow angle of
flow coefficient in Figure 3-1a was determined using the axial velocity
β = 70.0◦ .
Vx
The
from a pitot-
static probe upstream of the rotor face and at the mean radius. The axial velocity
at the rotor tip, however, is less than that at the mean radius due to the endwall
boundary layer, resulting in a locally lower flow coefficient and thus higher flow angle
and incidence. The endwall boundary layer velocity profile, shown in Figure 3-4, was
rd
previously measured by Gysling using a hotwire anenometer located 1/3
of a blade
chord upstream of the leading-edge.
The nominal stalling flow coefficient is reduced by 0.125 based on the decrease
in flow coefficient observed at 88.5% span, which represents the mean of the last
spanwise location with a nominal flow coefficient (77% span) and the blade tip. This
results in a local stalling flow coefficient of 0.2376 at the tip, corresponding to a flow
angle of
β = 76.5◦ .
The flow angle sets the angle between the tunnel axis and the
leading-edge plane during construction of the cascade. The blade stagger angle (γ )
and pitch (S) are taken from the compressor geometry and are
60◦
respectively. The blade with smoke injection is staggered an additional
and 31.8 mm
5◦
to promote
pre-cursor formation at the location of smoke injection.
One goal of this work is to assess whether pre-cursor formation can occur at locations below the tip span. This requires the incidence at lower spans to be equal to, or
greater than, that at the tip. Such a setup can be achieved by using twisted blades
43
100
0.125
Percent Span [−]
80
60
40
20
0
0
0.2
0.4
0.6
Φ [−]
Figure 3-4: Velocity profile of compressor endwall boundary layer (from [17])
in which the incidence increases from tip to hub.
This is the case for compressor
blades, and the same physical blades from the compressor were used in the cascade.
Using the compressor blades offered two additional benefits. First, the large number
of pre-fabricated blades enabled a high blade count of 20 in the cascade. This eliminated the need for boundary layer control along the sidewalls to maintain periodicity.
Furthermore, the cascade could serve as a test bed for smoke visualization techniques
for future use in the compressor.
The cascade was fabricated of optically clear polycarbonate to permit visual access
and the sidewalls were machined to produce the same average tip clearance as in the
compressor. Poor tolerance control during the manufacture of the blades, however,
prevented the precise control of tip clearances. The tip clearances varied by as much as
1.0% of chord, with the average tip clearance being 1.3% of chord. This is comparable
to that of the single-stage compressor which has tip clearance variations of up to
1.3% chord. A trip strip was installed upstream of the rotor blades on the top and
bottom casing to force transition of the endwall boundary layer. The trip strip was
installed parallel to the leading-edge plane such that the boundary layer thickness
was approximately the same at each blade.
44
3.1.3 Smoke Generation and Injection
Smoke has long been used as a tool for flow visualization in experimental aerodynamics. In typical wind tunnel experiments, smoke is injected upstream of the object
under study. Such setups use large contractions downstream of injection to reduce the
velocity, and hence Reynolds number, at the smoke injection point. Lower Reynolds
numbers reduce the mixing and diffusion of the smoke, producing more coherent
streaklines downstream. The Reynolds numbers of smoke flow experiments are typically an order of magnitude lower than those found in research compressors [16].
Constraints on the size of the smoke generating apparatus are also less severe as the
injection occurs well upstream of the object being studied.
This work seeks to visualize the leading-edge separation of the suction surface
boundary layer and consequent vortex shedding. To improve the visualization, it is
desirable to inject smoke directly into the suction side boundary layer. Once injected,
the smoke would remain with the boundary layer fluid throughout the formation
process.
This, however, requires injection at the test velocity rather than at the
reduced velocity upstream of a contraction, resulting in higher Reynolds numbers
and increased diffusion. Furthermore, the injection apparatus must be small relative
to the blade to reduce its aerodynamic influence.
While the Reynolds number in
the cascade can be made small by reducing the free-stream velocity, the impact of
low Reynolds number on pre-cursor formation is unknown.
A study of pre-cursor
formation at low Reynolds number was performed prior to flow visualization and is
discussed in Section 4.2. The study identified the lowest Reynolds number for which
visualization is feasible while spike stall pre-cursors are still formed.
No commercial smoke generator was suitable for the current study due to their
size relative to the blade, and a miniaturized smoke generator was instead developed.
It was found that the best visualization was achieved when the smoke was made
in-situ, rather than being piped from an external location.
The smoke generator
was originally designed to be placed into a modified blade for use in the compressor,
however, it could also be used detached from the blade. As the modified blade was
45
Heated Nichrome Wire Fed
Through Outer Bores
Enamel Seals Outer Bores
Mineral Oil Flows
Through Inner Bores
+
V
-
Plastic Tubing
Ceramic
Thermocouple Tube
Figure 3-5: Smoke generator schematic
ultimately not used in this study, the details are not given here and can be found in
[20].
The smoke generator, shown in Figure 3-5, consists primarily of a quad-bore,
ceramic thermocouple tube. The tube has a diameter of 1.6 mm, corresponding to
4% of the blade chord and 46% of the maximum blade thickness.
Mineral oil is
pumped through two of the bores. A nichrome wire runs through the remaining two
bores and the mineral oil is heated to the point of evaporation via conductive heat
transfer through the walls of the thermocouple tube.
The two bores carrying the
nichrome wire are sealed with high temperature enamel to prevent oil leakage. While
a dual-bore design in which the nichrome is directly submerged in the oil would be
more efficient and produce greater volumes of smoke, it was found that such a design
produced excessive oil leakage.
3.1.4 Instrumentation
There are three types of data to be acquired in the cascade experiment: fast-response
static pressure and velocity measurements to capture the spike pre-cursor, high-speed
video of the smoke visualization, and total and static pressure from a pitot probe to
set the cascade operating point. Kulite model XCQ-062 15 PSI fast-response pressure
transducers were installed in the top casing to record the unsteady static pressure field.
Two different top casings were used. The first, shown in Figure 3-6a, had an array of
possible Kulite locations available. The first row of Kulite holes were placed 10% chord
upstream of the leading-edge plane, aligned with the path of the leading-edge vortex.
They were spaced at one third of a blade pitch apart for three passages downstream
46
Blade with Smoke Injection
Blade with Smoke Injection
K1 K2
K3
K4
K5
Hotwire
= Installed Kulite
(a) Casing with Kulite array
(b) Casing with reduced instrumentation for
flow visualization
Figure 3-6: Dual cascade top casings facilitate instrumentation and flow
visualization
of the blade with smoke injection. Holes with the same pitchwise spacing were also
placed within the passage to provide flexibility, in case the leading-edge vortex were
to convect down a passage. They proved to be unnecessary and were covered with
Kaptan tape during operation to prevent leakage.
While this top casing provides the required spatial resolution of the unsteady static
pressure field, the installed Kulites and unused holes obscured the smoke visualization when viewing the cascade from the top. A top-down perspective is preferable
as it provides resolution of both the pitchwise and axial positions of any visualized
structures. A second top casing, shown in Figure 3-6b, was manufactured with only
two Kulites. The first is located two thirds of a blade pitch upstream of the blade
with smoke injection. The second is located two blade pitches downstream, at the
same location as K5 in Figure 3-6a. The upstream Kulite is used to ensure that the
visualized structure did not convect from upstream and the downstream Kulite is
used to assess whether the observed structures produce the characteristic up-down
waveform of spike pre-cursors. A TSI Model 1210 hotwire was also used to record
unsteady velocity measurements. It was placed in the leading-edge plane, with the
shaft running axially through the passage to the trailing-edge. The hotwire offered
greater sensitivity than the Kulites and could be placed at any span. Voltage signals
from both the Kulites and the hotwire were amplified and sampled at 10 kHz, approx-
47
imately 10 times the equivalent blade passing frequency, by a National Instruments
9215 A/D converter.
The smoke visualization was recorded using a Photron Fastcam SA5 high-speed
video camera.
A Unilux 1xF strobe was used to provide illumination, providing a
maximum bandwidth of 833 Hz and a short flash duration of 100
blur.
µs to reduce motion
Due to the bandwidth limitations of the strobe, the SA5 was operated at a
frame rate of 750 Hz. The rate at which the pre-cursor propagates one blade pitch is
on the order of 35% of blade passing frequency, or 154 Hz for the fastest equivalent
rotor speed tested with smoke injection.
propagate only 0.2 passages per frame.
For this case, the flow structure would
The camera and strobe were synchronized
using a voltage pulse output by the camera.
The voltage pulse was also recorded
by the A/D converter to allow synchronization of the video frames and the pressure
and velocity measurements from the Kulites and hotwire. The free-stream total and
static pressure from the pitot probe were recorded using a Scanivalve DSA3217 1PSID
pressure transducer.
In summary, the linear cascade described is designed to match the blade tip incidence of the compressor at stall in order to generate a spike pre-cursor. The use of
twisted blades allows investigating spike pre-cursor formation at lower spans, away
from the tip. To facilitate flow visualization, a miniaturized smoke generator was designed to inject smoke directly into the suction surface boundary layer. Finally, the
cascade incorporates the necessary instrumentation to capture the unsteady pressure
and velocity field.
3.2 Computational Setup
A brief description of the solver is provided and turbulence modeling, inlet and outlet boundary conditions, and time-stepping for unsteady calculations are discussed.
Mesh generation and validation are discussed next and the procedure for performing a
simulated throttle ramp is outlined. While the specific blade geometry presents some
numerical challenges, which will be described in detail, the computational methodol-
48
ogy described below will be shown to be capable of capturing the spike pre-cursor.
3.2.1 CFD Solver Description
All computations in this thesis were produced using a proprietary Reynolds Averaged
Navier-Stokes (RANS) solver.
The solver is a finite-volume code designed specifi-
cally for the simulation of turbomachinery flows and utilizes a structured hexahedral
mesh. The equations are solved in the frame of reference of the blade row, i.e. the
rotating frame for compressor computations and the stationary frame for cascade
computations. Details of the solver settings and models are given below.
Turbulence Modeling
The
k−ω
turbulence model is used for all computations in this thesis.
It is a
two equation model used to provide closure for the RANS equations. In this model,
two transport equations are used to determine the turbulent kinetic energy
specific rate of dissipation
two quantities as
νt =
ω.
k
and the
The turbulent eddy viscosity is then formed from these
k
. The
ω
k−ω
model has been shown to capture flows with
adverse pressure gradients [21], making it particularly suitable for compressor flows.
Further details on the
k−ω
model can be found in [22].
Both high and low Reynolds number treatments for near-wall modeling are available in the
k−ω
model.
In the high Reynolds number treatment, the first cell is
placed in the log-layer and the log-law is used to model the velocity profile within
the boundary layer. In the low Reynolds number treatment, the first cell is placed in
the viscous sub-layer and the boundary layer is fully resolved. Low Reynolds number treatments are more accurate in capturing and predicting separation than high
Reynolds number treatments, but require very fine meshes near the wall, increasing
computational cost. The low Reynolds number treatment is required in this work as
separation is fundamental to the hypothesized pre-cursor formation mechanism. The
flow results were examined to ensure the first cell is located at
y+ ∼ 1
mesh met the requirements for the low Reynolds number treatment.
49
and that the
Inlet Boundary Conditions
For all computations, total pressure, total temperature, and flow angle were specified at the inlet. Total temperature was held at the standard day value (288.15K).
Axial inlet flow was used for all compressor computations. For cascade computations,
the inlet flow angle (β in Figure 3-3) was varied to set the incidence angle. Both total
temperature and velocity direction were set to be spatially uniform. In compressor
computations, a radial total pressure profile was used to simulate the inlet boundary
layer as the inlet of the computational domain was shorter than the compressor inlet.
The axial velocity profile at the rotor inlet was set to that measured by Gopalakrishnan [18]. This approach was not necessary for the cascade computations as the inlet
of the domain was of the same length as the inlet in the cascade experiment and the
boundary layer could develop naturally.
Outlet Boundary Conditions
During a typical stall inception experiment, a compressor is driven into stall by
closing the downstream throttle.
The compressor operating point is set by the in-
tersection of the resultant throttle line, shown in Figure 3-7, and the pressure rise
characteristic.
While the behavior of a throttle can be modeled numerically (e.g.
[23]), this requires the implementation of an actuator disk or the added computational cost of meshing a variable area nozzle. It is more common to set the operating
point by either specifying the outlet mass flow or static pressure.
Given a specified mass flow at the outlet of the domain, the solver varies the
outlet static pressure until the appropriate operating point is found. The mass flow
boundary condition was used for all steady simulations. For time-accurate unsteady
simulations, however, this type of boundary condition is not suitable as the timevarying backpressure introduces an artificial source of unsteadiness. A constant static
pressure boundary condition was used instead for all unsteady computations.
As can be seen for the lower chained line in Figure 3-7, two valid solutions can
exist for a given pressure boundary condition, one on the negatively sloped side of
the characteristic and the other on the positively sloped side. The lack of a unique
50
Mass Flow B.C.
Ψ
pout
Pressure B.C.
Throttle Lines
ṁ
Φ
Figure 3-7: Relationship of compressor operating point and outlet boundary
condition
solution can lead to numerical divergence, especially near the peak of the characteristic.
This is less of a concern for this work, however, as compressors that exhibit
spike-type stall inception typically stall on the negatively sloped side of the characteristic. The calculation also diverges if an exit pressure above the maximum pressure
rise of the compressor is imposed, as in the upper chained line in Figure 3-7. As the
compressor characteristic is not known a-priori, the back pressure must be increased
by small increments and in many calculations to prevent such a condition, increasing
the computational cost. The details of the computational procedure for the unsteady
computations are given in Section 3.2.3. A non-reflecting method of characteristics
formulation of the mass flow and static pressure boundary conditions were used in
all cases.
While this serves only to reduce computational time for steady calcula-
tions, as the solution is driven to the time-average and any waves are damped, it is
of greater importance for unsteady calculations. A constant pressure boundary condition can reflect unsteady pressure waves emanating from the blade row back into
the computational domain. These reflections would interact with the blade row, artificially changing its behavior. The non-reflecting formulation seeks to prevent these
reflections, however, some amount of reflection always occurs.
51
An extended outlet
domain and cell-stretching were also used to further damp reflections and prevent
any coupling between the blade row and the outlet boundary condition. Details of
the computational mesh are given in section 3.2.2
Temporal Resolution
All unsteady compressor computations were performed with 100 physical time
steps per blade passing period.
This is consistent with the temporal resolution of
other numerical work on spike-type stall inception (e.g. [13, 15]). Unsteady cascade
computations were performed with 100 physical time steps per
ing period, i.e.
equivalent
blade pass-
the blade passing period for the equivalent compressor rotational
speed such that the same temporal resolution is maintained between cascade and
compressor calculations.
3.2.2 Mesh Generation and Validation
All meshes used in this work were produced using Numeca AutoGrid 5 (AG5). AG5
is a tool designed specifically for the rapid meshing of turbomachinery geometries
and offers great control of the meshing process. All meshes were of an O4H topology
and contained 1.2 million cells per blade passage.
is shown in Figure 3-8.
The blade mesh at 90% span
Single passage calculations were performed with increased
refinement (1.6 million cells per blade passage) and the pressure rise characteristic
was unchanged, indicating the mesh was converged. The tip gap was meshed with
additional blocks in an OH topology with 17 points in the tip gap. The blade stagger
◦
was set to that of the compressor (60 at the tip) and was uniform for all blades.
The computational domain, shown in Figure 3-9, extends 0.8 tip radii upstream and
1.5 tip radii downstream of the blade row, 10.5 and 18 axial chords respectively, and
is similar in size to that of Pullan et al.
[13].
Cell-stretching has been reported
to damp reflections from the outlet boundary and was utilized by Everitt [24] in
an investigation of spike-type stall inception in centrifugal compressors.
The cell-
stretching domain began 8 axial chords downstream of the blade row with a stretching
factor of 1.05. The stretching factor is 4 times less than that used by Everitt, however,
52
the base cell size prior to stretching was several times larger than those for Everitt due
to the large outlet domain. The final cell of the outlet domain is approximately one
axial chord long and further stretching was found to be unnecessary. The same mesh
refinement and topology were used for the compressor and cascade computations to
maintain consistency.
Figure 3-8: Blade mesh at 90% span
1.5x Tip Radius
Cell Stretching Domain
0.8x Tip Radius
Figure 3-9: Computational domain size
53
3.2.3 Computational Procedure
To reduce computational cost, steady computations were carried out as close to the
stall point as possible. The first steady computations were initialized from a uniform
flow field and run at an operating point that presented the least separation to the
flow solver to aid in convergence, e.g. at high flow for the compressor computations or
at low incidence for the cascade computations. Consequent steady calculations were
initialized using the results from the previous calculation and were driven towards
the stall point by decreasing the mass flow or increasing the inlet flow angle.
The
steady computations diverged for even relatively moderate operating conditions, likely
due to the large amounts of separation expected from this blade geometry, at which
point unsteady computations were used to further approach the stall point.
The
first unsteady computations were initialized with the results of the last converged
steady computations.
Consequent calculations were driven to the stall point with
step increases in the outlet static pressure or incidence angle. A step increase was
only performed after physical quantities such as mass flow or inlet static pressure
reached steady levels for 1.5 rotor revolutions. In other words, when the computation
had settled at the new operating point.
These step changes were initially large to
reduce the computational cost, on the order of a change in flow coefficient of 0.05,
but were decreased in size as the operating point approached stall.
3.2.4 Numerical Challenges
This rotor geometry is known to exhibit hub separation, even at high flow coefficients
near the design point.
The hub separation was further exacerbated by the blade
twist in the cascade configuration. Figure 3-10 shows the limiting streamlines on a
single blade both near design and near stall. Even near design, the hub is separated
and the separation continues to mid-span. Close to stall, the separation has grown
significantly and exists along the entire span.
The unsteadiness of this separation posed a challenge to the steady flow solver,
resulting in the steady computations diverging at a higher flow coefficient. The lim-
54
(a) Near design
(b) Near stall
Figure 3-10: Limiting streamlines showing large hub separation
ited utility of the steady computations necessitated a greater number of unsteady
computations. To reduce computational cost, only four passages, or an eleventh of an
annulus, were simulated. It was found that the limited domain of the computations
was capable of capturing the spike pre-cursor, as will be shown in the next section.
3.3 Rotor-Only Axial Compressor Computations
In this section, the results of the rotor-only compressor computations are shown and
the steady-state performance and unsteady stalling behavior of the computations are
validated with experimental data.
The computations capture the formation of the
spike pre-cursor and the formation process is consistent with that proposed by Pullan
et al. [13].
3.3.1 Validation with Experimental Data
Capturing the shape of the pressure rise characteristic is a primary requirement of
the compressor computations as this governs the stalling behavior. Figure 3-11 shows
55
0.4
0.35
Experiment
Rotor−Only
0.3
Ψ
0.25
Computation
Rotor−Only
0.2
0.15
0.1
0.05
0
0.25
0.3
0.35
0.4
0.45
Φ
0.5
0.55
0.6
0.65
Figure 3-11: Shape of time-averaged pressure rise characteristic in good agreement
with experiment
the time-averaged pressure rise characteristic of the compressor computations and
experiment. The shape of the characteristic from the computations agrees well with
that of experiment. The characteristic from the computations, however, is shifted to
lower flow coefficients. RANS calculations have known limitations in quantifying the
impact of large separations.
It is believed that the large hub separation results in
an over-prediction of the overall blockage, resulting in the shift of the characteristic.
As the shape of the characteristic is the primary concern, and this was in good
agreement with experiment, the discrepancy in blockage was considered acceptable
for the present study.
3.3.2 Simulation of Stall Pre-cursors
The first unsteady computation was initialized at a flow coefficient of
φ = 0.475.
The
operating point was brought to stall via step changes in the back pressure, as detailed
in Section 3.2.3. Figure 3-12a shows pressure traces for the stalling calculation at six
locations uniformly distributed across the four passages and 10% chord upstream of
56
35
420
76% Ω
30
360
77% Ω
25
300
1
ρU 2
2 t
240
1
ρU 2
2 t
θ location
θ Location
20
15
180
10
120
5
60
0
0
−5
1.3
1.4
1.5
1.6
1.7
1.8
Rotor revolutions
1.9
−60
2
−7
−6
−5
−4
−3
−2
−1
0
Rotor revolutions
(a) Compressor computation, rotor-only
(b) Compressor experiment, rotor-only
Figure 3-12: Pressure traces for compressor computation and experiment at stall in
good agreement
the blade row. The equivalent pressure traces for the experimental stall ramps are
shown in Figure 3-12b. The abscissa in Figure 3-12a has been scaled such that an
angled line represents the same propagation speed on both plots.
The stalling behavior of the compressor computation is in good agreement with
the experiment. The characteristic “up-down” waveform of the spike pre-cursor is first
observed in the computation at
t1 = 1.48
rotor revolutions and grows in magnitude.
The propagation rate of the pre-cursor in the computation is 76% of rotor speed and
agrees with the measured 77% in the experiment. It should be noted that the stall
in the computation was not triggered by an imposed perturbation or a re-staggered
blade.
While the step change in back pressure used to change the operating point
does produce a large perturbation to the flow field, the calculation had settled at
the new operating point and continued for one rotor revolution without any significant behavior prior to the stall event. The stalling behavior was likely triggered by
numerical turbulence inherent to the calculation.
Figure 3-13a shows a contour plot of non-dimensional radial vorticity
57
ω˜r
at
t1 =
1.48 for a 90% span slice.
ficient
The two lines above the contour plot show the pressure coef-
∆p̃ across the domain and 10% chord upstream of the blade row (corresponding
to the dotted line in the contour plot). The solid line is the pressure coefficient for
the time presented while the dashed line is the steady pressure coefficient prior to the
stall event.
∆p̃
1
2
2 ρUt
∆p̃
ω˜r
1
2
2 ρUt
ω˜r
1
2
3
4
1
(a) t1 = 1.48
2
3
4
(b) t2 = t1 + 7τ = 1.64
Figure 3-13: Compressor computation captures spike pre-cursor formation
At time
t1
the leading-edge of blade 3 has separated, producing blockage and
a corresponding increase in static pressure upstream.
The shed vorticity from the
leading-edge separation propagates to the adjacent passages.
passing periods later, at
t2 = 1.64,
Seven blade passing
a finite vortex is seen at blade 1 in Figure 3-13b.
The core of the vortex produces a region of low static pressure corresponding to the
down-spike seen in the pressure trace.
Blade 4, while beginning to recover, is still
separated. The separation blocks the passage between blades 1 and 4, producing a
region of high static pressure, corresponding to the up-spike.
Figure 3-14a compares the leading-edge separation with that found by Pullan et
al. and Figure 3-14b compares the resulting leading-edge vortex. The two flow fields
are in good agreement, further supporting the proposed mechanism.
58
(a) Leading-edge separation
(b) Roll-up of vorticity into vortex core
Figure 3-14: Pre-cursor formation mechanism in compressor computations agree
with that of Pullan et al.
To summarize, the compressor rotor-only computations capture the performance
of the compressor and the formation of the spike pre-cursor in the compressor environment. The shape of the pressure rise characteristic is in agreement with experiment,
as are the unsteady static pressure measurement at the rotor tip during stall. This
demonstrates that the computational methodology, including the limited domain of
four passages, is capable of characterizing the formation mechanism of spike-type stall
pre-cursors and that this methodology can be used to characterize spike pre-cursor
formation in the cascade. Furthermore, the formation mechanism is in agreement with
the hypothesis of Pullan et al. and provides further numerical evidence in support of
the hypothesis.
59
3.4 Summary
In this chapter, all the elements necessary to assess the leading-edge vortex shedding
hypothesis have been developed. The cascade design reproduces the incidence of the
blade tip in the compressor at stall. Furthermore, the use of twisted blades to produce
a range of incidences enables the investigation of pre-cursor formation at lower spans,
in accordance with the incidence driven mechanism of Pullan et al. A miniaturized
smoke generator has been developed to visualize the formation process and the cascade
is instrumented with fast-response pressure transducers and a hotwire anemometer
to capture the unsteady pressure and velocity field. 3D URANS calculations of both
the compressor and cascade are used to support the experiment. The computational
methodology is capable of capturing the spike pre-cursor formation in the compressor
computation, indicating its applicability for simulating pre-cursor formation in the
cascade.
60
Chapter 4
Experimental Assessment of
Formation Mechanism
In this chapter it is shown that the cascade captures the spike pre-cursor at the
blade tip. The pre-cursor topology and propagation rate in the cascade is in agreement with that of the compressor experiment. Spanwise traverses of the hotwire are
performed and demonstrate pre-cursor formation at lower spans, supporting the previously proposed incidence driven mechanism. To assess the feasibility of smoke flow
visualization, a study of the impact of Reynolds number on pre-cursor formation is
performed. The study found no changes in pre-cursor formation for Reynolds numbers between 90,000 (the same as that in the compressor experiment) and 30,000.
At a Reynolds number of 15,000, however, pre-cursor formation was observed only
at mid-span and not at the blade tip.
From this result, pre-cursor formation was
visualized at mid-span for a Reynolds number of 15,000 and a corresponding cascade computation was performed. The visualization is in good agreement with the
cascade computation and both indicate the pre-cursor formation mechanism in the
compressor and the cascade are identical.
61
4.1 Demonstration of Spike Pre-cursor in the Cascade Experiment
Given the change of reference frame, it is useful to first consider the expected behavior
of a spike pre-cursor in the cascade. In the pressure traces from the compressor experiment, an up-spike, associated with the blockage from the leading-edge separation,
leads the down-spike, associated with the low pressure region in the vortex core. In
the compressor experiment, pressure transducers are mounted on the casing and are
in the stationary frame. In this frame, the spike pre-cursor propagates in the direction
of rotor rotation, but at a rate less than rotor speed.
Thus in the rotating frame,
i.e. the blade relative frame, the spike pre-cursor propagates
opposite
the direction
of rotor rotation. A pressure transducer in the blade relative frame, as is the case for
the the cascade experiment, thus observes a down-spike followed by an up-spike. The
change in behavior is shown schematically in Figure 4-1
Compressor
Cascade
dp
dp
time
time
x
Ωr
Transducer
Absolute Frame
θ
Ωr − cs
cs
Transducer
Relative Frame
Figure 4-1: Spike pre-cursor behavior with change in reference frame: up-spike leads
down-spike in compressor, down-spike leads up-spike in cascade
Pressure traces from the cascade and compressor experiments are given in Figure
4-2.
The cascade is operated at a blade chord Reynolds number of 90,000, corre-
sponding to the same conditions as the single-stage compressor experiment.
The
characteristic sharp waveform of the spike pre-cursor is observed in the cascade pres-
62
sure traces, with the down-spike leading the up-spike as expected from the previous
discussion. The waveform propagates in the pitchwise direction at 37% of equivalent
rotor speed, corresponding to 63% of rotor speed when viewed in the absolute frame.
While this propagation rate is less than the 77% observed in the compressor experiment, it is within the range of observed spike pre-cursor propagation rates in the
literature.
420
30
63% Ω
360
25
Θ position (deg, Θ opp. rotor direction)
77% Ω
300
1
ρU 2
2 t
θ location
240
180
120
60
1
ρU t2
2
20
15
10
5
0
−60
−7
−6
−5
−4
−3
−2
−1
0
−2.8
0
Rotor revolutions
(a) Compressor experiment
−2.6
−2.4
−2.2
−2
Rotor revolutions
−1.8
−1.6
(b) Linear cascade experiment
Figure 4-2: Spike pre-cursor demonstrated in cascade experiment
The cascade experiment captured the spike pre-cursor at the blade tip, meeting
the first objective of this work. Another objective is to assess the incidence driven
mechanism.
The mechanism does not limit pre-cursor formation to the blade tip
and suggests that pre-cursor formation should be possible at any location where
the critical incidence is met. The cascade design incorporated twisted blades, with
increasing incidence at lower spans, specifically to assess this hypothesis.
Figure 4-3 presents the recorded velocities of a spanwise hotwire traverse at 10%
chord upstream of the leading-edge plane.
As only one hotwire was available, the
data at each spanwise location was recorded at different moments in time, but are
presented together on a single plot. Figure 4-3 is meant only to evaluate the formation
63
of pre-cursors at different spans and should not be viewed as coherent in time. Note
that the cascade operating point during the hotwire traverse resulted in a Reynolds
number of 30,000, as opposed to the Reynolds number of 90,000 in Figure 4-2b. The
role of Reynolds number on pre-cursor formation is discussed later in Section 4.2.
100
90
80
Ut
Spanwise Position
70
60
50
40
30
20
10
0
0
1
2
3
4
Rotor revolutions
5
6
7
8
Figure 4-3: Spike pre-cursor formation captured at lower spans. Data shown is for a
Reynolds number of 30,000 and is not coherent in time
The characteristic up-down waveform of the spike pre-cursor is observed at 90%
span, for example at
t = 6.2, as expected from the cascade pressure traces.
waveform can also be seen at 70% and 60% span at
The same
t = 3.0, indicating pre-cursor for-
mation at these spans. At even lower spans, such as 30%, large magnitude turbulence
is observed and no coherent structures are discernible. The incidence at this span is
sufficiently high to produce continuous separation and is more representative of of a
blade row in rotating stall. In fact, the velocity trace at 30% span is similar to those
recorded in a compressor in rotating stall (such as in [7]). The observed formation
of spike pre-cursors at lower span provides experimental evidence for the incidence
driven mechanism of Pullan et al. Furthermore, it is another example of pre-cursor
formation in the absence of the tip-leakage vortex.
64
4.2 Reynolds Number Effects on Pre-cursor Formation
Low-speed testing is common in the investigation of compressor stall, and specifically
spike-type stall inception.
The Reynolds numbers of these low speed experiments
are typically on the order of 100,000 and an order of magnitude below those seen
in gas turbine engines.
The impact of Reynolds number on pre-cursor formation,
however, has yet to be characterized. Pre-cursor formation at low Reynolds number
is of particular interest in this work as an objective is to visualize the formation with
smoke. Smoke visualization at high Reynolds number is challenging due to the rapid
diffusion of smoke and operating at lower Reynolds numbers is desirable to improve
visualization quality.
Pre-cursor formation in the cascade was demonstrated at a Reynolds number of
90,000, the same as that in the compressor.
is too high to perform smoke visualization.
Such a Reynolds number, however,
To characterize any changes from this
baseline condition, pressure and velocity measurements were taken at successively
lower Reynolds numbers, from 60,000 to 15,000 in increments of 15,000, and are
shown in Table 4.1.
The first column presents the casing pressure traces from the
same configuration used to produce Figure 4-2b. The second column presents results
produced from a configuration similar to that shown in Figure 3-6b. The hotwire was
placed at 85% span and located at the same pitchwise location as the downstream
Kulite in Figure 3-6b. The hotwire trace is used to assist in evaluating the pre-cursor
topology, as the signal to noise ratio of the Kulites degrades at low Reynolds numbers
(i.e. low free-stream velocities). The results shown in Table 4.1 are for representative
events at each of the Reynolds number and many such events were observed in each
data set.
65
Table 4.1: Reynolds number study: Pre-cursor topology and propagation rate
unchanged for Reynolds number range of 30,000 - 60,000. Pre-cursors not observed
near blade tip for 15,000 Reynolds number
Propagation (Pressure Perturbations)
60,000
Θ position (deg, Θ opp. rotor direction)
30
Topology (Velocity Perturbations)
65% Ω
25
Θ position (deg, Θ opp. rotor direction)
Reynolds #
1
2
2 ρUt
20
15
10
5
30
25
20
15
10
-5
-10
0
0
0
0.2
0.4
0.6
0.8
Rotor revolutions
1
Ut , 12 ρUt2
0.2
0.4
0.6
0.8
Rotor revolutions
1
1.2
0.4
0.6
0.8
Rotor revolutions
1
1.2
0.4
0.6
0.8
Rotor revolutions
1
1.2
1.2
30
25
Θ position (deg, Θ opp. rotor direction)
45,000
Θ position (deg, Θ opp. rotor direction)
60% Ω
1
2
2 ρUt
20
15
10
5
30
25
20
15
10
-5
-10
0
0
0
0.2
1
64% Ω
25
1
2
2 ρUt
20
15
10
5
30
25
20
15
0
0.2
0.4
0.6
0.8
Rotor revolutions
1
1.2
Continued on next page
66
Ut , 12 ρUt2
10
-5
-10
0
0
0.2
1.2
Θ position (deg, Θ opp. rotor direction)
30,000
Θ position (deg, Θ opp. rotor direction)
30
0.4
0.6
0.8
Rotor revolutions
Ut , 12 ρUt2
0.2
Reynolds #
Continued from previous page
Propagation (Pressure Perturbations)
Not shown due to poor
signal to noise ratio
15,000
Topology (Velocity Perturbations)
Θ position (deg, Θ opp. rotor direction)
Table 4.1:
30
25
20
15
Ut , 12 ρUt2
10
-5
-10
0
0.2
0.4
0.6
0.8
Rotor revolutions
1
1.2
Pre-cursor formation is observed for Reynolds numbers of 60,000, 45,000, and
30,000. The same characteristic waveform is found in the pressure and velocity traces
as in the baseline case. Furthermore, the propagation rates for the three cases are
within three percentage points of the baseline (63% rotor speed). These results suggest
that pre-cursor formation and topology is unchanged when the Reynolds number is
reduced from 90,000 to 30,000.
At a Reynolds number of 15,000, however, pre-
cursor formation was not observed throughout the 5,000 rotor revolutions of data
acquired. No activity is observed beyond a periodic oscillation in the hotwire signal
at approximately five times rotor frequency. It is believed this oscillation is associated
with unsteadiness of the tip-leakage flow and was masked in the results at higher
Reynolds number by frequent pre-cursor formation.
In the previous section it was demonstrated that pre-cursor formation occurred
at lower spans.
Given the absence of pre-cursor formation at the blade tip for a
Reynolds number of 15,000, it was of interest to assess whether this was also true at
lower spans. Figure 4-4 shows the results of a spanwise traverse at a Reynolds number
of 15,000. Pre-cursor formation can be observed at 50% span, such as at
t = 4.0.
t = 3.1
and
The oscillation discussed prior is observed at 90% span but not at 80% span,
providing evidence that it is due to unsteadiness in the tip-leakage flow.
67
100
90
80
Ut
Spanwise Position
70
60
50
40
30
20
10
0
0
1
2
3
4
Rotor revolutions
5
6
7
8
Figure 4-4: Spike pre-cursor formation at 50% span for 15,000 Reynolds number.
Data not coherent in time
Even at these low Reynolds numbers, airfoils of similar design and loading have
demonstrated transition of the suction surface boundary layer [25]. Furthermore, the
rotor blades used were built with a leading-edge radius to maximum thickness ratio
of only 0.098.
Such “sharp” leading-edges have been shown to promote transition
[26]. Given these two factors, it is likely that the suction surface boundary layer is
undergoing transition. Counter to the observed trend, however, turbulent boundary
layers generally grow
less
resistant to separation as the Reynolds number decreases
[27].
Movement of the transition location is one possible mechanism for this behavior.
The incidence at any span is set only by the cascade geometry and is not a function
of free-stream velocity (and hence Reynolds number). For a constant incidence, the
transition location moves further aft along the suction surface as the Reynolds number
decreases [27]. Thus as the Reynolds number decreases, the transition location at all
spans moves aft. For a given Reynolds number, however, the transition location moves
forward as incidence increases [27].
As the mid-span operates at an incidence
68
15◦
greater than the blade tip (from the blade twist), at any given Reynolds number the
mid-span transitions earlier than the blade tip. The absence of pre-cursor formation
at the tip suggests there may be a threshold transition location, beyond which precursor formation is affected. It is hypothesized that at even lower Reynolds numbers,
pre-cursor formation would be absent from the mid-span as well.
The discussion above suggests that the role of transition and transition location
are valuable topics for future work, especially as pre-cursor formation near the laminar
regime has yet to be characterized. While the Reynolds numbers of future small-core
compressors are estimated to be an order of magnitude larger than in the present
study [28], these compressors will likely experience later transition as well, further
motivating characterization of spike pre-cursor formation at low Reynolds number.
4.3 Visualization of Pre-cursor Formation
The Reynolds number study indicated that pre-cursor formation occurs at 50% span
for a Reynolds number of 15,000. Given the constraints of smoke flow visualization,
this Reynolds number and location was chosen for visualization. A cascade computation was first performed to characterize the pre-cursor formation mechanism. Figure
4-5 shows contours of non-dimensional radial vorticity at 50% span from the cascade
computation. In Figure 4-5a the leading-edge of blade 2 is separated and the vorticity
from the suction side boundary layer can be seen along the leading-edge plane between
blades 2 and 3. In Figure 4-5b, 1.2 blade passing periods later, the shed vorticity from
the leading-edge separation has propagated to the adjacent passage, between blades
3 and 4. The cascade computation shows the same pre-cursor formation mechanism
as in the compressor computations.
It should be noted that while the cascade experiment showed periods of precursor formation interspersed with periods of little activity, pre-cursor formation was
continuous in the computation.
in the computation, e.g.
This is attributed to the lack of non-uniformities
each blade is geometrically the same, the tip-clearance is
uniform, the inlet condition is uniform etc.
69
In the cascade experiment there are
ω̃r
1
2
3
4
(a) Leading-edge separation on blade 2, t∗ =
ω̃r
1
2
3
t
τ
=0
4
(b) Propagation of vorticity to adjacent passage, t∗ = 1.2
Figure 4-5: Cascade computation show same pre-cursor formation mechanism at
50% span as in compressor computations
inherent non-uniformities not present in the computation.
Prior to examining the flow visualization results, it is valuable to consider what is
to be expected to be seen. Vorticity convects with the fluid, i.e. vortex lines are fluid
lines. Smoke particles also convect with the fluid into which they are released. As the
smoke is injected directly into the suction surface boundary layer, it is expected that
the smoke particles will mark the bound vorticity. For example, consider the leadingedge separation of blade 3 shown in Figure 4-5a. The suction surface boundary layer is
separated and the bound vorticity can be seen within the passage, along the leadingedge plane. In the experiment, it is expected that the smoke trail would lift off from
the suction surface and become parallel to the leading-edge plane. The smoke would
then propagate along the leading-edge plane, as the shed vorticity does in Figure
4-5b.
Figures 4-7 to 4-10 show a series of direct comparisons of the flow visualization
and computation, each separated in time by 1.2 blade passing periods. At the top
of each comparison is a contour plot of non-dimensional radial vorticity at 50% span
70
from the cascade computation. Inset in the top left is a velocity trace for the location
marked on the contour plot with a cross. Directly below the contour plot is a frame
showing the smoke flow visualization.
To assist the reader, the suction surface at
mid-span is outlined with red lines. Smoke is injected at the leading-edge of blade
2.
The hotwire is located approximately 10% chord upstream of the leading-edge
plane in the adjacent passage (between blades 3 and 4) and the velocity measured
by the hotwire is inset in the top left of the frame. For reference, Figure 4-6 shows
the flow visualization before pre-cursor formation, at a time of little activity.
The
suction surface boundary layer of blade 2 is attached. All the smoke convects down
the passage between blades 2 and 3, with no smoke visible in the adjacent passage.
Ṽ
Ut
0
0.1
1
0.2
0.3
0.4
Rotor Revolutions
0.5
0.6
2
3
4
Suction side boundary
layer attached
Smoke
convects
down passage
1
2
3
4
Figure 4-6: Flow visualization prior to pre-cursor formation
71
Ṽ
Ut
t1
0
0.1
0.2
0.3
0.4
Rotor Revolutions
0.5
0.6
2
1
Ṽ
3
4
Ut
t1
0
0.1
1
0.2
0.3
0.4
Rotor Revolutions
0.5
0.6
2
Boundary layer
beginning to separate
1
3
Some smoke visible near
leading-edge of blade 3
2
Figure 4-7: Flow visualization at
4
3
t1 :
4
partial leading-edge separation at blade 2
72
Ṽ
Ut
0
0.1
0.2
0.3
0.5
0.6
2
1
Ṽ
0.4
Rotor Revolutions
3
4
Ut
0
0.1
0.2
0.3
0.4
Rotor Revolutions
0.5
0.6
2
1
3
4
Smoke seen connecting leading-edges and is
visible upstream of blade 3 leading-edge
Boundary layer
fully separated
1
2
Figure 4-8: Flow visualization at
3
t1 + 1.2τ :
73
4
blade 2 leading-edge fully separated
Ṽ
Ut
0
0.1
0.2
0.3
0.5
0.6
2
1
Ṽ
0.4
Rotor Revolutions
3
4
3
4
Ut
0
0.1
0.2
0.3
0.4
Rotor Revolutions
1
0.5
0.6
2
Smoke convects from within
passage to leading-edge of blade 3
due to backflow
Smoke from blade 2 separation
visible in adjacent passage
Boundary layer
beginning to reattach
1
2
Figure 4-9: Flow visualization at
3
t1 + 2.4τ :
propagation of shed vorticity to adjacent
passage
74
4
Ṽ
Ut
0
0.1
0.2
0.3
0.5
0.6
2
1
Ṽ
0.4
Rotor Revolutions
3
4
3
4
Ut
0
0.1
1
0.2
0.3
0.4
Rotor Revolutions
0.5
0.6
2
Some smoke visible
adjacent blade 4, but most
has dissipated
Boundary layer re-attached and
smoke follows suction surface
contour
1
2
Figure 4-10: Flow visualization at
3
t1 + 3.6τ :
75
4
blade 2 boundary layer re-attached
In the first comparison, Figure 4-7, the computation shows the flow over blade 2
has just begun to separate, with some shed vorticity visible at the leading edge of
blade 3.
Correspondingly in the experiment, the flow has begun to separate from
the suction surface and some smoke is visible at the blade 3 leading-edge. This time
corresponds to the peak velocity in both the velocity traces.
1.2 blade passing periods later, in Figure 4-8, the computation shows the leadingedge of blade 2 is fully separated, with the separation spanning the width of the
passage between blades 2 and 3.
At the same time, a smoke “plume” can be seen
connecting the leading-edges of blades 2 and 3. No smoke is visible along the suction
surface of blade 2, further indicating that the flow is fully separated. For both computation and experiment, the velocity is decreasing and at the mid-point between the
maximum and minimum values.
At the next time step in Figure 4-9, the computation shows the vorticity shed from
the leading-edge separation of blade 2 has propagated to the adjacent passage and
the flow over the suction surface of blade 3 has begun to separate. Correspondingly,
smoke from the previous separation of blade 2 is visible in the adjacent passage, albeit
more diffuse than before due to mixing.
The computation indicates some trailing-
edge backflow, seen as negative vorticity from the trailing-edge convecting upstream
into the passage. Backflow is also observed in the experiment visualization as a small
smoke tube connecting the mid-point of the blade 2 suction surface and the leadingedge of blade 3. Finally, the blade 2 suction side boundary layer begins to re-attach
in the computation. This is mirrored in the smoke flow visualization which can be
seen following the contour of the suction surface.
For both the computation and
experiment, the velocity is near its minimum.
In the final comparison, Figure 4-10, the computed vorticity shed from blade 2 has
propagated two passages to blade 4. Some smoke is visible in the passage adjacent
to blade 4, however, it is faint and has mostly dissipated.
The computation also
shows that the flow over blade 2 has recovered and the suction side boundary layer
is attached. The same is seen in the experiment, with the smoke injected at blade
two fully contained in the passage and following the suction surface contour. Both
76
velocity traces show recovery to the value prior to the event.
The flow visualization results are in good agreement with the cascade computations. The same mechanism of leading-edge separation and shedding of vorticity
was observed in the flow visualization and the computation, supporting the previously established hypothesis. Furthermore, the cascade experiment demonstrated the
feasibility of using smoke flow visualization in the study of stall pre-cursors.
The
ability of cascade experiments to capture spike pre-cursors also facilitates the use of
higher fidelity visualization techniques, such as particle image velocimetry, which is
challenging in a compressor environment and a potential area for future work.
77
4.4 Major Findings
The major findings of this chapter can be summarized as follows:
•
Rotor-only compressor computations successfully captured the formation of the
spike pre-cursor and are in agreement with the previously established leadingedge vortex shedding hypothesis.
•
A spike pre-cursor has been demonstrated for the first time in a non-rotating,
cascade experiment.
•
Pre-cursor formation was not observed at the baseline incidence for blade chord
Reynolds numbers below 30,000. Increasing incidence from the baseline value,
however, produced spike pre-cursors at a Reynolds number of 15,000.
It is
hypothesized that transition location plays a role in pre-cursor formation.
•
Spike pre-cursor formation has been demonstrated at 50% span. Cascade computations captured the spike pre-cursor formation and show the same incidence
driven, leading-edge vortex shedding mechanism as in the compressor.
•
The formation and topology of the spike pre-cursor has been visualized in the
cascade experiment. The visualizations are in good agreement with the cascade
computations, providing experimental evidence in support of the leading-edge
vortex shedding hypothesis.
78
Chapter 5
Transient Heat Transfer Effects on
Compressor Stability
5.1 Introduction
During a transient event, convective heat transfer occurs between the exposed surfaces
of the compressor and the main gas path. Differences in the characteristic time scales
of the main gas path temperature and component temperatures drive the transient
heat transfer.
The flow through the compressor can be considered quasi-steady as
the reduced frequency, based on the flow through time of the compressor and the
rotor acceleration time constant, is typically on the order of
10−3 .
The time scale
of the main gas path temperature is thus governed by rotor speed. The component
temperatures, however, lag behind the main gas path temperature due to thermal
inertia. Figure 5-1 illustrates the typical time scales for component and main gas path
temperatures. The discrepancy in time scales produces large temperature differences
between the components and the main gas path, relative to those for steady state
operation, which in turn drives the transient heat transfer.
Transient heat transfer impacts compressor stability in three different ways. First,
changing component temperatures result in thermal growth of the rotors and casing,
changing the tip clearances.
clearances.
Compressor stability is known to be sensitive to tip
Second, heat transfer from the main gas path changes the matching
79
1.2
Gas Path
Temperature
(Rotor Speed)
T − Ti
Tf − Ti
[−]
1
Blade
Temperature
0.8
Casing
Temperature
0.6
0.4
Platform
Temperature
0.2
0
0
1
2
3
4
5
6
7
8
9
10
Non-dimensional Time [-]
Figure 5-1: Unsteady component temperatures for typical acceleration transient.
Differing time scales of component and main gas path temperatures drive transient
heat transfer
between the different compressor stages and drive the transient operating line towards
the stability limit. Changes in stage matching can also result in a blade row stalling
at a lower overall pressure ratio than in steady state operation, further reducing stall
1
margin .
Finally, heat transfer between the blade surface and the gas path alters
the development of the blade boundary layer, changing the blade row total pressure
loss and deviation. Changes in blade row loss and deviation further impact the stage
matching. While the impact of the thermal growth of the components on compressor
stability has received much attention, the effects of heat transfer on the stage matching
are less well characterized. As stage matching is central to the investigation, a brief
summary of the topic is provided here.
Stages must be matched to ensure the inflow requirements of a stage are met by
the outflow of the upstream stage. This is challenging as small excursions of the inlet
corrected flow of a stage result in large excursions of the outlet corrected flow, as
indicated in Figure 5-2.
1 In
−P Rop
this thesis, stall margin is defined using the common industry definition: SM = P Rstall
P Rop
where P Rop is the pressure ratio at the operating point and P Rstall is the pressure ratio at the stall
line for fixed inlet corrected flow
80
(a) PR vs. inlet corrected flow
(b) PR vs. outlet corrected flow
Figure 5-2: Stage pressure ratio as functions of inlet and outlet corrected flow.
Stage outflow sensitive to excursions in inflow (reproduced from [29])
The multiplicative nature of multi-stage compressors exacerbates this effect. For
example, a small reduction in the compressor inlet corrected flow, and hence the inlet
corrected flow of the first stage, moves the operating point from point
c
in Figure 5-3.
a
to point
The reduction is multiplied through each stage and the resultant
change in inlet corrected flow is much greater for the rear stage and the rear stage
is brought close to stall. Specifically, each stage produces a greater density rise (and
hence total pressure rise) than for which the area reduction schedule was designed,
resulting in lower axial velocity and inlet corrected flow in the rear stages.This example
highlights the sensitive nature of stage matching and also demonstrates the potential
for compressor instability from stage matching effects.
If heat is transferred to the flow throughout a stage, the exit total temperature
of the stage rises relative to the adiabatic case.
The outlet corrected flow of the
stage rises, reducing the incidence, and therefore loading, of the downstream stage.
This can be augmented by the changes in loss and deviation due to the effect of heat
transfer on the blade boundary layer.
81
Figure 5-3: Demonstration of stage stacking behavior. Small excursions in front
stages bring rear stages close to stall (reproduced from [29])
5.2 Previous Work
Much of the literature has focused on investigating changing tip clearances and its
impact on compressor stability (e.g.
[30, 31]).
The literature on the impact of the
heat transfer to the main gas path is limited.
Maccallum and Grant [32] developed a boundary layer model to asses the effect
of heat transfer on blade deviation. Simulating the heat transfer in a high altitude
deceleration, the change in deviation was found to be approximately
1◦ .
The results
of the boundary layer code were incorporated into a mean line model to assess the
impact of heat addition on the stall line for a 12 stage compressor with an overall
pressure ratio of 5. Heat transfer was found to reduce the stall margin by 12.2 points,
as shown in Figure 5-4, with 60% attributed to deviation effects and 40% to stage
matching effects.
Crawford and Burwell [33] later attempted to experimentally assess the findings
of Maccallum and Grant.
Using experimental data from several “Bodie” transient
events, a rapid deceleration from takeoff power to idle followed by an immediate
re-acceleration, the heat flux was calculated from the unsteady compressor total temperature and the known steady state adiabatic efficiencies. While no statistically significant correlation of stall margin loss with heat flux could be derived, it was found
that the time-averaged heat flux was greater for transients in which the compressor
stalled.
82
Figure 5-4: Stall line reduction due to heat transfer as predicted by Maccallum and
Grant [32]. Note: “bulk heat transfer effects” refers to stage matching
More recently, the concept of compressor cooling in high Mach number aircraft
was investigated by Shah [34]. 2D cascade computations on recent blade geometries
indicated that cooling reduced both loss and deviation uniformly across the incidence
range, as shown in Figure 5-5.
and were as great as
3◦
Changes in deviation increased with Mach number
for large heat transfer rates at high subsonic conditions.
The reduction in loss was as great as 8% and well represented by constant area,
compressible channel flow.
From these computations, generic correlations for the effects of heat transfer on
blade loss and deviation were formulated. These correlations were implemented in a
mean line model for a single stage fan and an eight stage compressor of generic design
with a pressure ratio of 5. Heat extraction of 1% of inlet stagnation enthalpy flux
produced a 23% improvement in compressor pressure ratio and 12% improvement in
efficiency.
3D computations of NASA Rotor 35 with heat extraction indicated the
same levels of pressure ratio and efficiency improvement.
83
(a) Total pressure loss
(b) Deviation
Figure 5-5: Results of Shah indicate impact of heat extraction on loss and deviation
approximately uniform across incidence range (reproduced from [34])
5.3 Motivation and Objectives
A literature review indicates that there is both numerical and experimental evidence of
the adverse effects of transient heat transfer on compressor stability. Little capability
exists, however, to capture these effects from first principles and empirical models are
often used to predict the stall margin loss during the design process. The accuracy of
these estimates are often assessed late in the development program, typically through
experiment. A first principles based model could increase the accuracy of predicted
stall margin loss in the early design phase.
Furthermore, the mechanisms of the transient stall margin loss are not well characterized. The work of Maccallum and Grant indicates that boundary layer effects are
a significant driver of stall margin loss, however, the boundary layer model utilized
showed limited agreement with experiment [35]. Furthermore, the pressure ratio of
the compressor used by Maccallum and Grant is several times smaller than that of
recent compressors.
The impact of heat transfer on boundary layer development has since been characterized with higher fidelity computations by Shah [34]. Loss and deviation correlations
were formulated and implemented in a mean line model to assess the effect of heat
extraction. Only the effects on steady state performance were assessed, however, and
the impact of heat transfer on stability was not examined.
84
This work aims to rigorously assess the effects of transient heat transfer.
In
particular the objectives are to:
•
Quantify stall margin loss due to transient heat transfer using a first-principles
based approach
•
Quantify the relative contribution of stage matching and changes in blade loss
and deviation to the total stall margin loss
•
Characterize the mechanisms that drive stall margin loss from transient heat
transfer
•
Assess the sensitivity of stall margin loss to heat transfer magnitude and deviation effects
85
5.4 Technical Roadmap
Adiabatic Validation
Input
Parameter
Development
Stall Criterion
Development
Steady
Performance
Validation
Heat Transfer
Implementation
Reference
Mean Line
Model Data
Transient
Simulation
Development
Stall Margin
Loss Mechanism
Characterization
Diabatic
Transient
Simulation
Sensitivity
Studies
Transient
Performance
Validation
Loss & Deviation
Correlations
Engine System
Model Data
Figure 5-6: Technical roadmap for transient heat transfer investigation
The technical roadmap is shown in Figure 5-6. A recently developed mean line
model serves as the basis for this investigation. Model inputs such as loss, deviation,
and blockage models are derived for an advanced, high pressure ratio compressor
using data from a reference mean line developed by the sponsor.
The mean line
model is combined with a combustor model and a choked turbine is assumed to
enable the simulation of transient operation. The adiabatic steady state and transient
performance of the mean line model is validated with data from the reference mean
line and an engine system model. The mean line model is modified to implement the
effects of heat transfer and validated with analytical results.
Previously developed
loss and deviation correlations are implemented to capture the effect of heat transfer
on these quantities.
Diabatic, transient computations of the re-acceleration phase of a Bodie transient
event are performed using heat transfer data from the engine system model. Computations are performed both with and without the effect of heat transfer on deviation
and the contribution of these effects on stall margin loss is quantified.
The stage
matching for these results is examined to characterize the mechanisms that govern
the changes in matching. Finally, sensitivity studies of stall margin to heat transfer
magnitude and the deviation correlation sensitivity are performed.
86
Chapter 6
Development and Validation of a
Diabatic Mean Line Model
Loss, deviation, and blockage models are developed for a compressor of technical interest using data from a reference mean line model developed by the sponsor. The
modeling assumptions necessary for the simulation of transient operation are discussed and the calculation procedure outlined. Adiabatic steady state and transient
calculations are validated with data from the reference mean line model and an engine system model of the sponsor. The adiabatic model is modified to incorporate
heat transfer effects and previously developed loss and deviation correlations are
implemented.
The chapter ends with validation of the heat transfer capability in
preparation for the simulation of diabatic transient operation.
6.1 Object-Oriented Turbomachinery Analysis Code
(OTAC)
The mean line model used in this work is the Object-Oriented Turbomachinery Analysis Code (OTAC). OTAC is an extension of the larger Numerical Propulsion System
Simulation (NPSS) framework. For detailed information on NPSS and OTAC, the
reader is referred to [36, 37], and only a brief overview is provided here.
87
NPSS is a framework originally developed for the simulation of fluid systems, such
as a gas turbine engine.
It is object-oriented and NPSS models consist of a series
of objects, or “elements” in NPSS nomenclature, that are linked by fluid “stations”
which define the fluid state at a given location in the system. A gas turbine engine
is simulated by linking elements such as a compressor, combustor, and turbine. Each
element performs a series of calculations that relate the inlet fluid state to the outlet.
For example, a nozzle element calculates the pressure drop for a given area ratio. More
complex elements contain sub-elements that perform further tasks. For example, a
compressor element computes the total pressure and temperature at the outlet given a
pressure ratio, efficiency, and inlet corrected flow. Sub-elements within the compressor
element specify the relationship between these quantities in the form of compressor
maps.
The heart of the NPSS framework is the linear solver.
The solver operates on
the concept of “independents,” which are quantities the solver is permitted to vary,
and “dependents” which are constraints on the system, given in the form of an equation. Typical independents are compressor pressure ratio, rotor shaft speed, or fuel
flow. These are varied to satisfy the dependents describing continuity, conservation
of energy, and shaft power balance. There must be an equal number of independents
as dependents such that the solver can drive all the dependents, and the equations
they represent, to be satisfied within some tolerance. To solve the system, the solver
first forms a Jacobian matrix by perturbing each independent, evaluating the system
model, and determining the change in the error of each dependent. The solver then
uses Newton iterations to drive each dependent to be satisfied, calculating updates
to the Jacobian matrix when deemed necessary. The solver is another element within
the overall model and multiple solvers can exist within one model, as will be discussed
shortly.
Traditionally NPSS has been used for cycle analysis, performing only one-dimensional
calculations. It has been recently extended for the purpose of mean line and streamline calculations through the development of OTAC. OTAC simulates each blade row
as an element. Within the blade row are further sub-elements called blade segments
88
which represent a finite segment of the blade span. A single blade row element contains multiple blade segments if performing a streamline calculation, however, only
one is necessary for the purposes of a mean line calculation. As this study is limited to
mean line calculations, the streamline capabilities of OTAC are not discussed further.
The blade segment contains data on the blade geometry, namely the metal angle,
radius, and meridional area at blade row inlet and exit.
The blade row contains
other sub-elements which are used to predict loss, deviation, and blockage.
Fluid
conditions at the exit of the blade segment (total pressure and temperature, flow
angle, and Mach number) are cast as independents.
These independents are used
to satisfy the dependents describing continuity and conservation of rothalpy (the
Euler turbine equation), and ensure that the total pressure loss and exit relative flow
angle are consistent with the estimated loss and deviation from the respective models.
Figure 6-1 summarizes the structure of the blade row element of OTAC.
NPSS Model
BladeRow
Pt,in
Tt,in
Min
αin
Dependents:
Iin = Iout
Af low = Amodel
ωf low = ωmodel
δf low = δmodel
BladeRow
Solver
BladeSegment
rin , rout
κin , κout
Independents:
Pt,out
Tt,out
Mout
αout
ωmodel
δmodel
Amodel
Loss
Model
Deviation
Model
Blockage
Model
Figure 6-1:
BladeRow
89
element structure
Theoretically, the independents and dependents of every blade row could be solved
simultaneously by a single “top level” solver, however, in practice it is found that such a
large quantity of independents and dependents leads to numerical divergence. Instead,
each blade row contains a solver which is responsible only for the independents and
dependents of that particular blade row.
The model is then executed upstream to
downstream as seen in Figure 6-2. Each blade row is provided an inlet condition from
the upstream element. The blade row solver must reach a converged outlet condition
prior to the next blade row being executed.
NPSS Model
Top Level
Dependents
Inlet
IGV
Top Level
Independents
Top Level
Solver
Rotor 1
···
Stator 8
Outlet
Top Level Solver Execution Sequence
Figure 6-2: Compressor model execution sequence
As a result of the upstream to downstream execution sequence, if the compressor
operating point is specified in terms of an inlet condition, i.e. compressor inlet corrected flow and corrected speed, the top level solver executes the entire model only
once. The first blade row produces a converged outlet condition from the imposed
inlet condition, which in turn produces the inlet condition for the next blade row
etc. The compressor operating point, however, is typically dictated by the matching
of the compressor and a downstream component, such as a turbine or nozzle. The
matching condition specifies the compressor
exit
corrected flow, which is defined as a
top level dependent. The compressor inlet corrected flow is cast as a corresponding
independent. The top level solver varies the inlet corrected flow, executing the model
upstream to downstream for each step, until the matching condition dependent is
satisfied. Such a setup was used for performing a transient calculation with a choked
turbine, as will be discussed in Section 6.3.
90
6.2 Mean Line Model Input Parameters
The input parameters that govern the steady state compressor performance, as predicted by a mean line model, are as follows:
•
Blade row geometry consisting of metal angle, radius, and meridional area at
blade row inlet and outlet
•
Variable guide vane schedule
•
Blade row total pressure loss and deviation characteristics
•
Flow blockage
The blade row geometry and variable guide vane schedule of an eight stage, high
pressure ratio compressor was implemented. The reference mean line model produced
the total pressure and temperature, Mach number, and flow angle at the inlet and exit
of each blade row for several lines of constant corrected speed. From this data, blade
row quantities such as loss parameter
ω
and deviation
δ
were derived as a function of
incidence for each speed line. Representative loss and deviation “buckets” are shown
in Figure 6-3a and Figure 6-3b.
Two complications arose from the resultant loss and deviation buckets. First, the
buckets are functions of incidence at constant corrected speed. Loss and deviation
are typically defined as functions of incidence and relative Mach number as the Mach
number governs the effect of compressibility on these quantities.
The resulting set
of loss or deviation, incidence, and relative Mach number triplets, however, was too
sparse to extract the Mach number dependence. Therefore, loss and deviation were
instead cast as functions of incidence and corrected speed.
The second complication stems from the discrete nature of the data set.
Data
was provided only for a limited incidence range at each corrected speed, and for
a discrete set of speed lines.
The mean line model, however, must be capable of
operating at an arbitrary corrected speed and for a wide range of incidences.
interpolation scheme is necessary to permit such operation.
91
An
While NPSS supports
75.0% Nc
80.0% Nc
85.0% Nc
90.0% Nc
95.0% Nc
100.0% Nc
105.0% Nc
Design Point
Deviation [deg]
Loss Parameter [-]
75% Nc
80% Nc
85% Nc
90% Nc
95% Nc
100% Nc
105% Nc
Design Point
0.5
0.05
5
5
Incidence [deg]
Incidence [deg]
(a) Loss bucket
(b) Deviation bucket
Figure 6-3: Representative loss and deviation buckets derived from reference mean
line data
multi-dimensional interpolation through its implementation of look-up tables, testing
indicated this functionality was overly simplistic and not appropriate for this application. Instead, polynomial fitting of the data was used to provide a rigorous and well
behaved interpolation scheme. Both loss and deviation were specified as functions of
incidence and corrected speed using the polynomial form,
x = c1 + c2 i + c3 Nc + c4 iNc + c5 i2 Nc
where
i
is the blade incidence and
Nc
(6.1)
the corrected speed. The polynomial form has
three coefficients that are linear, as well as two coupled terms. Although cubic and
higher order terms could reduce fitting error in the vicinity of the data points, they
were not used due to oscillations in regions not well specified by the data. The term
c4
is used to allow for some surface curvature and the quadratic term,
c5 ,
is used as
both loss and deviation are known to have higher surface curvature with incidence.
92
Equation 6.1 can be written in matrix form,



x
1
 1 
  
 x2  1
  
  
 x3  = 1
  
 ..   ..
 .  .
  
xm
1
i1
Nc,1
i1 Nc,1
i2
Nc,2
i2 Nc,2
i3
Nc,3
i3 Nc,3
.
.
.
.
.
.
.
.
.
im Nc,m im Nc,m
 
c
  1



i22 Nc,2  c2 
 
 
i23 Nc,3  c3 
 
 
.
.
  c4 
.
 
i2m Nc,m
c5
i21 Nc,1
(6.2)
or more compactly,
x = Ac
Equation 6.2 cannot generally be solved as the system is over-specified when the
number of data points exceeds the number of coefficients (i.e.
m > 5).
To determine
the coefficients, a least squares solution was found via
c = (AT A)−1 AT x
Attempting to fit the data across all speed lines with a single polynomial surface
produced relative errors as high as 100% and was unacceptable for use in the mean
line model. Instead, separate coefficient sets were derived using the data for each pair
of adjacent speed lines. The coefficient set used in calculating loss or deviation then
becomes a function of corrected speed as well. For example, if the compressor was
operating at a corrected speed of 78%, the coefficient set derived using only the data
from the 75% and 80% speed lines would be used. The separate polynomial surfaces
were combined to produce a polynomial surface, an example of which is shown in
Figure 6-4, that spanned the entire corrected speed range while still capturing the
local curvature of the data.
With this method, maximum relative errors were of
order 1%, with a few occasional outliers of order 10%.
Section 6.4 shows that the
compressor performance is well captured with this level of error.
93
Loss [-]
0.02
0.75
0.8
0.85
2
0.9
0.95
1
Nc [-]
1.05
Incidence [deg]
1.1
Figure 6-4: Combined loss parameter polynomial surface
Blockage is defined as the ratio of the geometric area to the effective flow area
and is a number greater than unity. The blockage was computed at two inlet corrected flows, one near choke and one near stall, for each speed line. These operating
points are shown as black circles on the compressor map in Figure 6-5. Note that all
compressor maps in this thesis are presented with the inlet corrected flow and pressure ratio normalized to the values at the design point. The blade row blockage was
determined by matching the computed incidence to that specified by the reference
mean line model.
The blockage was assumed to be constant from leading-edge to
trailing-edge and only a function of inlet corrected flow and corrected speed. Linear
interpolation was used to define the blockage at intermediate inlet corrected flows
and speeds.
Figure 6-6 shows the blockage distribution through the compressor at
design speed. The large decrease in blockage at rotor 5 is attributed to a bleed at
that location.
Bleeds are located at the inlet of rotor 6, rotor 7, and stator 8 and
bleed a fixed percentage of the mass flow.
The bleed amount did not change with
compressor operating point and the bleeds were assumed to be ideal.
94
1.5
1
102.5
0.75
105
100
98.0
0.5
95.0
92.5
90.0
0.25
85.0
75.0
0
0.1
0.2
80.0
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
Design Normalized Corrected Flow [-]
Figure 6-5: Operating points for blockage calculation
Near Choke
Near Stall
Blockage [-]
Design Normalized Pressure Ratio [-]
1.25
0.01
R1
S1
R2
S2
R3
S3
R4
S4
R5
S5
R6
S6
R7
S7
Blade Row
Figure 6-6: Blockage distribution at design corrected speed
95
R8
S8
6.3 Simulation Setup of an Acceleration Transient
A rapid deceleration from full power to idle followed by an immediate re-acceleration
back to full power, or a so called “Bodie” transient, is a common stability test for
gas turbine engines. Compressor instability is typically encountered during the reacceleration portion of the transient as the compressor transient operating line moves
closer to the stall line.
During the re-acceleration phase, component temperatures
are higher than their steady state values at idle, as the engine was previously stable
at full power, and heat is transferred from the compressor components to the main
gas path. As the re-acceleration of the Bodie transient is amongst the most taxing
transient operations, it was the focus of this investigation.
During an engine transient, the only input to the system is a change in fuel flow,
which governs the total temperature rise in the combustor. The operating points of
the components, such as compressor pressure ratio, shaft rotational speed etc. are set
by the component matching conditions. Engine transients are regularly simulated in
NPSS cycle models. Given that OTAC operates in the NPSS framework, the mean
line model could serve as a drop-in replacement for the standard NPSS compressor
element. Doing so, however, would require specifying the component characteristics of
the high pressure turbine, the entire low pressure system, the fan etc. This is beyond
the scope of this investigation, although implementation of the mean line model within
an engine cycle model is a potential area for future work. Some assumptions were
made to simplify the problem and prevent the need to specify the entire engine system.
A schematic of the transient calculation procedure is given in Figure 6-7 and the
assumptions are discussed below.
The reduced frequency based on the flow through time of the compressor and the
acceleration time constant is about
10−3 .
The flow through the compressor can thus
be considered quasi-steady, eliminating the need for an unsteady solver. To simulate
the transient, the inputs to the system are advanced through time and the steady
solver used at each moment in time.
A transient fuel flow schedule was provided and the default NPSS combustor
96
Top Level
Solver
Dependent
ṁ
= c,4Adesign
4
Independent:
ṁ25 (t)
ṁc,4 (t)
A4
Mean Line Model (OTAC)
ESM Data:
Pt,25 (t)
Tt,25 (t)
IGV
R1
···
S8
ṁ3 (t)
Pt,3 (t)
Tt,3 (t)
Combustor
ṁ4 (t)
Pt,4 (t)
Tt,4 (t)
ESM Data:
ṁf uel (t)
ESM Data:
Nc (t)
Figure 6-7: Schematic of transient calculation showing use of engine system model
(ESM) data and choked HPT assumption
element was placed downstream of the mean line model to produce the proper total
temperature rise for a specified fuel flow.
the total pressure loss from heat addition.
The combustor element also calculates
It was assumed that the nozzle guide
vanes of the high pressure turbine (HPT) remained choked throughout the transient,
i.e. the corrected flow per unit area at the HPT inlet is constant in time. At high
power, the HPT typically
is
choked, but the nozzle guide vanes un-choke at low
power and the Mach number is set by the matching of the HPT, the low pressure
turbine, and the propelling nozzle. To capture the turbine un-choking would require
the characteristics of these three downstream components.
To maintain the choke
condition in the calculation, the compressor inlet corrected flow is specified as a top
level solver independent. A dependent is used to hold the HPT inlet corrected flow
per unit area constant through time.
The upstream-to-downstream execution sequence demands that the upstream
state and corrected speed be defined prior to model execution. As neither the low
pressure compressor nor the HPT are modeled, the inlet stagnation conditions and
corrected speed are imposed as functions of time using data from the engine system
model. Representative unsteady heat fluxes for each blade row were also derived from
the engine system model. The implementation of heat transfer effects is discussed in
Section 6.5, after validation of the adiabatic mean line model.
97
6.4 Adiabatic Validation of the Mean Line Model
Steady state calculations were performed and validated with a compressor map produced by the reference mean line model. Figure 6-8a compares the compressor map
from the mean line model (speed lines in green) with the reference compressor map
(speed lines in black). A more detailed view of the speed line at the design operating
point is provided in Figure 6-8b.
The map computed by the mean line model is in overall good agreement with
the reference compressor map. The model over-predicts the loss near the stall line,
producing an error in stalling corrected flow and pressure ratio of 0.7% at the design
speed. The error is greater at low speed, approximately 1.2% at 75% corrected speed.
The goal of the mean line model development, however, was not to precisely reproduce
the reference compressor map, but rather to produce performance representative of
compressors of interest. Given this, and the small magnitude of the error, the steady
state performance was considered acceptable.
To evaluate changes in the stall line with heat transfer, a blade row stall criterion
was implemented based on the Lieblein diffusion factor [38],
DF = 1 −
Vo Vθ,i − Vθ,o
+
Vi
2σVi
where the velocities are in the blade relative frame and
σ is the blade solidity.
(6.3)
The stall
point at fixed corrected speed is determined when the critical value of the diffusion
factor (from the reference mean line model) is exceeded by any blade row. The stall
line produced by this criterion is shown in Figure 6-9 and is in acceptable agreement
with the stall line from the reference mean line model. Only 5 points were used to
define the criterion so as not to over-fit the data, resulting in the minor discrepancies.
The final assessment of the adiabatic capabilities of the mean line model was a
transient calculation. The transient operating line from the mean line model, as well
as that from the engine system model, are shown in Figure 6-10. The nozzle guide
vane area, and hence flow capacity of the turbine, was sized such that the operating
point at idle was matched to the transient operating line from the engine system
98
Design Normalized Pressure Ratio [-]
1.5
Reference Data
Mean Line Model
1.25
1
105
0.75
102.5
100
98.0
0.5
95.0
92.5
90.0
0.25
85.0
75.0
0
0.2
80.0
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
Design Normalized Corrected Flow [-]
(a) Comparison of adiabatic compressor maps from mean line model and reference mean
line model
Design Normalized Pressure Ratio [-]
Reference Data
Mean Line Model
1.25
1
0.75
100
0.95
1
Design Normalized Corrected Flow [-]
1.05
(b) Comparison of design speed line with
reference mean line model data
Figure 6-8: Mean line model captures adiabatic compressor performance and agrees
with reference mean line model data
99
model. The model was then advanced through time as specified in Section 6.3. The
trends in the two operating lines agree, with a minor discrepancy in the shape and
final operating point. The discrepancies are consistent with the behavior of the HPT
un-choking, which is captured by the engine system model.
In summary, the mean line model captured the adiabatic performance of the
compressor. The steady-state performance is in agreement with the reference mean
line data, with errors of at most 1.2%.
The stall line computed based on a stall
criterion using the Lieblein diffusion factor is in good agreement with the stall line
from the reference mean line model.
Finally, the mean line model is capable of
simulating compressor transient operation and the resultant transient operating line
is in reasonable agreement with that from the engine system model.
100
1.5
Reference Stall Line
Stall Line from DF Criterion
Design Normalized Pressure Ratio [-]
1.25
1
105
0.75
102.5
100
98.0
0.5
95.0
92.5
90.0
0.25
85.0
75.0
0
0.1
0.2
80.0
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
Design Normalized Corrected Flow [-]
Figure 6-9: Stall line from diffusion factor stall criterion in agreement with reference
mean line data
1.5
Engine System Model
Mean Line Model
Design Normalized Pressure Ratio [-]
1.25
1
105
0.75
102.5
100
98.0
0.5
95.0
92.5
90.0
0.25
85.0
75.0
0
0.1
0.2
80.0
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
Design Normalized Corrected Flow [-]
Figure 6-10: Mean line model produces representative transient operating line, with
some discrepancy due to choking assumption
101
6.5 Implementation of Heat Transfer Effects
The mean line model was expanded to include the effects of heat transfer as OTAC’s
standard implementation assumes adiabatic conditions. Simulating heat transfer effects is achieved through modification of the
BladeRow
element and a schematic of
the modifications is given in Figure 6-11.
IGV
R1
S1
BladeRow
LE Heat Transfer
HeatXferDuct
Q̇LE = (1 − Cdq )Q̇net
BladeSegment
Loss
Model
Deviation
Model
TE Heat Transfer
HeatXferDuct
Blockage
Model
Q̇T E = Cdq Q̇net
Shah
Correlation
Heat
Flux Tables
Figure 6-11: Schematic of
BladeRow
element modifications for heat transfer
capability
In the modified
BladeRow
element, a newly developed heat transfer element
(HeatXferDuct) is placed upstream and downstream of the
BladeSegment sub-element.
Given a heat flux, the heat transfer element calculates the change in fluid state and
the details of the heat transfer element are discussed shortly. A control parameter
Cdq , ranging from zero to one, designates what percentage of the net heat flux is input
at the leading and trailing edges respectively. Note that for all calculations in this
work,
Cdq = 1 and all of the blade row heat input was at the trailing edge.
Previously
developed correlations by Shah [34] are used to calculate the changes in blade loss
and deviation based on the total blade row heat flux. These changes are fed into the
overall loss and deviation models. To assess the contribution of deviation effects, the
deviation correlation was neglected and the adiabatic deviation model was used.
102
The heat transfer element calculates the change in fluid state from inlet to outlet using a set of dependents and independents.
A constant area, constant radius,
swirling, compressible, and frictionless flow (Rayleigh flow) is assumed and the outlet
stagnation quantities, flow angle, and Mach number are cast as independents. Dependents are formed based on conservation of energy, continuity, and the axial and
tangential momentum equations. The set of dependents and independents is summarized in Table 6.1. These are solved in parallel with the independents and dependents
of the
BladeSegment
sub-element by the blade row solver.
Table 6.1: Heat transfer element independents and dependents
Independent
Dependent Equation
Tt,o
ṁo cp,o Tt,o = ṁi cp,i Tt,i + Q̇
Pt,o
po Ao + ṁo Vm,o = pi Ai + ṁo Vm,o
αo
ṁVθ,i ri = ṁVθ,o ro
Mo
ṁo = ṁi
As a test case, the heat transfer element was used to compute the Rayleigh line for
both subsonic and supersonic inlet conditions and the results are in good agreement
with the analytical result as shown in Figure 6-12.
6.5.1 Diabatic Loss and Deviation Correlations
The correlations for changes in loss and deviation are functions of the non-dimensional
heat flux, defined as
q∗ =
Q̇
ṁht,i
(6.4)
Two forms of the non-dimensional heat flux are used in this work.
q ∗ is formed with the
stagnation enthalpy flux at the inlet of the blade row, which changes throughout the
compressor with temperature rise, while
flux at the inlet of the compressor.
∗
qcomp
is formed with the stagnation enthalpy
Typical values of
q∗
achieved in the cascade
computations of Shah [34] were on the order of -0.001 (negative as heat was extracted),
103
2.2
1.8
T/Tti [−]
M=0.845
M=0.7
M=1.0
1.4
M=0.6
1
√ = 0.845
γ
M=0.5
1
M=0.4
0.6
0
0.4
0.8
1.2
1.6
2
2.4
∆s/R [−]
1.4
1.2
T/Tti [−]
M=1.0
1
M=1.2
0.8
M=1.4
M=1.6
0.6
M=1.8
0.4
0
0.2
0.4
0.6
0.8
1
1.2
1.4
∆s/R [−]
(a) Heat transfer element
(b) Analytical result (from [39])
Figure 6-12: Heat transfer element reproduces Rayleigh line
although values as high as -0.005 were investigated, and the values of
q∗
in this work
are of comparable magnitude.
Deviation varies linearly with non-dimensional heat flux and the sensitivity increases with relative Mach number. The implemented deviation correlation is given
below,
q∗
ζ
0.001
∆δ =
The value of
ζ


ζ = 0.1◦
for

ζ = 0.25◦
for
Mrel,i = 0.4
(6.5)
Mrel,i = 0.8
for an arbitrary relative Mach number is found using linear interpola-
tion.
For small values of
q∗,
the change in blade row total pressure loss due to heat
transfer is well represented by constant area, compressible channel flow i.e.,
2
γMrel,i
∆Pt,HX
≈−
q∗
Pt,i
2
104
|q ∗ | 1
(6.6)
Based on this, the change in blade loss parameter yields,
∆ω =
2
γMrel,i
−∆Pt,HX Pt,i
1
=
q∗
γ
γ−1
2
γ−1
Pt,i
Pt,i − pi
2
1 − (1 + 2 Mrel,i )
There are thus two ways to model the total pressure loss from heat addition: through
the computation of Rayleigh flow in the heat transfer element or by changing the
blade loss parameter. For all cases in this thesis, the total pressure loss is modeled
with the blade loss parameter and the total pressure held constant through the heat
transfer element.
6.6 Summary
To summarize, all the necessary tools for the investigation of transient heat transfer
effects on compressor stability have been developed.
A mean line model has been
developed and the adiabatic performance is in good agreement with data from the
reference mean line and engine system models. The effects of heat transfer have been
implemented in the mean line model and the diabatic results are in good agreement
with the analytical solution.
105
106
Chapter 7
Assessment of Diabatic Stall Margin
Loss
7.1 Quantifying the Impact of Deviation Effects
Following the procedure outlined in Section 6.3, diabatic transient calculations were
performed, both with and without the deviation correlation such that the effect of
stage rematching could be isolated. The resultant transient operating lines are shown
on the adiabatic compressor map in Figure 7-1. For reference, the net heat flux is
given as a function of time non-dimensionalized by the acceleration time constant (set
by the rotor inertia) in Figure 7-2.
Heat transfer increases the transient operating line excursion from the adiabatic
case. For a constant fuel flow, the matching of the compressor and turbine requires
the compressor exit corrected flow be fixed.
Heat addition at the compressor exit
raises the pressure ratio for all stages and reduces the mass flow to maintain the
required exit corrected flow, resulting in the excursion of the transient operating line.
To characterize the effect of heat transfer on stall margin requires finding the
stall line. For the diabatic transient, the stall line is a function of time, as well as
corrected speed, as the heat release in the compressor changes with time.
Speed
lines were found for discrete moments in time using the criterion developed in Section
6.4. This resulted in a sequence of corresponding compressor maps and related stall
107
points. The temporal evolution of the corrected speed lines and stall line throughout
the transient can be represented in a “composite” compressor map with each speed line
and stall point taken from the corresponding compressor map for a specific moment in
time. The composite compressor map is shown imposed on the adiabatic compressor
map in Figure 7-3, for both the cases with and without deviation effects. Adiabatic
quantities (speed lines, stall line, and transient operating line) are presented in blue
whereas diabatic quantities are in red.
The speed lines with heat transfer are shifted to lower corrected flows, as is expected from the re-matching of the compressor and the turbine, and have greater
curvature due to the additional loss from heat addition. More notable, however, is
the change in the stall line. Early on in the transient, between 78% and 93% corrected
speed, there is little change in the stall line. Between 93% and 100% corrected speed,
however, the stalling pressure ratio is reduced by as much as 7% for the same inlet
corrected flow (note that this corresponds to different corrected speeds between the
adiabatic and diabatic case). The cause of this reduction in stalling pressure ratio
will be discussed in a larger examination of the compressor re-matching in Section
7.2. The composite map produced without deviation effects (Figure 7-3b) shows the
same trends as that with deviation effects, but the change from the adiabatic case is
smaller with a maximum reduction in the stalling pressure ratio of 5%.
108
1.5
Adiabatic
Rematch Only
Deviation & Rematch
Design Normalized Pressure Ratio [-]
1.25
1
105
0.75
102.5
100
98.0
0.5
95.0
92.5
90.0
0.25
85.0
75.0
0
0.1
80.0
0.2
0.3
0.4
0.5
0.6
0.7
Design Normalized Corrected Flow [-]
0.8
0.9
1
1.1
1.2
Figure 7-1: Heat transfer increases excursion of transient operating lines
0.06
95%
0.05
90%
[−]
0.04
100%
1.05
1
Nc = 85%
0.02
0.95
Nc [-]
blades
X
∗
(t)
qcomp
0.03
0.01
0.9
0.85
80%
0.8
0
0.75
0
1
2
3
4
Non-dimensional Time [-]
-0.01
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Non-dimensional Time [-]
Figure 7-2: Net heat flux as a function of non-dimensional time. Maximum heat
addition at 95.3% corrected speed
109
1.5
Design Normalized Pressure Ratio [-]
1.25
1
0.75
100.6
99.5
97.9
98.7
t̃ = 3.2
96.9
0.5
95.3
92.8
89.3
0.25
90.7
t̃ = 2.1
87.0
78.4
81.9
84.7
t̃ = 0.0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.1
1.2
Design Normalized Corrected Flow [-]
(a) With deviation effects
1.5
Design Normalized Pressure Ratio [-]
1.25
1
0.75
100.6
99.5
97.9
98.7
t̃ = 3.2
96.9
0.5
95.3
92.8
89.3
0.25
90.7
t̃ = 2.1
87.0
78.4
81.9
84.7
t̃ = 0.0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Design Normalized Corrected Flow [-]
(b) Stage matching effects only
Figure 7-3: Composite compressor maps for diabatic transient. 9.9 point reduction
in stall margin between 93% and 100% corrected speed
110
The stall margin for the adiabatic and diabatic cases was computed from the
composite compressor maps and is shown in Figure 7-4. A total stall margin loss of
9.9 points was found for the diabatic case with deviation effects. 2.5 points of the total
stall margin loss is due to deviation effects, with the remaining 7.4 points from the
effects of stage rematching. Of note is that the stall margin is essentially unchanged
from the adiabatic value for corrected speeds between 78% and 90%. This is similar
to the trend observed in the stalling pressure ratio in Figure 7-3 and is consistent with
the evolution of the heat transfer in Figure 7-2.
In the 90%-100% corrected speed
range, the non-dimensional heat flux is at its maximum, with heat flux doubling from
85% to 90% corrected speed alone. Furthermore, the relative Mach numbers of the
rotors increase with corrected speed, resulting in increased loss and deviation and a
greater impact of heat transfer at higher corrected speeds.
Stall Margin Points [-]
Adiabatic
Rematch Only
Deviation & Rematch
7.4
2.5
5
0.75
0.8
0.85
0.9
0.95
1
Nc [-]
Figure 7-4: Stall margin as a function of corrected speed for adiabatic and diabatic
calculations. Heat transfer results in a stall margin loss of 9.9 points
111
The predicted 9.9 point reduction in stall margin is comparable to the 12.2 point
reduction predicted by Maccallum and Grant [32].
Only 25% of the predicted re-
duction, however, is due to deviation effects as compared to the 60% predicted by
Maccallum and Grant. This discrepancy is attributed to the large differences in compressor architecture and performance between the current study and the literature.
Maccallum and Grant utilized a twelve stage compressor with a total pressure ratio
of five. The compressor of this study is only eight stages and has an overall pressure
ratio several times greater than that of Maccallum and Grant.
The importance of
stage matching increases with rising overall pressure ratios and falling stage count
and consequently the effect of stage re-matching from heat transfer is greater in this
study than in that of Maccallum and Grant.
7.2 Heat Transfer Effects on Stage Rematching
In this section, the rematching of the compressor is examined to identify the cause
of the reduction in stalling pressure ratio. It is useful to first determine which blade
rows limit the operating range of the compressor. Figure 7-5 presents the percentage
of the computed stall points that originated in each blade row (the results are the
same for the diabatic cases with and without deviation effects).
Four blade rows,
stator 2, rotor 5, stator 6, and rotor 8, limit the compressor operating range, with
the limiting blade row changing with corrected speed. With heat transfer, however,
the percentage of stalling events in stator 2 more than doubles and the rear blade
rows (stator 6 and rotor 8) stall less frequently. This suggests that the heat transfer
rematches the compressor such that the loading of the front blade rows increases and
the loading of the rear blade rows decreases.
This is supported in Figure 7-6 which presents the diffusion factor for these four
blade rows at the stall point (adiabatic results are presented with solid lines and the
diabatic results with dashed lines).
Throughout the transient, the diffusion factor
of stator 2 is increased with heat transfer, but the increase grows rapidly between
93% and 100% corrected speed, corresponding to when the net heat flux is near its
112
maximum.
The loading of stator 6 and rotor 8 is reduced and the diffusion factor
decreases. The increase in stalling events in stator 2 can be seen between 92.5% and
97.5% corrected speed. In this range, the diffusion factor of stator 2 is greater than
that of stator 6 for the diabatic case, whereas the opposite occurs in the adiabatic
case, and stator 2 reaches the diffusion factor limit.
The change in loading is shown in greater detail in 7-7, which shows the loss
buckets at the stall point at 95.3% corrected speed (at which heat flux is at its
maximum).
The loading of the front four stages increase from the adiabatic case,
whereas the loading decreases for the rear four stages.
incidence is approximately
3◦
The maximum change in
for both the front and rear stages (seen in rotor 1 and
stator 8). The relative change in incidence, however, is greater for the front stages
than the rear stages with the average design incidence range for the front and rear
stages being
2.8◦
and
9.7◦
respectively.
113
1
Adiabatic
Diabatic
0.9
Percentage of Stall Events [-]
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
R1
S1
R2
S2
R3
S3
R4
S4
R5
S5
Blade Row
R6
S6
R7
S7
R8
S8
Figure 7-5: Percentage of stalling events per blade row. Heat transfer increases stall
frequency in front blade rows
Diffusion Factor [-]
Stall Limit
0.02
S2
0.8
0.85
R5
0.9
S6
R8
0.95
1
Nc [-]
Figure 7-6: Diffusion factors at stall point for select blade rows. Heat transfer
increases loading for front blade rows and reduces loading for rear blade rows.
Adiabatic results given in solid lines and diabatic in dashed lines
114
S1
R2
S2
Adiabatic
Stall
Diabatic
Stall
0.1
Loss Parameter [-]
R1
Adiabatic
Choke
5
Incidence [deg]
R3
S3
R4
S4
R5
S5
R6
S6
R7
S7
R8
S8
Figure 7-7: Loss buckets showing compressor matching at stall for 95.3% corrected
speed. Incidence increases in front stages and decreases in rear stages with
◦
maximum change in incidence of 3
115
In order to characterize the mechanism for the increased loading of the front stages,
it is useful to first assess the impact of heat transfer at different axial locations. The
compressor is split into three blocks, as defined in Table 7.1. Three calculations are
rd
performed in which the heat flux within each block is 1/3
of the total heat flux and
is uniform across all blade rows. Heat transfer is only present in one of the blocks for
each calculation such that the effects of heat transfer on each block can be isolated.
Table 7.1: Compressor block definition
Block Name
Blade Rows Within Block
Front
IGV - S3
Middle
R4 - S6
Rear
R7 - S8
Figure 7-8 show the axial Mach numbers for each heat flux distribution with the
compressor exit corrected flow held constant. As the exit corrected flow remains fixed,
the Mach number reduces in the blade rows upstream of the heat addition in order
to pass the required physical mass flow. In other words, the heat addition at each
block back-pressures the blade rows upstream.
The blocks are de-coupled to some
extent as the effects of the heat addition are only felt by the blocks upstream, with
the downstream blocks unaffected by the heat addition.
For the case with heat addition throughout the entire compressor, the effect is
greatest on the front stages as they are upstream of the largest portion of the heat
addition. The greater decrease in Mach number in the front stages changes the loading
distribution, with the front stages operating more highly loaded relative to the rear
stages than in the adiabatic case. Stable operation becomes limited by stator 2 rather
than stator 6 and the compressor stalls at a lower pressure. Increases in deviation
exacerbate this effect by reducing the turning, and thus pressure rise of the stage.
Reduced pressure rise through the compressor requires a further decrease in mass
flow, and thus Mach number, to produce the required exit corrected flow.
116
Figure 7-8: Impact of heat transfer at different axial locations. Heat addition
back-pressures upstream blade rows
Axial Mach [-]
Front Block
Adiabatic
0.02
IGV
R1
S1
R2
S2
R3
S3
R4
S4
R5
S5
R6
S6
R7
S7
R8
S8
Blade Row
(a) Heat transfer in front block only
Axial Mach [-]
Adiabatic
Middle Block
0.02
IGV
R1
S1
R2
S2
R3
S3
R4
S4
R5
S5
R6
Blade Row
(b) Heat transfer in middle block only
117
S6
R7
S7
R8
S8
Axial Mach [-]
Adiabatic
Rear Block
0.02
IGV
R1
S1
R2
S2
R3
S3
R4
S4
R5
S5
R6
Blade Row
(c) Heat transfer in rear block only
118
S6
R7
S7
R8
S8
7.3 Quantifying Stall Margin Loss Sensitivity to Model
Inputs
Transient heat transfer has been shown to produce up to 10 points of stall margin
loss, with a quarter of that loss attributed to deviation effects.
Estimates of heat
transfer and deviation data, however, often have significant uncertainties, especially
in the early design phase.
It is therefore useful to characterize the sensitivities of
stall margin loss to heat flux magnitude and the deviation correlation such that the
applicability of these findings can be estimated for other data sets.
To assess the sensitivity of stall margin loss to the deviation correlation, two calculations were performed with modified values of the deviation correlation sensitivity
ζ
in Equation 6.5. Specifically,
ζ
was multiplied by factors of 0.5 and 1.5, and the
linear interpolation in relative Mach was re-computed. The results with modified
ζ
exhibit the same trends in the stall line and transient operating line as seen in Figure
7-3a.
As shown in Figure 7-9, stall margin loss is proportional to
ζ
for corrected speeds
above 90%, where heat transfer is predominant. To characterize the sensitivity of stall
margin loss with
ζ,
a sensitivity coefficient
Sζ
is defined as the ratio of the additional
stall margin loss from deviation effects to that for the baseline value of
Sζ =
The values of
Sζ
SM − SMrematch
SMbaseline − SMrematch
ζ,
(7.1)
for the two computations, shown in Figure 7-10, are approximately
equal to the multiplicative factors of
ζ,
indicating that dependence of stall margin
loss to the deviation correlation sensitivity
ζ
119
is approximately linear.
Stall Margin Points [-]
Adiabatic
Rematch Only
0.5 ·ζ
1.0 ·ζ (Baseline)
1.5 ·ζ
ζ
5
0.75
0.8
0.85
0.9
0.95
1
Nc [-]
Figure 7-9: Stall margin as a function of corrected speed for modified values of
stall margin loss is proportional to
ζ.
ζ
1.8
Sensitivity Coefficient Sζ [−]
1.6
1.4
1.5⋅ζ
1.2
1
0.8
0.5⋅ζ
0.6
0.4
0.2
0.92
0.93
0.94
0.95
0.96
0.97
0.98
Nc [−]
Figure 7-10: Sensitivity coefficient
Sζ
for deviation correlation. Stall margin loss is
approximately linear with
120
ζ
A similar procedure was performed with respect to the heat flux magnitude. The
unsteady heat flow rate
Q̇(t)
of each blade was modified by a factor of 0.75 and 1.25.
This is equivalent to modifying the net non-dimensional heat flux,
∗
qcomp,net
(t) =
X
∗
qcomp
(t)
blades
by the same factors. The calculations again exhibit the same trends in stall line and
transient operating line as seen in Figure 7-3a.
Stall margin loss is also proportional to
second sensitivity coefficient
Sq∗
∗
,
qcomp,net
∗
qcomp,net
,
Sq∗ =
The value of
Sq ∗
A
is defined as the ratio of the total stall margin loss
(including deviation effects) for the modified values of
value of
as shown in Figure 7-11.
∗
qcomp,net
to that for the baseline
SM − SMadiabatic
SMbaseline − SMadiabatic
(7.2)
for the two computations is again approximately equal to the multi-
plicative factors, as seen in Figure 7-12, indicating stall margin loss is approximately
linear with
∗
qcomp,net
The apparent linearity of stall margin loss with these quantities is consistent with
the stage rematching observed in Section 7.2. The maximum change in incidence was
on the order of
3◦ .
The non-linearity of the loss bucket plays a small role for a change
in incidence of this magnitude and a linear approximation about the adiabatic point
results in a maximum error of only 9%. Furthermore, the values of
compared to unity, with the maximum value of
q∗
were small as
on the order of 0.004. It is thought
that the impact on stall margin loss becomes non-linear for
121
q∗
q∗
amplitudes near unity.
Stall Margin Points [−]
Adiabatic
∗
0.75 · q comp,net
∗
1.00 · q comp,net
(Baseline)
∗
1.25 · q comp,net
∗
q comp,net
5
0.75
0.8
0.85
0.9
0.95
1
Nc [−]
Figure 7-11: Stall margin loss as a function of corrected speed for modified values of
∗
∗
heat flux (qcomp,net ). Stall margin loss is proportional to qcomp,net
2
1.8
Sensitivity Coefficient Sq* [−]
1.6
∗
1.25 · q comp,net
1.4
1.2
1
0.8
0.6
∗
0.75 · q comp,net
0.4
0.2
0
0.92
0.93
0.94
0.95
0.96
0.97
Nc [−]
Figure 7-12: Sensitivity coefficient
Sq ∗
for heat flow. Stall margin loss is
∗
qcomp,net
approximately linear with
122
0.98
7.4 Limitations and Expansion of Current Capability
The current modeling of compressors in the NPSS cycle model (with the default
Compressor
element) includes limited capability to model transient heat transfer.
The user provides NPSS the total thermal mass, an average surface area, specific
heat, and an estimated convective heat transfer coefficient. In a transient calculation,
the NPSS solver calculates the convective heat transfer from a weighted average of
the compressor inlet and outlet stagnation temperature, and models the change in
material temperature with a first order lag equation.
The NPSS solver adds the
calculated total heat flux to the flow at the compressor exit.
The heat transfer
does not change the compressor component characteristics and the effects of stage
rematching and deviation are not modeled. The heat transfer simply acts to change
the compressor exit corrected flow (through the change in total temperature), which
in turn changes the overall matching with the downstream components.
To assess the new capability provided by the diabatic mean line model, a calculation representative of the current NPSS capability was performed. The net compressor
heat flux was added to the flow at the exit of stator 8 and all the remaining blade
rows were adiabatic. The stage matching and deviation throughout the compressor
were unchanged from the adiabatic case, with only the exit corrected flow changing
due to the heat addition. The transient operating line and stall line produced with
both the current and new capability are shown in Figure 7-13. The heat release at
stator 8 back-pressures the compressor, but as the stage matching is unchanged and
the heat release is small (2.5% of that in the combustor), the change in the compressor
pressure ratio is at most 0.5% for the same corrected speed (compared to 2.5% with
the diabatic mean line model). More importantly, the stall line produced with the
current capability is unchanged from the adiabatic case. As shown in Figure 7-14, the
current NPSS capability captures a stall margin loss of only 0.7 points relative to the
9.9 points of the diabatic mean line model, emphasizing the importance of capturing
the effects of stage rematching and deviation.
123
1.5
Adiabatic
Current NPSS Capability
New Capability
Design Normalized Pressure Ratio [-]
1.25
1
105
0.75
102.5
100
98.0
0.5
95.0
92.5
90.0
0.25
85.0
75.0
0
0.1
0.2
80.0
0.3
0.4
0.5
0.6
0.7
Design Normalized Corrected Flow [-]
0.8
0.9
1
1.1
1.2
Figure 7-13: Transient operating lines from diabatic mean line model and current
NPSS capability
Adiabatic
Current NPSS Capability
New Capability
Stall Margin Points [-]
0.7
9.9
5
0.75
0.8
0.85
0.9
0.95
Nc [-]
Figure 7-14: Stall margin from diabatic mean line model and current NPSS
capability. Current capability understimates stall margin loss
124
1
Given the difficulty in modeling heat transfer within the compressor, the heat
flux may only be known on a stage-by-stage or block-by-block basis rather than for
each individual blade row.
It is therefore useful to characterize the sensitivity of
stall margin loss to the distribution of heat flux. A calculation of the limiting case
is performed, where only the net heat flux for the entire compressor is known. The
net heat flux at any moment in time was divided uniformly amongst all the blade
rows. For reference, the time averaged heat flux distribution is shown in Figure 7-15.
Even with this simplification, the mean line model captured 8.0 points of stall margin
loss, as shown in Figure 7-16, relative to the 9.9 points for the blade row specific
distribution. This suggests a reasonable first approximation of the stall margin loss
can be made with even a single, bulk value of the heat flux.
0.0018
0.0016
0.0014
q ∗ (t)dt
0.0012
0.0008
tend
1
Z
0
tend
0.001
0.0006
0.0004
0.0002
0
R1
S1
R2
S2
R3
S3
R4
S4
R5
S5
R6
S6
R7
S7
Blade Row
Figure 7-15: Time averaged heat flux distribution
125
R8
S8
Stall Margin Points [-]
Adiabatic
Uniform Heat Flux
Blade Row Specific Heat Flux
8.0
9.9
5
0.75
0.8
0.85
0.9
0.95
1
Nc [-]
Figure 7-16: Uniform heat flow distribution captures 80% of stall margin loss
7.5 Major Findings
In this chapter, the diabatic mean line model was used to evaluate the effect of heat
transfer on stall margin during the re-acceleration phase of a Bodie transient event.
Heat transfer was found to reduce the pressure ratio at stall by as much as 7% and
resulted in a total stall margin loss of 9.9 points. Of the 9.9 points, 7.4 points were
due to stage rematching effects, with the remaining 2.4 points from the effects of heat
transfer on deviation.
An analysis of the stage rematching revealed that the heat
transfer increases the loading in the front blade rows and reduces the loading in the
rear blade rows. This suggests the effect of transient heat transfer may be greater
for compressor with highly loaded front stages. Sensitivity studies indicate that the
dependence of stall margin loss to heat flux magnitude and the deviation correlation
sensitivity
ζ
is approximately linear, though it is thought the dependence becomes
non-linear as the magnitude of
q ∗ approaches unity.
Calculations representative of the
current NPSS modeling capability for transient heat transfer effect indicate that only
0.7 points of the total 9.9 stall margin point loss is captured by the current capability,
126
underscoring the importance of capturing stage rematching and deviation effects.
Assuming uniform heat flux for each blade row, the stall margin was reduced by 8.0
points, relative to 9.9 points using a distributed heat flux input. This suggests that
detailed knowledge of the heat flux distribution is not needed to capture a majority of
the stall margin loss and that a first approximation of stall margin loss can be made
knowing only the net heat flux magnitude.
127
128
Chapter 8
Conclusions
This thesis investigated two current problems in the field of compressor stability:
the development of spike-type rotating stall pre-cursors and the effects of heat transfer during compressor transient operation.
A summary of the major findings and
recommendations for future work for each of the two investigations is provided here.
8.1 Spike-type Rotating Stall Inception
The first investigation of this thesis focused on the experimental assessment of a
previously proposed mechanism that attributes pre-cursor formation to an incidence
driven leading-edge separation and consequent vortex shedding.
Spike pre-cursor
formation and propagation was demonstrated in a non-rotating, linear cascade experiment, for the first time in the published literature. The cascade was designed to
enable large changes in incidence throughout the span to assess whether pre-cursor
formation could occur away from the tip region. Pre-cursor formation was observed
at mid-span, providing experimental evidence in support of the previously proposed
mechanism.
To support the experimental program, 3D, unsteady cascade computations were
performed and captured the formation of the pre-cursor at mid-span. The cascade
computations attributed pre-cursor formation in the cascade to the same same mechanism of leading-edge separation and vortex shedding as was proposed in the litera-
129
ture [13]. The formation and propagation of spike pre-cursors was visualized in the
cascade experiment and the visualizations are in good agreement with the cascade
computations, and the computations in [13], providing further experimental evidence
in support of the mechanism. The cascade experiments indicated a Reynolds number
effect on pre-cursor formation, with formation suppressed at the blade tip but not at
the mid-span for low Reynolds number. As a result of the cascade design, transition
of the suction surface boundary layer occurs at different chordwise locations along
the span. Movement of the transition location with decreasing Reynolds number has
been proposed as a mechanism for the changes in pre-cursor formation, however, this
hypothesis has not been assessed.
8.1.1 Recommendations for Future Work
It is recommended that the role of transition location on pre-cursor formation be
investigated and the hypothesis assessed. While the investigation of Reynolds number
effects in this thesis was quantitative, these effects have not been characterized in
detail. An assessment of the hypothesis should thus also be part of a larger effort to
characterize pre-cursor formation at low Reynolds number and is of interest in the
development of the next generation of small core compressors.
It is also recommended that pre-cursor formation be investigated using higher
fidelity methods of flow characterization.
The use of smoke flow visualization in
this work limited the investigation to low Reynolds number. The demonstration of
pre-cursor formation in a cascade experiment enables the use of much higher fidelity
methods. The use of methods such as PIV are challenging in rotating machinery with
limited optical access. Cascade experiments present neither of these challenges and
offer greater potential for higher fidelity flow characterization.
This work, and much of the work in the literature, has focused on the mechanism
of pre-cursor formation.
Less is known, however, on the mechanisms of pre-cursor
propagation and growth into rotating stall and the characterization of these mechanisms is a useful area for future work. Possible mechanisms that effect the propagation
of spike pre-cursors are vortex line stretching, viscous diffusion of vorticity, and the
130
shedding of vorticity from adjacent blades. It is recommended that the magnitude
of these effects be quantified. It is also suggested that a simplified vortex model be
investigated as a means to capture these effects and to predict pre-cursor propagation
rate.
8.2 Transient Heat Transfer Effects
The second investigation of this thesis focused on the characterization of stall margin
loss from heat transfer during transient operation.
The limited literature on this
topic suggests that transient heat transfer may produce as much as 12 points of stall
margin loss. The capability to predict these effects, however, is limited primarily to
empirical models, motivating a first-principles based investigation.
In this work, a mean line model of an advanced, high-pressure ratio compressor
was extended to include the effects of heat transfer and the re-acceleration phase of
a “Bodie” transient event was simulated.
A total of 9.9 points of stall margin loss
were attributed to the effects of transient heat transfer, comparable to that found in
literature. The diabatic mean line model offers significantly improved capability over
the current NPSS models, the latter only capturing 0.7 points of stall margin loss. 7.4
points of the total stall margin loss are attributed to the effects of stage rematching,
with the remaining 2.5 points from the effects of heat transfer on blade row deviation.
An examination of the stage matching indicated that heat addition acts to increase
the loading of the front stages and front stage stall limited the overall stalling pressure
ratio. This suggests that effect of transient heat transfer may be greater for compressor designs with highly loaded front stages. Studies of heat addition at different axial
locations and fixed exit corrected flow indicate that heat addition acts to decrease
the axial Mach number in upstream blade rows, as predicted by one-dimensional gas
dynamics.
The sensitivity of stall margin loss to heat transfer magnitude and the deviation
correlation sensitivity was assessed and the dependence of stall margin loss on these
quantities was approximately linear, though it is expected that this dependence be-
131
comes non-linear as the value of
q∗
approaches unity. A stall margin loss of 8.0 points
was predicted by a computation in which the net heat flux was maintained but the
heat transfer was axially uniform. This suggests that a reasonable first approximation
of stall margin loss can be made with only knowledge of the bulk heat transfer for
the entire compressor.
8.2.1 Recommendations for Future Work
A major limitation of this investigation was the assumption of a choked HPT and the
use of an imposed inlet stagnation state and corrected speed. To accurately capture
the coupling of these quantities with the changing operating point of the high pressure
compressor requires the modeling of the entire engine system, which was beyond the
scope of this investigation. The first recommendation is thus that the diabatic mean
line model be implemented within a full engine simulation. The use of OTAC as the
mean line model reduces the complications of such a task as it operates within the
pre-existing and widely used NPSS framework. Transient engine operation is often
simulated using NPSS and the diabatic model could serve as a drop-in replacement for
the standard NPSS compressor model (guidelines for this are provided in Appendix
A).
This would enable the effects of the rotor dynamics, the coupling of the high
pressure compressor and low pressure compressor, and the un-choking of the turbine
to be represented. The coupling of the mean line model to a transient heat transfer
model, either within a larger engine simulation or independently, is also of interest as
this would capture the unsteady heat transfer dynamics.
This work utilized detailed heat transfer data in the prediction of stall margin loss,
but such data might not be readily available. It is therefore of interest to determine
what specificity of heat transfer data is required to adequately capture the stall margin
loss and how blade rows or stages may be combined for the purposes of heat transfer
modeling. The diabatic mean line model offers a tool for such an examination.
It was found that heat transfer acts to increase the loading in front stages and that
front stage stall limited stable operation. The first few stages of gas turbine engines
typically are equipped with variable guide vanes in order to aid in the compressor
132
matching at low power. The variable guide vanes offer a means to reduce the effects
of transient heat transfer through modifications of the transient vane schedule. The
diabatic mean line model offers a platform for the development of such schedules. The
use of variable bleed schedules could also be investigated, if such bleeds are available.
133
134
Appendix A
Guidelines for OTAC Implementation
and Usage
Several suggestions and guidelines for implementing OTAC in the NPSS framework
are given:
•
The top level solver can cause blade row solvers to diverge while solving the
linear system.
For example, the inlet corrected flow was cast as an indepen-
dent in the transient simulations.
To determine the Jacobian, the top level
solver perturbs the system by increasing the inlet corrected flow, executing the
model, and calculating the change in error quantities.
The perturbations in
inlet corrected flow can result in blade rows choking and the divergence of one
or more blade row solvers.
Constraints should be placed on the magnitude
of perturbations and updates from Newton iterations.
with the
perturbation and dxLimit quantities in the Independent object (for
reference, these were set to
•
This can be achieved
10−4
and
10−3
respectively).
The data flow of the system should be carefully considered when designing
the NPSS model. The use of multiple solvers within a single model can often
result in conditions where the quantities on which a dependent is based are
not updated, resulting in divergence. If divergence of the blade row solvers is
encountered, the Jacobian matrix should be examined to ensure there are no
135
all zero rows.
•
Large changes in the compressor operating point in a single calculation can
result in divergence. Smaller changes over several calculations should be made
instead.
•
Independents and dependents can be used as diagnostic tools or to assist in
model development. For example, the blockage distribution shown in Section
6.2 was calculated using an independent/dependent pair. The blockage value
was cast as an independent and an equation enforcing the incidence to the
prescribed value as a dependent.
This greatly reduced the time required to
make the blockage model.
136
Appendix B
Guidelines for Smoke Visualization
The following comments are made based on lessons learned and offer best practices
in performing smoke flow visualization:
•
Visualization and smoke injection is highly sensitive to Reynolds number. Increasing the Reynolds number from 15,000 to even 20,000 produced poorer
quality images. Efforts should be made to reduce Reynolds number as much as
possible.
•
A wide variety of injection locations relative to the object of interest should
be attempted. Moving the smoke injection location by even 5% of the chord
produced different views of the flow field.
Injection off the blade was also
attempted, such as at mid-pitch at the leading-edge plane. While these views
were not presented here, they served as useful diagnostic tools throughout the
experimental process.
•
Injection as close to the blade surface is preferable. As can be seen in Figure 4-6,
the smoke generator was angled such that the tip was flush with the suction
surface.
The smoke generator was even rotated such that one of the two oil
delivering bores was closer to the blade surface in an attempt to inject smoke
directly into the viscous sub-layer of the boundary layer.
•
Increasing smoke flow rate does not necessarily produce better visualization.
137
Often the extra smoke simply acts as visual clutter and obscures the structures
of interest. To that end, a wide variety of smoke flow rates should be attempted
at each injection location.
•
An unsteady pressure field can interact with the injection apparatus, producing
a coupling of static pressure and smoke flow rate. It was found that smoke flow
rate often decreased during the leading-edge separation, likely due to the locally
high static pressure back-pressuring the mineral oil pump.
Increasing the oil
pump pressure rise reduced this effect, but resulted in excess smoke production
immediately prior to the leading-edge separation. The optimum pump setting
was found only through experimentation.
138
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