Design of a film cooled MEMS micro turbine
by
Baudoin Philippon
Dipl6me d'ing6nieur, Ecole Polytechnique (June 1998)
Submitted to the Department of Aeronautics and Astronautics
in partial fulfillment of the requirements for the degree of
Master of Science in Aeronautics and Astronautics
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
at the
SEP 11 2001
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
LIBRARIES
May 2001
@ Massachusetts Institute of Technology 2001. All rights reserved.
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Author .........
6::31
Certified by.......
Department of Aeronautics and Astronautics
May 18, 2001
f
;-...............................
.................
Professor Alan H. Epstein
R. C. Maclaurin Professor of Aeronautics and Astronautics
Thesis Supervisor
Certified by........
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T YDr Chon
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Senior Research Scientist, Gas Turbine Laboratory
Thesis Supervisor
Accepted by ...................
Professor Wallace E. Vander Velde
Chairman, Department Committee on Graduate Students
Design of a film cooled MEMS micro turbine
by
Baudoin Philippon
Submitted to the Department of Aeronautics and Astronautics
on May 18, 2001, in partial fulfillment of the
requirements for the degree of
Master of Science in Aeronautics and Astronautics
Abstract
As part of an effort to develop a portable power generation system, a fluid dynamics and thermal transfer investigation of a micro radial inflow turbine was carried out.
The 3-D numerical performance assessment revealed that the baseline 2-D designed turbine
stage was not matched to the baseline compressor, resulting in off design operation. The CFD predicts that the baseline turbine has a total to static efficiency of 29%, and does not provide enough
power to drive the compressor at the matched pressure ratio of 1.65. Reasons for this low efficiency
are the blockage due to end walls effects and to the exit right angle turn, and 3-D secondary flows
in the blade passage leading to boundary layer separation.
The turbine was then redesigned. An analytical design procedure, based on a mean line analysis
and correlations from 3-D CFD solutions was formulated and validated against numerical results. It
was shown that significant performance gains could be achieved by increasing the turbine exit area
to reduce the exit viscous loss and by increasing the blade exit angle. Shaping of the exit diffuser
turned out not to be viable because of the difficulties in keeping the boundary layer attached. An
improved turbine was then designed. Numerical simulations of the improved design predicted a
20% gain in efficiency, at a matched pressure ratio of 2.1.
Still, the turbine cannot drive the compressor. The turbine is conduction cooled by the compressor, but the large heat addition to the compressor flow causes a 30% drop in efficiency. Film
cooling schemes for the turbine were investigated. An axisymmetric model showed that a coolant
layer flowing radially inward may sustain the adverse centrifugal force at design speed. Film cooling
schemes were then proposed for disk and blade cooling. Effectiveness drivers are surface coverage,
thermal mixing with the main flow, and coolant matching. The overall peak cooling effectiveness
of the proposed cooling schemes was approximately 30% for a 30% coolant flow.
Thesis Supervisor: Professor Alan H. Epstein
Title: R. C. Maclaurin Professor of Aeronautics and Astronautics
Thesis Supervisor: Dr. Choon S. Tan
Title: Senior Research Scientist, Gas Turbine Laboratory
2
Acknowledgments
I would like to express my gratitude to Prof. Alan Epstein for his encouraging support, and
for his many insightful suggestions throughout this project. By allowing me to work in this micro
engine project as the "turbine guy" for two years, he gave me a challenging position and a lot to learn
I also wish to thank Dr. Choon Tan for his constant encouraging support. His valuable guidance,
direction, and insistence through the course of this research are much appreciated. In addition, I
would like to acknowledge the guidance of Dr. Yifang Gong, and thank him for his help and his
suggestions which lead to many improvements in the project.
Finally, I would like to thank all people of the micro engine project for making the past couple
of years a memorable experience as a foreign student at MIT. I will definitely recommend this kind
of experience!
This work was sponsored by the United States Army Research Office and the Defense Advanced
Researched Project Agency.
Their support is gratefully acknowledged.
3
Contents
1 Introduction
1.1
1.2
1.3
1.4
1.5
11
Background . . . . . . . . . . . . . . . .
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The MIT Micro Engine ...
Challenges for the Turbomachinery . . .
Goals and Content of the Thesis . . . .
Contribution of the Research . . . . . .
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2
Assessment of the Baseline Turbine Stage
2.1 Consistency of the boundary conditions set . . . . .
2.2 Exploration of the Design Space . . . . . . . . . . .
2.3 End Wall and 3-D Effects Dominate over 2-D Flow .
2.4 1-D Design Procedure using 3-D Simulations Results
2.4.1 Outline of Design Approach . . . . . . . . . .
2.4.2
1-D Design Procedure Validation . . . . . . .
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3
Design Improvement Techniques
3.1 Increasing Turbine Exit Area . . . . . . . . . . . . .
3.2 Increasing NGV Turning . . . . . . . . . . . . . . . .
3.3 Exit Diffuser Shaping . . . . . . . . . . . . . . . . .
3.4 Comparison of Baseline and Improved Turbine Stage
3.4.1 Presentation of the Baseline and Improved Turbine Stage
3.4.2 Comparison at Expected Operating Point . . . . . . . . .
3.4.3 Comparison of Performance Maps . . . . . . . . . . . . .
31
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4
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Cooling Studies
4.1 Cycle Analysis with Conduction Cooling only . . . . . . . . . . .
4.1.1 Cycle Analysis . . . . . . . . . . . . . . . . . . . . . . . .
4.1.2 Discussion on Heat Transfer Predictions . . . . . . . . . .
4.2 Primary Study of Film Cooling: Risks and Potential Effectiveness (2- D
4.2.1
General Considerations on Film Cooling . . . . . . . . . .
4.2.2 Coolant Layer Centrifugation on a Rotating Disk (2-D)
4.3
36
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51
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51
52
4.2.3
Effectiveness of Disk Film Cooling (2-D CFD)
4.2.4
Effectiveness of Blade Film Cooling (2-D CFD) . . . . . .
55
55
59
63
66
. . . . . . . . .
71
Detailed Study of Disk Film Cooling (3-D CFD)
4
. . . . . .
4.3.1
4.3.2
4.3.3
5
Advantages and Disadvantages of Injection from the Static Structure and
from the R otor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Disk Cooling with Injection from the Static Structure . . . . . . . . . . . .
Disk Cooling with Injection from the Rotor . . . . . . . . . . . . . . . . . .
Conclusion and Recommendations
5.1 Conclusions on Performance Improvements and Film Cooling . . . . . . . . . . . .
5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A Validation of Fluent
A .1 The Fluent Code . . . . . . . . . . . .
A.1.1 The Segregated Solver . . . . .
A.1.2 The Coupled Solver . . . . . .
A.2 Validation in 2-D (Turbine Geometry)
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98
B Discussion on the Effect of the Journal Bearing Flow
C Discussion on Typical Flow Features in the Micro Turbine
C.1 Flow in the NGV for an Inlet Pressure of 2.1 atm . . . . . . .
C.2 Flow in the Rotor for an Inlet Pressure of 1.8 atm . . . . . .
C.3 Flow in the Rotor Matched to the Compressor . . . . . . . .
5
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101
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103
104
106
List of Figures
1-1
1-2
Cross-section of the demo-engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Picture of an early version of the baseline geometry turbine (October 1999 geometry)
12
13
2-1
2-2
3-D rotor calculations performed viewed in a Reynolds-Rossby number design space
2-D/3-D exit loss coefficient in the nozzle guide vanes (400 pm height, baseline
design) vs. exit Reynolds number . . . . . . . . . . . . . . . . . . . . . . . . . . . .
NGV loss coefficient for 3 different wall shear conditions . . . . . . . . . . . . . . .
Axial Mach number at the turbine exit annulus after the right angle exit turn (baseline design) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Description of the iterative turbine stage design . . . . . . . . . . . . . . . . . . . .
Correlation for the NGV loss coefficient . . . . . . . . . . . . . . . . . . . . . . . .
Correlations for loss coefficient at the turbine exit right angle turn . . . . . . . . .
20
2-3
2-4
2-5
2-6
2-7
Parametric study: turbine stage efficiency vs. rotor exit radius (NGV turning constant at 74 degrees) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-2 Fraction of the exit area used for exit mass through flow . . . . . . . . . . . . . . .
3-3 Parametric study: NGV turning vs. turbine stage efficiency (Rotor exit radius
constant at 2.0 m m ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-4 Parametric study: NGV turning vs. turbine mass flow (Rotor exit radius constant
at 2.0 m m ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-5 Schematic of the turbine rotor with a shaped exit diffuser . . . . . . . . . . . . . .
3-6 Perspective of the grid for baseline nozzle guide vane . . . . . . . . . . . . . . . . .
3-7 Perspective of the grid for baseline turbine rotor (top) and improved turbine rotor
(bottom ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-8 Top view of the baseline turbine stage (top) and the improved turbine stage (bottom)
(outer diameters of the rotor and stator are indicated) . . . . . . . . . . . . . . . .
3-9 Baseline stage (top) and improved stage (bottom): shaft work and loss distribution
at the predicted operating point . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-10 Performance map: efficiency contours of baseline design (top) and improved design
(bottom ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-11 Relative velocity vectors at mid span, for the improved rotor, at PR = 1.55 and
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3-1
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120% design speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3-12 Performance map: shaft work contours (reference
and improved design (bottom) . . . . . . . . . .
3-13 Performance map: disk Stanton number contours
proved design (bottom ) . . . . . . . . . . . . . .
6
= 80 W) of baseline design (top)
. . . . . . . . . . . . . . . . . . . .
of baseline design (top) and im. . . . . . . . . . . . . . . . . . . .
48
49
3-14 Performance map: blade Stanton number contours of baseline design (top) and improved design (bottom ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4-1
4-2
4-3
4-4
4-5
4-6
4-7
4-8
4-9
4-10
4-11
4-12
4-13
4-14
4-15
4-16
4-17
4-18
4-19
4-20
4-21
4-22
Normalized heat flux in the turbine rotor for various designs (see equation 4.3) . .
Required combustor exit temperature to reach a mass-average inlet total temperature
of 1,600 K with a cooling scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Minimum Rossby number to avoid coolant centrifugation of a cold film on a rotating
disk, inlet total temperature 1600 K . . . . . . . . . . . . . . . . . . . . . . . . . .
Minimum Rossby number to avoid coolant centrifugation of a cold film on a rotating
disk, inlet total temperature 1800 K (thin lines are Ttiniet = 1,600 K, figure 4-3) .
Schematic of the 2-D axisymmetric geometry . . . . . . . . . . . . . . . . . . . . .
Cooling effectiveness of radial injection over a 2-D rotating disk . . . . . . . . . .
Schematic of the 2-D axisymmetric geometry with a 15 p m step between the vanes
exit and the rotor inlet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cooling effectiveness of radial injection over a 2-D rotating disk with a 15 pm step)
View of the improved blade with coolant injectors at the leading edge . . . . . . .
Pressure surface blade cooling: isothermal cooling effectiveness and required coolant
pressure for a 30 pm slot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Suction surface blade cooling: isothermal cooling effectiveness and required coolant
pressure for a 30 pm slot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Blade cooling: turbine work variation due to coolant injection . . . . . . . . . . . .
Required compressor pressure to inject coolant at 77 degrees matched to the improved turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-D cooling effectiveness ON THE ROTOR for 3 coolant injection conditions (radial,
77 degrees, 77 degrees high pressure) . . . . . . . . . . . . . . . . . . . . . . . . . .
3-D cooling effectiveness ON THE DISK for 3 coolant injection conditions (radial,
77 degrees, 77 degrees high pressure) . . . . . . . . . . . . . . . . . . . . . . . . . .
3D cooling effectiveness ON THE BLADES for 3 coolant injection conditions (radial,
77 degrees, 77 degrees high pressure) . . . . . . . . . . . . . . . . . . . . . . . . . .
3-D cooling effect on shaft work for 3 coolant injection conditions (radial, 77 degrees,
77 degrees high pressure) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-D cooling effectiveness ON THE DISK for 77 degree injection, for coolant temperatures equal to 700 K, 900 K, and 1100 K . . . . . . . . . . . . . . . . . . . . . . .
Top view of a blade passage with first cooling slot geometry . . . . . . . . . . . . .
Top view of a blade passage with second cooling slot geometry . . . . . . . . . . .
Disk cooling effectiveness ON THE ROTOR of two cooling configurations with injection from the disk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Disk cooling effectiveness ON THE DISK of two cooling configurations with injection
50
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from the disk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4-23 Disk cooling effectiveness ON THE BLADES of two cooling configurations with
injection from the disk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4-24 Shaft work variation of two cooling configurations with injection from the disk . . .
88
89
Disk cooling injection from the rotor, with an additional cover plate to turn the
coolant towards the centerline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
93
5-1
7
B-1 Impact of the journal bearing flow on the turbine rotor efficiency (Baseline design)
B-2 Cooling effectiveness of the flow coming from the journal bearing (Baseline design)..
C-1 Reversible term of entropy in the NGV, for the baseline design (left) and improved
design (right), at 2.5% span (top), 50% span (middle), and 97.5% span (bottom),
for an inlet pressure of 2.1 atm . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
C-2 Irreversible term of local entropy production in the NGV, for the baseline design
(left) and improved design (right), at 2.5% span (top), 50% span (middle), and
97.5% span (bottom), for an inlet pressure of 2.1 atm . . . . . . . . . . . . . . . .
C-3 Total pressure in the NGV, for the baseline design (left) and improved design (right),
at 2.5% span (top), 50% span (middle), and 97.5% span (bottom), for an inlet
pressure of 2.1 atm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
C-4 Total temperature in the NGV, for the baseline design (left) and improved design
(right), at 2.5% span (top), 50% span (middle), and 97.5% span (bottom), for an
inlet pressure of 2.1 atm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
C-5 Mach number in the NGV, for the baseline design (left) and improved design (right),
at 2.5% span (top), 50% span (middle), and 97.5% span (bottom), for an inlet
pressure of 2.1 atm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
C-6 Path lines in the NGV, for the baseline design (left) and improved design (right),
starting at 2.5% span (top), starting at 50% span (middle), and starting at 97.5%
span (bottom), for an inlet pressure of 2.1 atm . . . . . . . . . . . . . . . . . . . .
C-7 Normalized absolute swirl in the rotor, for the baseline design (left) and improved
design (right), at 2.5% span (top), 50% span (middle), and 97.5% span (bottom),
for an inlet pressure of 1.8 atm . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
C-8 Reversible term of entropy in the rotor, for the baseline design (left) and improved
design (right), at 2.5% span (top), 50% span (middle), and 97.5% span (bottom),
for an inlet pressure of 1.8 atm . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
C-9 Irreversible term of local entropy production in the rotor, for the baseline design (left)
and improved design (right), at 2.5% span (top), 50% span (middle), and 97.5% span
(bottom), for an inlet pressure of 1.8 atm . . . . . . . . . . . . . . . . . . . . . . .
C-10 Static pressure in the rotor, for the baseline design (left) and improved design (right),
at 2.5% span (top), 50% span (middle), and 97.5% span (bottom), for an inlet
pressure of 1.8 atm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
C-11 Static temperature in the rotor, for the baseline design (left) and improved design
(right), at 2.5% span (top), 50% span (middle), and 97.5% span (bottom), for an
inlet pressure of 1.8 atm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
C-12 Path lines in the rotor, for the baseline design (left) and improved design (right),
starting at 2.5% span (top), starting at 50% span (middle), and starting at 97.5%
span (bottom), for an inlet pressure of 1.8 atm . . . . . . . . . . . . . . . . . . . .
C-13 Swirl relative to inlet (top), local irreversible entropy production (middle), and static
pressure contours (bottom) for the baseline rotor (left) and the improved rotor (right)
at their respective matched operating point (see table 3.2) . . . . . . . . . . . . . .
8
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100
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List of Tables
2.1
2.2
Geometrical parameters explored . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Operating parameters explored . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
27
3.1
Summary of design characteristics of the baseline turbine design and the improved
.......................................
stage...............
Summary of stage performance of the baseline and improved design . . . . . . . . . .
Reference and design quantities for the turbine maps . . . . . . . . . . . . . . . . . .
39
43
44
3.2
3.3
4.1
4.2
4.3
Physical scales used in dimensionless equations . . . . . . . . . . . . . . . . . . . . . 59
Advantages and disadvantages of coolant injection from a static or rotating structure 73
Boundary conditions for the coolant layer, in the three disk cooling cases with injection from the static structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
A.1
A.2
Fluent 2-D/MISES comparison for baseline NGV . . . . . . . . . . . . . . . . . . . .
Fluent 2-D/MISES comparison for baseline rotor . . . . . . . . . . . . . . . . . . . .
9
97
97
Nomenclature
Roman
CI
M
rh
P
Q
Re
T
u
jPt
,
Loss coefficient (dimensionless), defined as C, = Pt in
out -P 0 ~t
Mach number (dimensionless)
Mass flow (g.s 1 )
Static pressure (Pa)
Heat transfer, positive to the fluid (W)
Reynolds number (dimensionless), based on the specified length and location
Static temperature (K)
Vector position
Greek
6
Ratio of the total pressure at the rotor inlet to a total pressure of reference
Rotation speed (rad.s- 1 )
Ratio of the total temperature at the rotor inlet to a total temperature of reference
Subscripts
abs
exit
in
out
rel
t
w
In the absolute non-rotating frame
At the engine exit, after the exhaust right angle
At the inlet
At the blade trailing edge
In the rotor rotating frame
Total quantity in the absolute frame
Denotes a quantity on the wall surface, either blade or end wall
10
Chapter 1
Introduction
1.1
Background
Advances in micro machining techniques have lead to the development of numerous Micro
Electro-Mechanical Systems, known as MEMS, with applications in virtually every scientific field
such as medicine, electronics or aeronautics. Specifically, the current development of micro-scale
power generation systems demonstrate new directions in concepts for portable, disposable and low
cost systems.
An MIT program proposes to demonstrate the feasibility of a micro gas turbine engine. Based
on a Brayton cycle, this micro engine benefits from the square-cube law: at the scale of a shirt
button, its power density could be an order of magnitude larger than conventionally sized gas
turbine engines (Epstein et al [3]).
Applications include portable power generation (with a power density twenty times that of
batteries), micro blowers and compressors, micro rocket engines, and propulsion for micro air
vehicles. The effort is supported jointly by the Army Research Office and the Defense Advance
Research Project Agency (DARPA).
1.2
The MIT Micro Engine
Although based on the same fundamental principles, the MIT micro-engine cannot simply mimic
conventional gas turbine engines since it must take into account specific issues related to the micro
11
Starting
Air In
Compressor
Inlet
3.7 mm
Exhaust
21 mm
Turbine
Combustor
Figure 1-1: Cross-section of the demo-engine
scale of the device. The original baseline design is presented in Epstein et al [4].
Calculations
showed that such a micro gas engine could produce up to 50 W of electrical power for portable
power generation, or 0.2 N of thrust for a micro air vehicle.
The general approach of the engine is close to that of the first jet engines in the late fourties and
to current auxiliary power units. The micro engine consists of a single stage centrifugal compressor,
an annular combustor and a radial inflow turbine to spin the compressor and provide extra power
for the output (as shaft torque). Because of the required rotational speed, the rotor is supported
on air bearings. Two thrust bearings support the thrust load along the longitudinal axis and a
journal bearing supports the radial rotor load. A detailed discussion of the operating modes of the
journal bearing can be found under Piekos et al [10]. A cross sectional view of the baseline engine
is presented in figure 1-1. A photo of the baseline turbine is shown in 1-2.
1.3
Challenges for the Turbomachinery
At this size, thermodynamics is the same as for conventional gas turbine engines, but mechanics
and thus the optimum design trade-offs do change with scale. Moreover, fabrication constraints
in the micro scale prevent simply scaling down conventional turbomachinery. Design studies have
demonstrated the governing micro engine parameters, pointing out where they differ from those of
conventional engines. The work to date has emphasized the following points:
e Centrifugal stress at the turbine blade roots dominates but is compatible with the choice of
silicon and silicon carbide for fabrication reasons. The softening temperature of silicon at the
design rotation speed of 1.2 million RPM is 950 K, so the turbine rotor temperature must be
12
Figure 1-2: Picture of an early version of the baseline geometry turbine (October 1999 geometry)
13
maintained below this level.
" Very low Reynolds number is not a barrier to break-even. It was shown, using computational analysis and experimental data, that the design of turbomachinery components with
acceptable adiabatic efficiency was possible. Still, as the Reynolds number in the compressor
reaches 25,000 and 1,500 in the turbine, its influence remains strong and any improvement in
the cycle pressure ratio leads to significant gains in component efficiency.
" Fabrication restricted to pure 2-D extrusion is a direct consequence of the micro machining
techniques chosen. It precludes 3-D shape optimization, while all out-of-plane flow turns must
be right angles, which produces significant blockage and viscous loss.
" Large heat fluxes derive from the small scale and high thermal conductivity of the material.
To maintain the turbine rotor temperature below 950 K, it is currently cooled by thermal
conduction to the compressor.
But this heat addition drastically reduces the compressor
performance, a major parameter in a turbojet efficiency and power output. So, other techniques must be explored to maximize turbine gas temperature while limiting heat flux to the
compressor.
1.4
Goals and Content of the Thesis
The goals of this thesis are to explore the turbine design space, to determine the parameters
governing turbine efficiency and heat flux, and then to propose a new film cooled turbine design
with improved component efficiency.
The second chapter presents the initial design space exploration: the analysis performed on the
nozzle guide vanes and the turbine rotor concluded that viscous loss on end walls are an important
design factor (section 2.3). A new design procedure is introduced to remedy the short comings of
the previous 2-D only design procedure (section 2.4).
The third chapter focuses on using the new design procedure to realize improved designs. The
baseline design is compared with an improved design proposed for fabrication (section 3.4).
The fourth chapter deals with heat transfer in the micro engine, and presents a risk and performance analysis of film cooling on both the turbine disk and the turbine blades.
14
The last chapter presents the summary and conclusions of the research, as well as recommendations for future work.
1.5
Contribution of the Research
The research presented in this thesis has taken several steps in the development of the micro
engine turbine design:
e Complete and precise performance maps were established for both the baseline and improved
designs presented in the third chapter. They can be used in cycle and systems analysis and
are provided as a "best guess" as no experimental data is yet available. It was shown that
matching issues lead to unacceptable performance of the baseline design.
e A 1-D/3-D design procedure was implemented to remedy to the limitations of 2-D design.
Based on mean line analysis and 3-D CFD experience, the model was used to improve the
component efficiency by more than 20% to bring it up to 55%, closer to the expected turbine
performance in the early cycle studies.
e Parametricstudies have been performed to explore film-cooling techniques to limit heat addition to the compressor. It is shown that reverse flow in the coolant layer due to centrifugal
forces is not a limit in the planned operating range, and that turbine disk cooling can be very
effective if sufficient coolant pressure is available.
15
Chapter 2
Assessment of the Baseline Turbine
Stage
The baseline turbine was designed and optimized in 2-D by Harold Youngren [2]using a numerical code called MISES (Multiple blade Interacting Stream tube Euler Solver). This code creates
a 2-D mesh on a stream tube around the blades given by an inviscid Euler analysis, then uses the
boundary layer theory to compute the flow near the blade surface.
Then we performed a 3-D analysis of this design using a 3-D Reynolds averaged, steady, NavierStokes solver called Fluent (presentation and validation of this code is in appendix A). We found
that the 2-D designed components were seriously mismatched in 3-D, due to end walls effects and
blockage at the exit right angle turn.
Unmatched components result in off design operation of
the blade rows, which can drop turbine performance and engine efficiency. So this chapter discusses
the CFD analysis of the baseline turbine stage design with particular attention to the issue of turbine matching.
First, we discuss boundary conditions chosen for consistency set for each blade row. Confidence
in the numerics are then generated through an exploration of the design space. The next section
shows that end wall effects are dominant in the demo engine for etch depths up to 400 im. Last,
an alternative design method, based on mean line analysis with correlations from 3-D numerical
solutions, is explained and validated.
16
2.1
Consistency of the boundary conditions set
The performance estimation rests on several crucial considerations to provide accurate and consistent results within the scope of the chosen assumptions. A validation study has been performed
to gain confidence in the 3-D, Reynolds averaged, Navier-Stokes numerical tool, Fluent. Both the
code description and the validation study can be found in appendix A.
Also important are the boundary conditions used in the calculations and the understanding of
how they impact the final accuracy.
The first group summarizes the matching effort undertaken throughout this research and are a
basic requirement for accuracy.
" Pressure matching. We mean by that the total pressure at the NGV exit is equal to the total
pressure at the rotor inlet. Those values have to be precisely matched at a constant radial
plane (r = 3mm).
" Mass flow matching. We also demand the mass flow in the NGV to be equal to the mass flow
in the rotor. As calculations for the NGV and the rotor are done independently, we need to
iterate on the NGV inlet total pressure and on the NGV exit static pressure to match the
rotor mass flow. Practically, this is done using interpolations among at least four NGV cases
(two NGV inlet conditions and two NGV outlet conditions).
" Temperature matching. The temperature at the vane exit is equal to the temperature at
the rotor inlet. This requirement is approximately respected in the simulations, where total temperatures are imposed at the NGV inlet and rotor inlet. Adiabatic calculations are
performed in the NGV for several reasons. First, the NGV viscous loss does not decrease
drastically with heat transfer, so adiabatic calculations overestimate only slightly the NGV
pressure loss. Second, the total temperature does not change throughout the NGV passage,
so we don't have to iterate on the NGV inlet total temperature until the NGV exit reaches
the required 1,600 K. So, using adiabatic calculations in the NGV saves computer time while
providing realistic results for the matching process.
" Linear regression with the mass flow, between two numerical solutions, was used to reduce
17
the required number of different operating conditions. It was applied to the total pressure
between the nozzle guide vanes exit and the rotor inlet, to the turbine shaft work and to the
heat flux to the turbine wall.
Compressor matching. Matching the compressor means matching the rotation speed, the
mass flow, the pressure ratio, and the power. In the design procedure suggested later in this
chapter, the aim is to match the rotation speed, the pressure ratio and the mass flow and to
design a turbine rotor with the highest possible efficiency. As described in the next chapter,
this is insufficient: the power required by the compressor is still not balanced by the turbine
power. Reducing the heat flux to the compressor is necessary. At this point, the cycle analysis
is more complex and is not treated herein.
The second group deals more with assumptions used to reduce the numerical work load. It is
true that higher precision may result if the following assumptions were not made, but the goal of
the research is to obtain governing parameters and general trends rather than to reach a precision
expensive both in time and computer resources. The assumptions are:
" Steady calculations provides sufficiently good performance estimations for design purposes.
On the other hand, this ignores unsteady phenomena such as wake-blade interaction. But we
do not expect this to be an important factor given the expected accuracy of the calculations
and the required performance of the turbine stage.
" Uniform inflow conditions were stipulated at boundaries. When the outflow of one simulation
was used as input in another, total quantities and tangential velocity were mass-averaged
while static quantities and radial velocity were area-averaged. To validate this assumption, a
complete simulation of the turbine stage was performed. The flow quantities at the interface
between the NGV and the rotor were circumferentially averaged by the code, so the rotor
inlet conditions were non uniform in the longitudinal direction. The full stage efficiency was
only 2% lower than the efficiency predicted using uniform inflow conditions for the rotor. We
will generalize this to all results presented in the thesis.
" No boundary layers were specified at the domain inlet. Instead, the computational domain was
extended upstream and downstream of the specific domain of interest to improve convergence
18
and allow for an onset of viscous and thermal boundary layers. Due to the higher shear near
a boundary layer starting point, we can expect both the viscous loss and the heat flux to be
overestimated by this technique.
To assess the accuracy of these performance predictions, we consider the impact of:
* NGV-rotor flow temperature matching. Currently, only pressure and mass flow are matched
precisely, so that there is a temperature discontinuity between the nozzle guide vanes and the
turbine rotor: the computed total temperature at the NGV exit is approximately 10% lower
than the total temperature imposed at the rotor inlet. Consequently, the "matched" point
would be at a slightly lower mass flow, the total pressure between the NGV and rotor being
also reduced. Because the total temperature drop in the NGV is due solely to heat transfer to
the static structure, and heat transfer depends linearly on the temperature difference between
the wall and the inlet, improved estimates for the wall temperatures would be needed.
" Flow from the journal bearing. There is a 15 micron wide gap between the NGV exit and the
rotor inlet, through which approximately 5% of the main flow passes at design speed. This
flow, which is studied in appendix B, reduces the turbine performance in two ways. First, it
leaves the journal bearing gap at an angle of 90 degrees to the main flow, thus disrupting the
boundary layers and mismatching the rotor blades inlet flow angle. Second, as its temperature
is lower than the main flow (between the estimated static structure temperature of 1,200 K
and the rotor temperature of 950 K), less work can be extracted from this cold layer than from
the turbine main flow. In our performance estimations, a correlation of shaft work reduction
versus the fraction of the flow coming from the journal bearing has been calculated in 3-D
and used thereafter.
2.2
Exploration of the Design Space
The design space has conceptually a large number of dimensions, so it is truly impossible to
present it on a two dimensional sheet of paper. Even in the limited scope of this research, many
ideas have been explored (some unsuccessfully) in aerodynamic performance and cooling.
So the representation of the design space is restricted to two main parameters, Reynolds number
19
1
+
*
+
*
0
Baseline rotor
Improved rotor
*
0 0.8|-.
- .....
.
-......
...
+
1-
C
*
4
U)
+
-0.6
E
c: 0.5 1-
*
+
+
++
++
+,
+
+
+
0
*
*
*
*
*
cr 0.4
+
0 .1
10 4
10 3
105
Reynolds number (based on inlet conditions)
Figure 2-1: 3-D rotor calculations performed viewed in a Reynolds-Rossby number design space
and Rossby number (presented in appendix A).
Major calculations are shown in figure 2-1. The
points are fairly well distributed indicating an effort to simulate the flow under various conditions.
A shift of Reynolds number to higher values to the right is visible from the baseline rotor to the
improved rotor. It is due essentially to the improved compressor design and improved matching,
which resulted in a higher total pressure available at the rotor inlet, thus increasing Reynolds number.
To illustrate the work done and point out several flow features, some calculations are presented
in appendix C.
2.3
End Wall and 3-D Effects Dominate over 2-D Flow
Early calculations showed that the mass flows predicted in 3-D were generally 30 to 40% lower
than those predicted in 2-D. This pointed out the need for metrics to measure the blockage and
20
0.5.
*-- -
3D loss coefficient
2D loss coefficient
F
CD
0I)
N
0
F
C
0.3
W
0
1-..
%0.
0
(0
....
......
0
Lii
-- I--
0.1
-~
+
104
103
Exit Reynolds number
Figure 2-2: 2-D/3-D exit loss coefficient in the nozzle guide vanes (400 pm height, baseline design)
vs. exit Reynolds number
viscous loss due to low Reynolds number in the nozzle guide vanes and the turbine rotor.
First, for the blockage due to viscous loss in the nozzle guide vanes, a loss coefficient was defined
as follows:
out
C= Pt in-Ft
Pt out - Pout
(2.1)
This represents the total pressure drop in the nozzle guide vanes (due to viscous loss) over the
dynamic pressure at the passage exit (radius r = 3 mm).
Results are shown in figure 2-2, where the loss coefficient of the baseline NGV obtained with
Fluent in 2-D and 3-D are compared. As shown in the validation process in appendix A, MISES
and Fluent in 2-D are in excellent agreement. So for 2-D calculations, Fluent has been chosen to
make a fair back-to-back comparison.
In conventional modern turbines, the level of loss in 3-D is approximately 3 times higher than
21
that in 2-D. In our case, the factor is closer to 4 in this back-to-back comparison, prompting the
need for further analysis to determine the source of the higher loss: the boundary layer on the
blade surface, the boundary layer on the end wall surface, or the interaction of the two.
In numerical simulation, it is possible to set a no-shear condition on one wall independently of
the other, so that we were able to compute the viscous loss due solely to the blade surface and
solely due to the end wall surface. Figure 2-3 shows the 3-D computed loss coefficients.
Clearly, viscous loss on end walls is dominant. They represent roughly 2/3 of the loss in the
nozzle guide vanes. The fact that the sum of the loss coefficients for viscous end walls only and
viscous blade only approximates the total loss coefficient suggests that the interaction between the
two boundary layers is not an important factor. Strong secondary flow is observed on the NGV
blade surface. We can conclude they are due to the strong pressure gradient in the blade passage
influencing the end wall boundary layers. Increasing the etch depth above 400 microns would help
reduce this secondary flow and the associated 3-D loss.
The other dominant source of blockage is the right angle, out-of-plane turn downstream of the
rotor exit. As mentioned in the introduction, manufacturing constrains the design to 2-D etching,
so that all turns in the longitudinal axis are right angles. This sharp, right angle turn separates
the boundary layer, which produces significant recirculation and flow blockage.
To assess the reduction of effective exit area, we examine the axial Mach number at the turbine
exit, after the right angle turn. Figure 2-4 shows the exit Mach number of the baseline turbine,
operating close to the predicted matched operating point (PR = 1.65).
The axial Mach number
is at least 20% lower than its maximum value in the dark area, and is even negative in regions
of reverse flow indicating a recirculation near the turn. In the baseline case, the effective area is
30% lower than the physical flow area. It will be shown in section 3.1 in the next chapter that
the effective area is even smaller in the improved turbine while the right angle turn causes fewer loss.
Since the baseline design, based on 2-D CFD, does not take into account these 2 sources of
blockage, the mass flow we can expect in 3-D and in the experiment will be significantly lower
than the nominal design value. Thus, the velocity triangles are largely off-design, both for the
compressor and the turbine. For instance, the predicted turbine efficiency in 3-D with Fluent is
22
0..
0.3
C
60.2
0
CO)
CD
0
x
w
0.1
End wall and blade viscous Viscous end wall only
Viscous blade only
Figure 2-3: NGV loss coefficient for 3 different wall shear conditions
23
0.5
0.4
0.3
0.2
0.1
-0.0
-0.1
-0.2
-0.3
Figure 2-4: Axial Mach number at the turbine exit annulus after the right angle exit turn (baseline
design)
24
30% at this operating point, instead of approximately 60% predicted by MISES.
For this reason, there is a need for another design procedure, resting more on a prediction of
the blockage to yield the desired velocity triangles. 3-D CFD provides such a prediction capability
(2-D CFD may be sufficient for the right angle turn). This is the objective of the next section.
2.4
1-D Design Procedure using 3-D Simulations Results
The proposed design procedure is simple. It is based on a mean line analysis (as described
in Kerrebrock [9]), computing pressures, temperatures and velocities at each station: NGV inlet,
NGV outlet, rotor inlet, rotor outlet, and stage exit.
However, 3-D effects must be taken into consideration early in the design process, so they are
included either as correlations from 3-D solutions or best guesses. The result of this is an iterative
algorithm which computes the stage mass flow, the rotor blade leading edge and trailing edge
angles, specified operating conditions (total pressure and total temperature at the turbine stage
inlet, static pressure at the turbine stage outlet, rotation speed).
In the following sections, the design procedure is described and validated.
2.4.1
Outline of Design Approach
Figure 2-5 depicts the user inputs and the iterative process. The procedure is flexible, because
many geometrical and operational inputs can be chosen. So parametric studies can be performed
on any parameter or set of parameters.
The geometrical inputs are summarized in table 2.1. The operational inputs are shown in table
2.2. Typically, one wants to design a turbine stage given some operational requirements such as
those specified in the second table. So the optimization is carried out mostly on the geometrical
parameters.
It should be noted first that most operational parameters can be updated as experience builds,
so that the procedure accuracy can increase with time. Second, a rotor passage efficiency is required:
it represents the total to total isentropic efficiency of the blade passage only, excluding effects such
as the exit right angle turn. It turns out that this efficiency is fairly constant. The rotor efficiency
predicted in 2-D is a good first guess for this parameter.
25
Set stage geometry
(Blade height, inlet and exit radii,NGV turning)
I
Set stage flow conditions
(tinlet'
inlet'
outlet
h..- I Assume inlet mass flow
PPI
I
I
I
NGV loss coefficient = f(Reynolds or NGV turning)
(From 3D CFD)
Determine velocity triangles
(Rotor efficiency from 3D experience)
I
Exit loss = f(exit Mach number)
(From 3D CFD)
I
Determine outlet pressure
I
ZZIEIZ
I
Turbine stage performance
I
I
Figure 2-5: Description of the iterative turbine stage design
26
Parameter
Value or range
NGV blade height (pim)
NGV inlet radius (mm)
400
4.8
NGV outlet radius (mm)
NGV leading edge angle (degree)
NGV trailing edge angle (degree)
3.04
0
60-85
Rotor blade height (pm)
400
Rotor inlet radius (mm)
Rotor outlet radius (mm)
1.5-3
1.5-3
Table 2.1: Geometrical parameters explored
Parameters
Stage inlet total pressure (atm)
Stage inlet total temperature (K)
NGV loss coefficient (-)
NGV heat transfer estimation (W)
Rotor speed (RPM)
Rotor passage adiabatic efficiency (-)
Rotor deviation (degree)
Rotor heat transfer estimation (W)
Viscous loss of the exit right angle turn (-)
Stage exit static pressure (atm)
Value or range
1.5-3
1,600
Correlation
60
1.2 million
0.75
0-20
60
Correlation
1
Table 2.2: Operating parameters explored
27
2.4.2
1-D Design Procedure Validation
In table 2.2, two important parameters require a correlation: the nozzle guide vane loss and the
exit right angle turn loss. Those correlations have been established using a number of CFD cases.
For the NGV loss coefficient correlation presented in figure 2-6, different vane geometries were
drawn and simulated in 3-D with Fluent. The correlation adopted for the design procedure captures
the trend of increasing loss with increased turning to the first order. The fact that the loss coefficient
increases again at angles close to 60 degrees may mean that more cases would be required. This is
not so important for us as the baseline design has already a high turning angle, about 74 degrees.
It can also be noted that groupings represent the same geometry at different operating Reynolds
numbers, so that they have in each group an almost constant exit angle but diminishing loss with
increasing Reynolds number. The correlation does not currently take this effect into account.
The trend of highly increasing loss for angles above 70 degrees is what we expected, although
it is not possible to compare these results with correlations published in the literature such as the
D-factor. Our NGV geometries seem to have too high diffusion factors because the exit velocity
is very close to the maximum velocity along the blades, and Fluent cannot do post processing on
streamlines (which is necessary to calculate the diffusion factor). The trend of increasing loss for
angles below 70 degrees is probably wrong as we expect the loss to decrease continuously with the
exit angle. We could improve the correlation using more designs, but as we are more interested in
higher angles this is not necessary now.
The other correlation is that of the exhaust right angle loss as a function of the Mach number
(figure 2-7). For low velocities, viscous loss generally scales with the square of the Mach number,
so the initial correlation fit on baseline turbine data was of the form:
C, = 1 +#M
2
(2.2)
As it can be seen on the graph, the baseline turbine has a fairly high Mach number just before
the exit turn. Later, after many 3-D simulations of the improved turbine, more data was available
at lower Mach numbers, so that a better fit was made, using the same form specified in the equation
above. The latter can be used now for further designs, because it covers a wide range of exit Mach
numbers so that extrapolation is not needed.
28
0.8
+
o
C
0
CFD data
Correlation used in model
CFD data on improved design
).6
+
-
-+
0~
0
az
0.4
.....
. .. . .. .
..+. .. . . . . . . .
+
.. . . . . ..
+
.. . . . . . . . . . . . . . . . . . . . . .. . . . . .
0.2'
60
65
70
75
NGV exit angle
P (degrees)
80
Figure 2-6: Correlation for the NGV loss coefficient
29
85
0
1.2 -
+
CFD data on baseline design
o
Correlation based on baseline design, used in model
CFD data on improved design
Updated correlation based on both designs
-C
Wo
++
0
o ++
ol.
++
+ 0
01 +0+
00
1.q
+
.... ......... ........ .
L..0
~1 .0 5 .o.....
0
I
10
0.1
0.6
0.4
0.5
0.2
0.3
Mach number at the blade passage exit
0.7
Figure 2-7: Correlations for loss coefficient at the turbine exit right angle turn
It may be interesting to see if 2-D axisymmetric CFD (eventually with swirl) predicts the same
level of loss as a function of the Mach number. If so, then the phenomenon is truly 2-D which
would simplify the 3-D computations and the design procedure.
In this last section, we have implemented a 1-D design procedure which takes into account some
3-D effects. The object of the next chapter is to use this design procedure, using parametric studies,
to help redesign the turbine stage.
30
Chapter 3
Design Improvement Techniques
As explained in the introduction, the 3-D CFD analysis suggests that the baseline turbine design
has low efficiency. So a thoughtful and comprehensive improvement effort has been undertaken to
bring the turbine efficiency up to a level required by the cycle analysis, around 60%.
This study identified one major efficiency driver, the exit area of the turbine, presented in
section 3.1.
Another driver, the nozzle guide vane turning, was shown to be both required and
beneficial to the cycle performance (section 3.2). In section 3.3, an approach to reducing the exit
loss and increasing the effective exit area is presented. Although it was unsuccessful, it illustrates
the method used in the other sections. Finally, a detailed back-to-back comparison of the baseline
and improved turbine stage performance is shown.
3.1
Increasing Turbine Exit Area
There are many reasons to increase the turbine exit area. First, the baseline turbine operates
off design, so that it cannot extract enough enthalpy from the flow. Consequently, the flow exiting
the rotor blade passage has a high velocity, a high swirl, and suffers a high viscous loss at the exit
right angle turn because of this high dynamic head. Second, the exit right angle turn produces a
separation of the boundary layer with a large recirculation zone, so that the exit area available to
the flow is reduced, increasing velocities and loss.
In order to quantify the gain achievable, we used a two step method. The first was to identify
the sources of loss and inefficiency in the baseline design. Residual swirl, exit loss, and exit kinetic
31
energy account for 49% of total loss. The second step was to use the design procedure described in
the previous chapter to identify what fraction of this 49% can be recovered1 : results are discussed
below.
Figure 3-1 shows the impact on the rotor exit radius of the turbine isentropic efficiency. The
blade leading edge radius is constant. The efficiency improvement is on the order of 5 points, but
we must remember that the current baseline turbine is not matched: we can expect a much higher
increase when matched.
The main reason for this improvement is the reduction of exit Mach
number, leading to a drop in exit viscous loss. This can be seen by analyzing the exit right angle
turn loss in each design.
For a given inlet radius there is a physical limitation in the increase of the rotor exit radius,
which is set by the blade deviation and the requirement of zero swirl at the blade passage exit. As
the flow tangential velocity must match the disk speed at the exit radius, both the blade angle and
the flow velocity become large at large exit radii. At this point, we can expect the flow deviation.
Several rotor exit radii were tested, with relevant cases at 2, 2.2 and 2.3 mm. It turned out that
the stage efficiency did not improve significantly above 2.0 mm for a fixed inlet radius of 3 mm.
To confirm the effect of the increased exit radius, the fraction of the exit area which is used
by the through flow was computed, for both the baseline and improved design. Results plotted
in figure 3-2 confirm that in the baseline design, the effective exit area was 30% lower than the
geometric exit area, leading to an increased exit Mach number and viscous loss. The redesign effort
increased the nonuniformity at the exit to allow for a lower exit velocity.
3.2
Increasing NGV Turning
In this section, we analyze a much more subtle source of improvement, changing the nozzle
guide vanes exit angle. This is motivated by two reasons.
The first reason is that examination of the rotor calculations showed an efficiency improvement
'It must be understood that the fraction of loss we want to recover cannot be set arbitrarily as a design goal.
Modifying the design means also changing the operating point, so that a gain on one side could provoke increased
loss. The design procedure is very helpful in the sense that it gives a realistic upper bound of the expected gain
32
0.65
0.64
PR = 2
0.63
PR - 1.65
.0 0.62
PR= 1.65
--
C
C.,
PR=2
a, 0.6
0.59
.58
1.5
..... .
1.6
1.7
2
2.1
2.2
1.8
1.9
Rotor exit radius (mm)
2.3
2.4
2.5
Figure 3-1: Parametric study: turbine stage efficiency vs. rotor exit radius (NGV turning constant
at 74 degrees)
1
-
*
-
0.80
-K-
C,,
E 0.6 /-
-
0
C
U-.4
.
0.2
* ..-.....
- Baseline designImproved design (Exit area increased by 91%)
-_Uniform exit, no back flow
-*-
0
0.2
0.6
0.4
Fraction of exit area used
0.8
1
Figure 3-2: Fraction of the exit area used for exit mass through flow
33
at higher flow angles than that delivered by the baseline NGV. So increasing the loading on the
NGV may help if the efficiency improvement is not offset by the NGV loss increase. The baseline
turbine stage has a reaction of 0.27, so this redesign effort will tend to decrease the reaction.
Usually, impulse turbines (reaction equal to zero) have a lower efficiency because they have a small
pressure drop in the rotor and thus more viscous loss, so our redesign effort may not be successful.
As the design procedure integrates a vane loss coefficient which depends on the turning angle,
as shown in section 2.4.2 page 28, we can find the optimum NGV angle for stage efficiency and
know if we should increase or decrease the reaction.
Figure 3-3 shows that the baseline nozzle guide vanes already have a well chosen exit angle
at 74 degrees. The graph shows also that an increase of a few degrees may gain a few points of
efficiency. The higher the pressure ratio, the larger the gain. If we add the fact that in the design
procedure, the pressure ratio (and thus the Reynolds number) does not affect the nozzle guide vane
loss coefficient, we can expect a larger gain when the stage pressure ratio increases with the new
compressor design (from 1.65 for the baseline to 2.1 for the improved compressor). Anticipation
of engine future growth and gain in Reynolds number may be a good reason to increase the NGV
turning angle.
The second reason to increase the NGV exit angle is the need to control the turbine stage mass
flow. For the baseline design, we have demonstrated previously in section 2.3 that the mass flow
predicted by the 3-D CFD is less than the design mass flow. The baseline turbine operating at a
pressure ratio of 1.65 (near the optimum of the baseline compressor) requires a blade height of 450
pm to pass the design mass flow. This is equivalent to a blade height 12% higher than that of the
compressor. If the turbine blade height is set as a requirement, then we can exercise this control
on the mass flow to match the compressor mass flow from a specified blade height.
The nozzle guide vane exit angle exercises a tight control on the stage mass flow, well before
choking, because of the large pressure drop in the vanes and the associated impact on the stage
performance. As sketched in figure 3-4, the mass flow varies considerably from the design value of
0.36 g/s. In order to match the improved turbine stage to the improved compressor (hollow blades,
open trailing edge), the NGV was rotated by 4 degrees. The resulting turbine mass flow computed
in 3-D matched that predicted by the design procedure. This implies the turbine etch depth can
be the same as that of the compressor if the compressor delivers the expected pressure ratio of 2.1
34
0.66
PR
=2
0.64>-0.62
a
PR071.6
0.58 0.56 PR
2
0.540.52
60
65
75
70
80
85
NGV exit angle (degrees)
Figure 3-3: Parametric study: NGV turning vs. turbine stage efficiency (Rotor exit radius constant
at 2.0 mm)
35
PR
w1.2
E
2
0.8
0
S0.4 .....
7
70
6
D0.6
E
80
8
80
85
.
.2
60
65
75
70
NGV exit angle (degrees)
Figure 3-4: Parametric study: NGV turning vs. turbine mass flow (Rotor exit radius constant at
2.0 mm)
at a mass flow of 0.29 g.s- 1 .
3.3
Exit Diffuser Shaping
We present here an effort to reduce the viscous loss at the exit right angle turn and to decrease
the exit flow kinetic energy 2
The initial analysis, performed on the baseline turbine, estimated the combined loss and kinetic
energy at the stage exit as 27% of the total power available (figure 3-9 page 44).
Before geometric design, it is useful to make a rough estimation of the fraction we could recover,
to set a realistic design goal. This process, used in the other sections, is illustrated here:
2
Reducing the exit flow kinetic energy means a reduction in the engine thrust and higher power extraction under
the form of shaft power. This is desired for the portable power generation with a generator mounted on the compressor,
but not for a micro jet engine.
36
e Choose simplifying assumptions to estimate best scenario: in our case, we assumed we could
avoid viscous loss in the shaped exit diffuser (in particular no separation) and that the flow
can be diffused to the maximum available exit area, down to the minimum velocity satisfying
mass conservation. Using this set of assumptions, it was determined that 21% out of 27%
might be recovered.
" Redistribution of the recovered work: the work which is recovered is not recovered fully as
shaft work, because the operating point is displaced by the design change. So marginally,
we can reasonably assume that the recovered work is redistributed between the remaining
categories, proportionally to their current relative importance. In the case of the baseline
design, the shaft work would then increase from 30% to 38%.
" Decision to pursue: the estimated gain of 8% of shaft work is valuable, so the decision was
taken to design a shaped exit diffuser and estimate its performance with CFD.
The first geometric iteration was designed by Professor Mark Drela, using the 2-D code MISES
and operating data from Fluent in 3-D. A quick optimization resulted in the shape drawn in figure
3-5.
The first 3-D calculations showed that the concept did not look promising:
" 2-D design predicts that a very long diffuser is required to increase the effective area. In
other words, the boundary layer is very sensitive to diffusion and attempts to increase the
area abruptly lead to separation.
" 3-D simulations confirmed that: the boundary layer separated very soon in the diffuser, so
that there was no increase in effective exit area compared to a case with a sharp right angle
turn.
" Because of the diffuser length, viscous loss was not negligible.
* Finally, the shaft work increase was only on the order of 1% rather than the 8% expected.
This 1% improvement may be due to CFD uncertainties, so it is not significant.
Other issues also make this diffuser concept less viable:
37
Centerline
Rotor disk
Rotor inlet
-
blade
Rotor hub
J,
Exit diffuser
i
I hrust bearing
Rotor outlet
Figure 3-5: Schematic of the turbine rotor with a shaped exit diffuser
* Shaped diffuser are usually not robust to off design operation and there is still a large uncertainty in the operating point of the micro engine.
" Manufacturing of a curved shape is difficult in silicon (other materials may be used, but must
sustain high temperature).
For the reasons above, the concept was put aside to give more time to work on film cooling
studies.
3.4
Comparison of Baseline and Improved Turbine Stage
This section focuses on the comparison of the baseline design with the improved design. Three
types of information are presented.
The first is simply a view of the turbine stage geometry, along with views of the mesh used to
simulate the flow with Fluent.
The second is a comparison of the expected operating point of the stages, at 100% design speed,
with a balance of mass flow and pressure (but not heat flux or shaft work). It is very important
38
Metrics
Nozzle Guide Vane
Baseline stage
Baseline design (8 blades)
Improved stage
Baseline + 4 degrees
NGV exit angle (degree)
74
77
Rotor inlet radius (mm)
Rotor exit radius (mm)
Number of rotor blades
2.5
1.5
15
2.96
2
20 (21 for fabrication)
Table 3.1: Summary of design characteristics of the baseline turbine design and the improved stage
to remember that the baseline turbine stage is coupled to the baseline compressor, whereas the
improved turbine stage is coupled to the improved compressor rotor with hollow blades and open
trailing edge.
Third performance maps of the turbines are presented. They provide data for comparison across
an operating range.
3.4.1
Presentation of the Baseline and Improved Turbine Stage
Figure 3-6 and 3-7 show example of the meshes which were used for the computations. The
number of nodes ranged from 100,000 to 150,000 to allow for fast computations and design studies.
Boundary layers are resolved on end walls, on the blade surface (including the blade tip) and appear
on the figures as dark and thick lines. The new stator is not included because the only difference
from the baseline stator is a rotation of 4 degrees as detailed in table 3.1.
A top view of the baseline and improved turbine stage is presented in figure 3-8. The improved
rotor is quite different, because the leading edge radius has been moved upstream up to 2.96 mm
and the trailing edge radius moved upstream to 2 mm to increase the exit area as explained in
the first section of this chapter. All calculations on this rotor have been performed with a 20
blades rotor, but to limit unsteady interaction with the nozzle guide vane wake, a 21 blades rotor
is proposed for fabrication. The impact of the addition of a blade has been assessed on another
design (iteration 3) and has showed a 1.5% efficiency improvement and 0.5% mass flow decrease.
39
Figure 3-6: Perspective of the grid for baseline nozzle guide vane
3.4.2
Comparison at Expected Operating Point
Table 3.2 summarizes the design point performance of the two turbine stages. These figures
could be used later as a starting point for further analysis on the engine.
In this thesis, the efficiency is based on the pressure ratio between the total pressure at the NGV
inlet (radius 4.8 mm) and the static pressure at the engine exhaust, after the right angle turn. This
means this definition includes loss at the nozzle exhaust. For instance, the peak efficiency of the
improved turbine stage, with this convention including the exhaust nozzle, is around 58% whereas
for the same case, the total to total efficiency excluding the nozzle exhaust turns out to be 74%.
We should keep this in mind and estimate the total to total efficiency of the turbine stage alone to
be 15% (low mass flow) to 17% (high mass flow) higher than all figures presented here.
It should also be noted that the stage efficiency does not include the effect of the flow exiting
the journal bearing, which results in an efficiency drop of 2 to 5% according to the study performed
on the baseline design presented in appendix B.
Another way to look at this performance is to assess the sources of useful work and loss in the
stage. The following pie charts, in figure 3-9, were useful in prioritizing the issues for improvement.
It should be noted that the way exit loss, exit swirl and residual kinetic energy are calculated is
somewhat arbitrary: the residual swirl can be computed at the blade exit or after the right angle
40
O
e-
-D
O
C
Q
0
-
bO0
1-4
0.6 cm
0.96 cm
Figure 3-8: Top view of the baseline turbine stage (top) and the improved turbine stage (bottom)
(outer diameters of the rotor and stator are indicated)
42
Metrics
Stage pressure ratio (-)
Baseline stage
1.65
Improved stage
2.1
Mass flow (g.s- 1 )
Shaft work (W)
Stage efficiency
0.228
15
0.3 (0.6 in 2-D)
0.293
49
0.54
0.27
0.13
32
25
22
37
Reaction
Heat to disk (W)
Heat to blades (W)
Table 3.2: Summary of stage performance of the baseline and improved design
turn. We have chosen to calculate it after the right angle turn, consistently.
3.4.3
Comparison of Performance Maps
Table 3.3 gives the reference and design quantities used to draw the turbine maps. The reference
power is the power provided by the improved turbine stage, at 100% speed, for a pressure ratio of
2.5. This power reference is then used to non-dimensionalize the power maps of the baseline and
improved turbine. This convention is prefered to a power reference related to the engine cycle to
make it independent of the compressor performance.
For the heat flux, an average Stanton number is defined as followed:
Q = St S pU CPref (Ttiniet - Twau1 )
(3.1)
Q in the dimensional heat flux (in W) and S is the surface area. In order to calculate pU, a
reference value has been calculated at 100% speed and a pressure ratio of 2.5, at the rotor inlet.
Then for all other operating conditions, a correction based on the mass flow has been applied.
Figure 3-10 shows baseline and improved turbine stage maps, with efficiency contours. Apart
from the net efficiency improvement, we can also notice the location of the peak efficiency: for the
baseline turbine, it is located very low in the map, at a pressure ratio near 1.5, whereas the peak
efficiency is reached for a pressure ratio above 2.5 for the improved stage. The new turbine has a
much better growth capability, as its efficiency increases, helping to close the thermodynamic cycle
even faster. We can also note a sharp decrease of the efficiency at high speed and low pressure ratio:
43
18%
Shaft work: 28%
losses: 7%
c energy: 12%
Residual swirl: 20%
Journal bearing effect: 1%
Exit viscous losses: 13%
Rotor viscous losses: 14%
NGV viscous losses: 13%
Shaft work: 54%
Residual kinetic energy: 7%
Exit viscous losses: 7%
Journal bearing effect: 3%
Residual swirl: 2%
Figure 3-9: Baseline stage (top) and improved stage (bottom): shaft work and loss distribution at
the predicted operating point
1,600
Reference Tt (K)
Reference Twau1 (K)
950
101,325
Reference P (Pa)
Reference Cp (J.kg- 1 .K- 1 )
1075
Reference power (W)
Design pressure ratio (-)
Design mass flow (g.s- 1 )
80
2.5
0.36
Table 3.3: Reference and design quantities for the turbine maps
44
in this area, the numerical convergence becomes bad. The flow quantities still have large residuals
(1/100 compared to a required maximum of 1/1000), the mass flow at inlet and outlet can differ by
up to 3%, and a large separation at the blade pressure side due to the very negative angle of attack
of the flow is probably not well handled by the code, as it can be observed in figure 3-11. For these
reasons, we do not have as much confidence in the results in this region of the performance map.
Work contours are shown in figure 3-12. They are provided as complements to the efficiency
maps to express turbine performance in terms of dimensional numbers.
The Stanton number, which was introduced previously, is of importance in the next chapter.
The Stanton number maps 3-13 and 3-14 on the rotor disk and on the rotor blades provide general
information on heat transfer in the micro turbine.
First, we can notice that the Stanton number on the turbine disk has been reduced by approximately 40% by the redesign effort. The suggested explanation for this is the fact that the blades
were moved upstream, so that the flow temperature drop (due to work extraction) occurs sooner.
Second, the Stanton number on the blade has not changed from one design to another. This is
at first glance surprising, because the number of blades has been increased from 15 to 20 and heat
transfer occurs mostly at the leading edge of the blades and at the trailing edge on the pressure
surface, both areas where the friction is high. However, it turns out that the surface of each blade
remained nearly constant (5% increase); as the physics has not changed, the Stanton number can
be expected to remain constant. The only change is the total blade surface which increased by
40%, leading to an equivalent increase in the dimensional heat transfer
Q.
To conclude this comparison, it is clear that the design procedure has helped improve turbine
performance.
But still, the cycle cannot be closed with the projected non-adiabatic compressor
performance. The next chapter focuses on film cooling to reduce heat flux to the turbine and thus
the compressor.
45
-A
5.5
I
54.54-
4/0, fraction of design
3.51.0
0.9
0.8
3
2.5-
.
-
21.51
'
0.6
0.8
1
1.2
1.4
(Mass flow 40/8) (Q/40), fraction of design
5.5
5/40, fraction of design
4.50.9
0.8
1.2
1.0
4-
3.5-
32.5-. .
-.-0.55
. .---......--
2-
1.5-
1
0.6
1
0.8
1.2
1.4
(Mass flow 40/8) (Q/'9), fraction of design
Figure 3-10: Performance map: efficiency contours of baseline design (top) and improved design
(bottom)
46
-4
Vt
4'J
Figure 3-11: Relative velocity vectors at mid span, for the improved rotor, at PR = 1.55 and 120%
design speed
47
5.5
54.54W/A, fraction of design
3.51.0
0.9
0.8
3
0.7-
2.5
05
06
.- -
. 0.5
0.4
2-
0 .3 ..... .. . . .... . .. ..
0.3-2
0.2 -- - Z
1.51
..-.-.-
1.4
1.2
1
0.8
(Mass flow I0/S) (Q/0), fraction of design
0.6
5.5
I
5-
Q/O, fraction
of design
4.51.0
0.9
0.8
1.2
2
43.5-
1.5-
3 --
2.5-1*......
... ...........
...
---
2 .5 -
2-
- s
-..
1- .....
-..
0.5
-
-
1.51
'
0.6
1.2
1
0.8
(Mass flow '0/S) (Q/1), fraction of design
1.4
Figure 3-12: Performance map: shaft work contours (reference = 80 W) of baseline design (top)
and improved design (bottom)
48
5.5
54.54WA/O, fraction of design
3.51.0
0.9
0.8
3_
... ...01
2.5 -
4
0
0...
0 15-0.016.-.
2-
0.017..
0.018
0.019
1.51
1.4
1.2
1
0.8
(Mass flow A0/8) (Q/O), fraction of design
0.6
5.5
5-
Q/O, fraction of design
4.51.0
0.9
0.8
1.2
4
0.00
.
...
0
3.5 -
-006 .............
2.5S0.008 0.009
-
-- 01.--0
.
1.5-
1
.0.01
008
.........
0
.-
...
12-
0.6
0.8
(Mass flow 40/1)
1.2
1
(Q/O), fraction of design
1.4
Figure 3-13: Performance map: disk Stanton number contours of baseline design (top) and improved
design (bottom)
49
5.5
54.54-
Q/O, fraction of design
3.51.0
0.9
0.8
3_
0.
4.
-
2.5 -
0.0 16 - . . .. .
... . .
.
..
0.018-
2 -
-- 0.02-
1.5-
- 0.022
1
'
0.8
(Mass flow
0.6
1.2
1
1.4
0/S) (Q/O), fraction of design
5.5
5-
Q/40,
fraction of design
4.51.2
1.0
0.9
0.8
4-
-
3.5-
-
0.1
32.5
-
1
.
2-
0-1
-.
16~
00.06
1.51Q
0.6
1.2
1
0.8
(Mass flow 40/) (Q/4), fraction of design
1.4
Figure 3-14: Performance map: blade Stanton number contours of baseline design (top) and improved design (bottom)
50
Chapter 4
Cooling Studies
Having addressed the turbine aerodynamic performance alone, the next step is to address the
heat transfer issue.
It has been shown that the compressor efficiency and pressure ratio drop
significantly with heat addition from the turbine. The impact on the cycle performance is even
more dramatic as the pressure ratio affects other components' efficiency, such as the combustor.
In this chapter, we first estimate the heat flow without cooling and then the fraction of it
we can remove with film cooling. The first section summarizes the current engine performance
with conduction cooling and estimations of heat transfer levels. The second section provides a
basic assessment and classification of the risks and of the potential gains, both using simplified
axisymmetric and 2-D representations of the turbine. The last section presents a more detailed
study of disk cooling using 3-D configurations.
4.1
4.1.1
Cycle Analysis with Conduction Cooling only
Cycle Analysis
Early in the design process it has been estimated that heat flux to the turbine rotor was high and
that silicon would soften if its temperature was to reach 950 K at the design speed. So a shaftless
design was adopted as the baseline, to avoid the presence of high thermal resistance between the
compressor and the turbine. Currently, those two components are diffusion bonded back-to-back,
so that the contact surface, a disk of radius 3 mm, has no thermal resistance.
With this design, however, the compressor efficiency is well below its adiabatic value. A cycle
51
1 .2 ,1
I
I
'c'C
0
O.8
0........
0.~.*
C
0
. .. . . . .. . . .. ... . . .. . . . . . ... .. . . .. . . . . .
0
~0.28
,I
0-
Baseline design
~
+-- Design iteration 1
-x - Design iteration 5
Improved design (iter. 10)
-*-
0.2
0.
0.25
0.3
0.35
0.4
Mass flow (g/s)
Figure 4-1: Normalized heat flux in the turbine rotor for various designs (see equation 4.3)
analysis performed by Dr. Yifang Gong [8], assuming a pressure ratio of 2.5 and a design mass flow
of 0.36 g.s-1, showed that the compressor performance was a limiting factor.
4.1.2
Discussion on Heat Transfer Predictions
Level of Heat Transfer
The level of heat transfer causing this compressor efficiency drop is presented on the graph 4-1.
Results are formatted to show the assumed relation between heat flux and mass flow for a laminar
flow, using the Reynolds analogy.
This analogy states that for fluid with a Prandtl number close to 1 (it is 0.7 for air, almost
constant with temperature), the Stanton number St and the friction coefficient Cf are related by
the following relation:
52
St
=
- C5
2
(4.1)
First, if we assume the flow is laminarl only, we know that the friction coefficient on a flat plate
is related to the Reynolds number (based on the plate length) according to the following relation:
C5 c
1
1
Re
(4.2)
Second, as the heat capacity Cp is almost constant in our temperature range, we get the
following relation between the dimensional heat flux
Q
=
St p U Cp (T i
Q
and the Reynolds number:
- Twaul) o( Cf Re oc VRe
(4.3)
Thus, the dimensional heat flux should be, for laminar flow assuming the Reynolds analogy
applies, proportional to the square root of the Reynolds number. In our case, we have compared
the heat flux to the square root of the mass flow.
The graph 4-1 presents the results of this comparison for different designs. It appears that the
approximation holds well in the range considered and could be applied to other designs. It can
be noted that the normalized heat flux is lower for the improved design compared to the baseline,
because the Stanton number on the improved turbine disk is lower than on the baseline turbine
disk (as noted in figure 3-13 page 49).
Uncertainty on Heat Transfer
Several factors may also be taken into consideration to help understand that these heat transfer
estimation are approximations:
* All calculations assume there is no boundary layer or thermal boundary layer at inlet. So the
friction and the heat transfer at the turbine disk leading edge are overestimated.
'Reynolds number Re in the turbine ranges from 1,000 to 3,000 depending on the length scales and locations of
reference. In general, flow disturbances can be observed at Re as low as 500, but transition occurs above 5,000, well
beyond the micro turbine Reynolds number. So we can reasonably assume the flow is and remain laminar in the
turbine.
53
"
A uniform combustor exit temperature profile was assumed. It was found in the literature that
non uniformities tend to increase heat transfer. The dual zone micro combustor apparently
produces a highly non uniform exit profile, which may reduce the heat flux to the turbine
disk but increase that to the turbine blades, and may change the need for blade cooling [7].
* The flow from the journal bearing may reduce the heat flux to the turbine disk. This effect
has been studied on the baseline geometry only, the results are presented in appendix B. This
effect should not be dominant if the journal flow represents less than 10% of the total mass
flow.
" The uncertainty of the code itself is unknown. This commercial code is widely used, including
the design of heat exchangers.
Metrics for Film Cooling Effectiveness
To conclude this section, the goal of the following studies is to determine the feasibility of film
cooling, the main drivers of effectiveness, and to quantify the cooling effectiveness under realistic
conditions in the domain of operation. The metric used throughout this chapter is the isothermal
cooling effectiveness, defined as:
_
Qwith cooling
Qwithout cooling Qwithout cooling
(4.4)
The comparison is made on cases with the same mass flow and the same inlet total temperature
(1,600 K averaged on the main inlet and coolant inlet). In the numerical simulations, the mass
flow of the non-cooled cases are interpolated using a first order approximation, whereas the hot
flow total temperature of the cooled case is increased until the mass averaged over the hot inlet
and coolant inlet is 1,600 K ± 1 K.
Another possible metric is the adiabatic effectiveness, defined as a ratio of adiabatic wall temperatures. This is often used in research papers, because of the analogy of heat transfer with mass
transfer: instead of maintaining fixed wall temperatures (difficult) or maintaining adiabatic wall
conditions (very difficult), people use tracers and measure their concentrations. Then they deduce
an adiabatic cooling effectiveness using the heat-mass transfer analogy (R.J. Goldstein has pub-
54
lished several literature reviews, a good introduction to heat transfer problems [7]). But there is an
argument on the relations between the adiabatic and isothermal effectiveness. As the micro engine
structure is mostly isothermal, the latter metrics is preferred here.
4.2
Primary Study of Film Cooling: Risks and Potential Effectiveness (2-D)
As shown in the previous section, the turbine is cooled by conduction to the compressor. An
additional cooling scheme is then required to limit heat transfer to the turbine and, by doing so,
to significantly improve the engine performance.
Because maintaining a large temperature gradient in the rotor is difficult due to the high thermal conductivity and small scale of the device 2 , almost all of the heat transfered into the turbine
is ultimately transfered to the air being compressed. So limiting heat transfer before it occurs is a
good strategy.
Also any cooling scheme using a coolant layer can be combined with others techniques to further
limit heat transfer. Turbine blades with passages for blade cooling, silicon carbide inserts for higher
turbine temperature, reduce shaft area for lower compressor temperature, and higher etch depths
are some of the techniques currently being investigated to explore the cooling design space.
The first and second sections present several risks associated with film cooling and analyze the
risk of coolant layer centrifugation. The third and fourth sections present the 2-D study performed
to estimate the effectiveness of film cooling and its price in terms of mass flow, for two configuration
of disk and blade cooling.
4.2.1
General Considerations on Film Cooling
We describe and discuss here the importance of detrimental effects on film cooling generally
observed in conventional turbomachines and studied in research papers:
2
A heat transfer model built by J. Protz and updated by S. Evans shows that a shaft area of 1% of the turbine disk
area is required to establish a temperature gradient in the rotor and cut heat transfer to the fluid in the compressor.
Structural simulations by H.S. Moon predicted a somewhat higher minimum shaft area.
55
"
Centrifugation of the coolant layer due to rotation. Because the coolant layer has a higher
density and lower momentum than the main flow, it is more sensitive to the adverse reduced
pressure gradient, which is a combination of the favorable static pressure gradient and adverse
centrifugal force. The risk of centrifugation of the coolant layer is considered the most critical
for film cooling. A detailed study is presented in section 4.2.2.
" Appropriate coverage of the cooled surface. Because coolant injection reduces the average inlet
temperature at the rotor inlet, we must compensate with an adequate increase of the main
flow temperature. If part of the rotor surface is not covered by coolant, it will have a much
higher heat transfer and may make the cooling scheme ineffective. Appropriate coverage was
found to be critical for successful disk cooling, as shown later in section 4.3.
" Injection angle. Normal injection is the worst case, because it can lead to a blow off effect;
the coolant velocity is too high and separates the boundary layer downstream of the injection
slot. Tangential injection is the best case, because in this case the high coolant velocity may
help the boundary layer to stay attached. But tangential injection is difficult to manufacture.
For blade cooling, cooling slots with an angle close to zero could be achieved because of the
2-D etching process. But for disk cooling, the choice is limited to tangential injection from
the static structure (this requires another wafer in the stack) or normal injection on the rotor
itself (this requires another wafer for the rotor).
" Temperature non uniformities at the main inlet. It was generally observed in conventional
turbomachines that temperature non uniformities at inlet induce higher heat transfer than
uniform temperature profiles (with the same mass average).
Both the dual-zone combustor
and the nozzle guide vanes produce significant temperature non uniformities, the former
because of incomplete thermal mixing and the later because of secondary flows. Those factors
were not included in this study because they require a higher complexity in the simulation
effort.
" Preexisting boundary layer before the injection location. A preexisting viscous and thermal
boundary layer may reduce the initial mixing of the coolant and increases the cooling effectiveness. This effect is not well known, and no clear trend can be drawn. For instance, in a
research paper by Seban [11], the resulting effect was found to be small.
56
* Curvature effects. Curvature may help for blade cooling on the pressure surface, because high
coolant tangential velocity helps to keep the boundary layer attached, whereas on the suction
side, curvature is detrimental for both normal and tangential coolant velocities because of the
blow off and mixing effects (Conclusion from Schwarz et al [12]).
* Secondary flows. The strong secondary flows observed in the blade passage in the NGV and in
the rotor may impact on film cooling effectiveness. Those secondary flows cannot be avoided,
but more understanding is required to carefully optimize a film cooling scheme.
* Disturbancesof the boundary layer. Generally, any disturbance of the boundary layer, including film cooling, will increase the heat transfer coefficient. Features like slots, holes, bumps
and steps also increase thermal mixing, so that the cooling effectiveness may be reduced.
Worse of all are 3-D secondary flows which provoke drops in cooling effectiveness. For this
reason, blade cooling is probably more difficult than disk cooling. Unfortunately, this was not
confirmed with 3-D calculations as a part of this effort: 3-D calculations for blade cooling are
challenging because of the mesh complexity, so only 2-D calculations were performed (Section
4.2.4). Those do not capture the secondary flows observed generally on the NGV and rotor
blades in 3D without cooling.
* Wakes of upstream stages. The wakes from the NGV provoke a sweeping effect and increase
heat transfer. This is an unsteady effect, beyond the scope of this work.
Usually, no single film cooling scheme is sufficient to provide needed cooling effectiveness so
that several schemes are used and tailored to the local needs. Since low coolant velocity usually
gives the best results because thermal mixing and boundary layer disruption remain low, the area
covered by the coolant is small. Multiple injection slots or holes are then required. To estimate the
performance of multiple rows or holes, the resulting effectiveness of N cooling slots can be estimated
using the following formula:
N
1
-
?effective =
JJ(1
-
rT)
(4.5)
i=1
This equation is valid only near the injection slots because it assumes no mixing between
the coolant layers.
The downstream validity range is not well defined and depends on the slot
57
2400*
Model for Tt coolant = 700 K
Model for Tt coolant = 950 K
CFD points for Tt coolant = 700 K
ct2200 E
-.
2000 -.
-
E
:3 1800 -
1600
0
0.1
0.2
0.3
Fraction of coolant mass flow
0.4
0.5
Figure 4-2: Required combustor exit temperature to reach a mass-average inlet total temperature
of 1,600 K with a cooling scheme
geometry (slot width) and the blowing parameter (ratio of the density times the velocity for the
coolant relative to that of the main flow). Thus equation 4.5 should be used as an initial estimate
of complex geometries, before more precise calculations.
Also, from a systems point of view, the available amount of coolant is limited by two other
important factors.
The first is the effect of bleed on the cycle performance.
There is no short
answer to this question, and a cycle analysis is being performed by S. Evans [5] using results from
this thesis. The other important factor is the need to increase the combustor exit temperature
as the coolant bleed increases; to balance the injection of cold flow in the turbine, the main flow
temperature coming from the combustor is increased. To maintain a mass averaged temperature of
1,600 K at the turbine inlet, the combustor exit temperature has to match the temperature profile
in figure 4-2.
We can see that using a maximum combustor temperature of 2,000 K, we are limited to 30%
to 40% of bleed depending on the coolant temperature when it reaches the turbine.
58
R
Length
Velocity
Angular velocity
Density
Pressure
Vo
Qdesign
Poo
PoV
Table 4.1: Physical scales used in dimensionless equations
4.2.2
Coolant Layer Centrifugation on a Rotating Disk (2-D)
Centrifugation of the coolant layer, or reverse flow, can occur on a rotating disk when forces
induced by rotation overcome the favorable static pressure gradient and slow down the fluid. The
situation is worse for cold fluid. This mechanism is studied first by examining the momentum
equation and second with a 2-D axisymmetric CFD model.
The momentum equation of an incompressible fluid in a rotating frame can be written, in steady
state, as:
( . V)u =
VP
p
x r) - 2
-QOx (
xu+ vV 2 u
(4.6)
It can be rendered dimensionless using the characteristic variables specified in table 4.1 .
In dimensionless term, equation 4.6, with ' denoting dimensionless variables, can be rewritten
as:
Ro (u' * V')u' = -VP* - 2_'
x u' + Ek V' 2 u'
(4.7)
where Ro and Ek are the Rossby and Ekman numbers, defined as:
Ro
2QR
2QR
Inertia f orce due to f orced convection
Coriolis force due to rotation
Ek =
v
2QR 2
Viscous force
Coriolisforce
(4.8)
(4.9)
The Rossby and Ekman numbers are the governing parameters in this equation. The Ekman
number is very low in the micro-engine, on the order of 10-6 or less, so that the Coriolis force
59
dominates over the viscous force. As the estimated Rossby number is in the range 0.2-0.5, the
inertia force due to convection must be considered.
The following remarks and assumptions can be made:
" Centrifugation of some flow in the boundary layer is almost certain. Because the velocity is
close to zero in the boundary layer, the centrifugal force is larger than the pressure gradient at
the rotor disk leading edge. The flow entering the rotor initially has low momentum near the
end walls, so that this low momentum flow will almost certainly be centrifuged. Apart from
this, what we wish to know is whether a coolant layer can by its own momentum overcome the
adverse reduced pressure gradient (static pressure gradient plus centrifugal force) experienced
at the rotor inlet.
" The total temperature of the cold film and static temperature of the rotating disk are identical.
As noted previously in section B, the disk temperature is a lower bound for the cold film
temperature. However, results are not sensible for a temperature difference between the wall
and cold layer of up to 200 K, because mixing of the cold layer occurs both with the main
hot stream and with the thermal boundary layer on the disk.
" A constant coolant layer height has been used. For this problem, the relevant scale is the order
of magnitude of the thermal boundary layer on the rotating disk. As the Prandtl number
for air is 0.7 (near 1) and almost constant with the fluid temperature, the thermal boundary
layer has approximately the same thickness as the momentum boundary layer. The cold film
thickness has been fixed to the boundary layer thickness at the disk trailing edge on one
computed case without cooling, i.e. at 136 pm for a blade span of 400 pm.
e The model built to predict reverse flow in the coolant layer assumes the static pressure gradient
is constant and the Coriolis forces are small compared to centrifugalforces. The first assumption on the pressure gradient is reasonable because the static pressure gradient is roughly set
by the boundary conditions and the inviscid flow. The relative velocity in the boundary layer
should also stay small, which validates the second assumption. Consequently, the reverse flow
mechanism on the disk surface is set by the reduced pressure gradient (the static pressure
gradient and the centrifugal force). The model states then that reverse flow will be reached
60
1600 -*
1400
Reverse flow points from CFD
Reverse flow line from model
100% speed line
125% speed line
W1200 E
.2 1000
I-
4 <- Demo Engine
600
0.55
Zone of reverse flow
-+
0.5
-
erating Point
0.45
0.35
0.4
Rossby number
-
0.3
0.25
Figure 4-3: Minimum Rossby number to avoid coolant centrifugation of a cold film on a rotating
disk, inlet total temperature 1600 K
with a constant static pressure gradient and different wall temperatures T 1 , T 2 and angular
velocities Q 1 , Q 2 as long as the ratio of the centrifugal force to the pressure force is constant:
Centrifugalforce
-=CSTPressureforce
Q2
P1
_
2
P2
o<
2
- Twau
(4.10)
From figure 4-3 and figure 4-4 we can estimate that reverse flow in the coolant layer does not
appear at first glance to be a major issue. The operating point has been set arbitrarily at a wall
temperature of 950 K (weakening point of silicon at the design speed) because of similarity with
conventional gas turbine engines, where the turbine temperature is set very high. In our case, heat
transfer is a major driver to increase the turbine wall temperature.
However, the model is optimistic due to the simplifying assumptions. In particular, the cold film
may have a lower dynamic head due partly to total pressure loss in cooling ducts and due partly to
the boundary layer development in the nozzle guide vanes. The cold film could reverse in direction
because of this low dynamic head, although no modeling or estimations has been undertaken so
61
1600-1400--
*
-- -
Reverse flow point fro n CFD
Reverse flow line from model
100% speed line
-125% speed line
1,800 K
CD
1,600 K
Cz1200-
aE
0 1000-
Ne
operating po
0
Im 800
600
0.55
Zone of reverse flow
0.5
0.45
0.4
0.35
Rossby number
0.3
0.25
Figure 4-4: Minimum Rossby number to avoid coolant centrifugation of a cold film on a rotating
disk, inlet total temperature 1800 K (thin lines are Ttiniet = 1,600 K, figure 4-3)
62
Centerline
Main flow in
out
Coolant in
Figure 4-5: Schematic of the 2-D axisymmetric geometry
far. In terms of potential growth for the engine, any increase in rotation speed would have to be
balanced by a higher sustainable wall temperature or higher Rossby number (higher velocity).
4.2.3
Effectiveness of Disk Film Cooling (2-D CFD)
After the assessment of the risk of coolant centrifugation, we estimate with a simple CFD
model the potential cooling effectiveness of film cooling. The model uses the code Fluent on a
2-D axisymmetric disk. This allows a fast estimate to be used later as a "best case" goal in 3-D
calculations. Any discrepancy between the 2-D goal and 3-D results will prompt further in-depth
studies that lead to a determination of film cooling requirements.
The regular configuration presented first will be our 2-D baseline. The second configuration,
with a step between the main inlet and the rotating disk, is a first unsuccessful attempt to improve
film cooling effectiveness.
Regular Configuration
A perspective view of the regular configuration is presented in figure 4-5. The model is a 2-D
axisymmetric rotating disk, with a 400 pm high main inlet and a 15 pm cooling gap.
In this simplified model of the micro turbine disk, we used the following boundary conditions:
63
"
The coolant is injected normal to the main flow, through a 15 pm wide gap. This configuration
is the easiest to manufacture, but normal injection may not prove efficient. It turns out that
the largest issue is the presence of the blades which prevent the coolant to spread over the
whole disk surface.
e The coolant total temperature and the disk wall temperature are identical. As the coolant has
to go from the compressor exit through the static structure to the injectors, its temperature is
at least equal to the rotating structure temperature. This temperature ranges from 700 K to
1,000 K, which covers the range from the lowest estimate of the compressor disk temperature
to the highest sustainable turbine temperature.
" The coolant mass flow is increased by increasing the coolant total pressure. If the required
total pressure is not available at the compressor exit, then the width of the coolant injectors
must be increased.
e The mass average total temperature of the inlet and coolant flow is maintained at 1,600 K.
The inlet enthalpy has to remain constant because the turbine must extract the same power
with or without cooling.
" The operating conditions are close to the design operating point. It is not possible in this very
simplified model to have a high fidelity mainly because the work extracted by the rotating
disk through friction is very small compared to the work extracted in a turbine. The rotation
speed is 100% of the design value, the inlet pressure 1.5 atm, and the outlet pressure 1 atm.
Reynolds and Rossby number are respectively 2,070 and 0.523, for an uncooled case. As it
can be seen in the design space (figure 2-1 page 20), these Reynolds and Rossby numbers are
representative of operating conditions we simulate. So we have some confidence the operating
conditions considered in 2-D are representative.
The results of the first calculations are presented in figure 4-6, for wall temperatures of 600 K
and 1,000 K. The first observation is that it is possible to totally isolate the rotating disk with
30% of coolant.
The cooling effectiveness may also rise above 100% because the coolant static
temperature is lower than the disk wall temperature, the disk then heats the coolant.
The sec-
ond observation is that the cooling effectiveness does not change with the temperature (with our
64
-++-
Disk and coolant temperature: 600 K
Disk and coolant temperature: 1000 K
........................
..................................................
.... . .
.....
)0.
.
. . . . . . . . . .. . . . . . . . .. . . .
....................
.. . . . . . . . . . .
.............
0
0
S0.6
. ........ ................
.
..........
. ... ...
.......
..........
a)
0 0.4
..
........
............. ....................
...... ..
.........
0.2
0
0.1
0.2
0.3
Fraction of coolant mass flow over total mass flow
0.4
Figure 4-6: Cooling effectiveness of radial injection over a 2-D rotating disk
assumption that the coolant total temperature can be as low as the rotor temperature). But the
dimensional heat flux does increase when the disk temperature drops. This confirms we could find
an efficient cooling scheme at high rotor temperature (if thermal resistance is introduced between
the compressor and the turbine) where the heat flux would be minimized.
It can also be noted that with such a normal injection configuration, some centrifugation of
coolant can be expected, although the Rossby number and disk temperature are inside the normal operating range predicted in the previous section (in figure 4-3). With tangential injection,
centrifugation of the coolant layer could be limited with an increase in the cooling effectiveness,
estimated at 10% using very early calculations.
Configuration with a Step
In this subsection, we test the idea of a step between the NGV exit and the rotor inlet. The
goal is to increase the thermal boundary layer thickness so that the temperature gradient near the
65
Centerline
out
Main flow in
Coolant in
Figure 4-7: Schematic of the 2-D axisymmetric geometry with a 15 p m step between the vanes
exit and the rotor inlet
rotating disk and hence the heat flux are lower.
A perspective view of this configuration is
drawn in figure 4-7. The rotor disk is now 15 pm lower than the NGV bottom plane. A comparison
of the performance of both configuration, planar and with step, are presented in figure 4-8 for a
disk temperature of 700 K.
We can observe that for low coolant fractions, the step configuration with the step performs
up to 10% better than the planar case. This is probably due to the high friction near the disk
leading edge (thus high heat transfer) being reduced. But as the coolant fraction increases, the
advantage diminishes and ultimately is reversed. For high coolant fractions, the step may create a
large recirculation zone, increasing the thermal mixing.
4.2.4
Effectiveness of Blade Film Cooling (2-D CFD)
Blade cooling appears to be a more complex problem than disk cooling:
* First, 2-D etching in the axial direction limit blade cooling to a combination of internal
cooling and slot cooling, where the slots are etched in the axial direction from the blade tip to
some distance from the rotor disk supporting the blades. We seek high cooling effectiveness.
66
1
0
0.1
0.2
0.3
Fraction of coolant mass flow over total mass flow
Figure 4-8: Cooling effectiveness of radial injection over a 2-D rotating disk with a 15 pm step)
67
Internal cooling was not investigated. However, slot cooling effectiveness may be below our
specified cooling effectiveness due to strong secondary flows on the blade surface, blade surface
curvature in the current design, and poor distribution of the coolant injected normal to the
main flow.
e Second, 3-D calculations with complex blade shapes require a mesh more complex than that
required in disk cooling schemes.
For these reasons, it was decided to first make an estimate of blade film cooling using 2-D
calculations on a simple configuration.
* Single injectors. We study here only a single injector on each side of the blade, knowing that
the efficiency of multiple injectors could be estimated using the equation 4.5.
* Based on improved design. To speed up the process, we chose to use the improved rotor
geometry and etch the injection slot in it, instead of designing a new geometry optimized for
blade cooling.
* 30 degrees/30 pm injection. The geometry of the injection slot was determined by manufacturing and fluid dynamics considerations. The angle was set to 30 degrees to avoid creating
very thin walls which might have stress problems (a tangential injection is preferable but
requires radical change to the blade shape; this process was not attempted). The slot width
was set to 30 pm so that the slot Reynolds number would be on the order of several hundred,
and the conservative minimum feature size for manufacturing consideration. Improvements
should be possible if the effect of the slot Reynolds number is determined and if a smaller
feature size is allowed.
The resulting blade geometry is shown in figure 4-9. The coolant is injected at 30 degrees too
the main flow either from the pressure side and suction sides. The coolant temperature was set to
950 K, the same as the blade walls.
The isothermal cooling effectiveness computed is the blade cooling effectiveness, so that an
effectiveness of 50% for one of the injection side means the heat flux on this side of the blade is
68
blow u
Figure 4-9: View of the improved blade with coolant injectors at the leading edge
zero. Figure 4-10 presents the results for pressure side cooling and figure 4-11 shows the results for
suction side cooling. The required coolant supply pressure in the absolute frame is normalized by
a pressure of reference, 2.5 atm.
It can be noted that pressure side cooling has a low effectiveness. The reason is simply a blow-off
effect. At the pressure ratio of 2.5, the improved rotor, because of its thin, curved leading edge,
has a zone of low relative dynamic head flow on the pressure side. Because the main flow has a
low dynamic head, the coolant blows through the boundary layer, disrupts it, and does not stick
to the blade pressure side. Then thermal mixing with the main flow occurs and the coolant heats
up to the average flow temperature.
So with the current improved design, tangential injection may be the solution: because the
coolant would be turned by the blade shape, its velocity can be very high with no penalty. Another
improvement is suggested in figure 4-10: by reducing the slot width from 30 Pm to 20 pm, the
cooling effectiveness has been reduced. This is consistent with what we said in the previous paragraph: for the same coolant fraction, the cooling effectiveness is higher when the injection velocity
is lower, thus when the gap width is larger. So large slot width is recommended on the pressure side.
In figure 4-11, we can see that suction side cooling has a higher effectiveness, but requires a
higher coolant pressure. The higher effectiveness comes from the fact that the main flow dynamic
head (in the relative frame) is on the same order of the coolant dynamic head, so it deflects the
69
1.4
-
0.3
1.2L
Coolant Pt over compressor Pt -
C.
E
0
0.2 0
CU
0I~0.1-08
0
0
.
'>
0.1
0.08
0.06
0.04
0.02
Fraction of coolant mass flow over total mass flow
0.12
Figure 4-10: Pressure surface blade cooling: isothermal cooling effectiveness and required coolant
pressure for a 30 pm slot
coolant against the suction surface.
Tangential injection would help, but the effect would not be as strong as on the pressure side.
The higher required coolant pressure derives from the injection direction being approximately the
same as the disk velocity (the coolant absolute velocity is roughly the sum of the two, where for
pressure side cooling the absolute coolant velocity is the square root of the sum of the squares).
Another suggested improvement is to reduce the width of the slot: as it can be seen in figure 4-11,
a slot with a width of 20 pm instead of 30 pm would improve the cooling effectiveness by a few
points. This effect is opposite to what was observed on the pressure side: here an increase of coolant
velocity leads to an improvement of cooling effectiveness. A possible explanation would be a slower
thermal mixing and improved insulation at higher velocities, but this would have to be confirmed
more precisely.
We must also take into account the effect of blade cooling on the shaft work extracted by the
turbine. Figure 4-12 presents the results for both pressure and suction side cooling. The results
70
1.4
Coolant Pt over compressor Pt --+
-
1.2
.0.2
0
Wo
>
EE
00
CZC
e
FD result for a 20 tm slot
Sin
Z
0
Co0.1
-
0
0
-- Cooling effectiveness
0.1
0.08
0.06
0.04
0.02
Fraction of coolant mass flow over total mass flow
0.80
0.6
0.12
Figure 4-11: Suction surface blade cooling: isothermal cooling effectiveness and required coolant
pressure for a 30 pm slot
must be interpreted with care, because the coolant pressure is usually higher than the main inlet
pressure, leading to a higher work extraction. For instance, suction side cooling requires higher
coolant pressure than pressure side cooling, hence more work can be extracted.
4.3
Detailed Study of Disk Film Cooling (3-D CFD)
In this section, we study two strategies for disk film cooling. One considers coolant injection
from the static structure, similar to that done for the main flow through the NGV, the other
considers coolant injection from the rotor, assuming pressurized coolant can be introduced in the
rotating structure. In the first section, both schemes are compared in terms of ease of fabrication
and expected performance.
In sections two and three, the performance is explored using 3-D
numerical simulations.
71
0.1
-+-*-
Suction surface cooling
Pressure surface cooling
0.05
0
0.1
0.08
0.06
0.04
0.02
Fraction of coolant mass flow over total mass flow
0.12
Figure 4-12: Blade cooling: turbine work variation due to coolant injection
4.3.1
Advantages and Disadvantages of Injection from the Static Structure and
from the Rotor
Table 4.2 presents the major advantages and drawbacks of coolant injection either from the
static structure or from the rotor.
According to the primary study, coolant injection from the static structure may be easier to
manufacture and to implement but coolant injection from the rotating structure, despite its complexity, has a higher potential .
4.3.2
Disk Cooling with Injection from the Static Structure
We study here a simple configuration with coolant injection from the static structure. In the
numerical simulations, it is modeled by imposing non uniform temperature and pressure profiles at
the domain inlet.
We present here the major assumptions used in the numerical simulations:
72
Injection
Manufacturing
Coolant
ture
tempera-
Coolant pressure
Coolant losses
Disk coverage with
coolant
Injection configuration
Thermal mixing
Impact on other
cooling schemes
Impact on rotor imbalance
from static struc-
Injection from rotating struc-
ture
ture
+1 wafer in static structure, easy
to implement
high, because of proximity with
combustor (may require thermal
isolation of the static structure)
close to that of compressor exit,
because short distance from compressor exit and large volume
available for ducts
low, because Mach number can be
small in ducts
+1 wafer in rotating structure, requires precise alignment
low, because rotor is coolest part
of engine
good at design point only (blades
sweep coolant layer if coolant velocity is small compared to disk
speed)
tangential to main flow, high
coolant velocity possible
could be high before coolant layer
reaches turbine disk
can be used also to isolate static
structure
small (requires "only" high etch
depths)
higher than that of compressor
exit, because the coolant is spun
up by rotor (up to 10 W is needed)
high, may occur mainly during
coolant transfer from static to rotating structure
good coverage, robust to off design
operation (injection takes place in
the relative frame)
normal to main flow, low coolant
velocity required to avoid blow-off
occurs only when coolant isolates
turbine disk
can be used for shaft and blade
cooling
larger (requires complex rotor
structure)
Table 4.2: Advantages and disadvantages of coolant injection from a static or rotating structure
73
"
Step temperatureprofile. We are looking for a best estimate of disk cooling, so we impose a step
temperature profile at inlet. The inlet total temperature ranges from the coolant temperature
at 0% span to the main flow temperature above the coolant layer, whose thickness varies.
" Mass averaged inlet temperature set at 1,600 K. The main flow temperature has to be raised
accordingly to the coolant mass flow to maintain an average of 1,600 K at inlet (see figure
4-2), to maintain the thermodynamic cycle performance.
" Cycle pressure ratio is 2.5. Because cooling reduces the heat flux to the compressor, the
pressure ratio of the cycle tends to increase with cooling. So to reflect this, we assume the
compressor can deliver 2.5 atm. We also assume the combustor has a pressure ratio of 0.95
(the Mach number is below 0.1 in the combustor so viscous loss should be small) and the
NGV a pressure ratio of 0.9 (all 3-D calculations predict an NGV pressure ratio between 0.95
and 0.9) to estimate the pressure at the rotor inlet and the pressure available for cooling.
" Coolant viscous loss is identical to main flow viscous loss. The coolant total pressure decreases
in the cooling passages, from the compressor exit to the injection location. We assume here
the coolant has the same pressure loss as the main flow, although they go through different
channels (combustor and NGV for the main flow, coolant passages for the coolant). Thus,
both the main flow and the coolant have the same total pressure at the rotor inlet, except
for the "turbocharged" case, for which we assume the available coolant pressure is higher (to
demonstrate that high cooling effectiveness can be achieved in this case).
" Coolant mass flow controlled by coolant layer thickness and coolant pressure. As the coolant
pressure has only two different values in our model, the coolant mass flow is adjusted by
varying the coolant layer thickness. The total thickness of the main flow and the coolant
layer remains equal to 400 pm, the design etch depth considered in this thesis.
With these assumptions, we compute the cooling performance for the three cases. The boundary
conditions are summarized in table 4.3.
In table 4.3, the total pressure for the 77 degrees turbocharged case was set to match the coolant
and the turbine. Because the coolant has a higher density than the main flow, the coolant has a
lower velocity when the Mach numbers of the main flow and the coolant are equal. Thus the coolant
74
Case
Radial injection
77 degrees
77 degrees turbocharged
Tt (K)
700
700
700
Pt (atm)
2.1 (same as main flow)
2.1 (same as main flow)
3.5
Injection angle (degree)
0
77
77
Table 4.3: Boundary conditions for the coolant layer, in the three disk cooling cases with injection
from the static structure
is not matched to the turbine if it has the same pressure as the main flow. The coolant pressure
should be higher.
So the coolant total pressure was calculated using the isentropic formula, to match the main
flow velocity triangle.
Figure 4-13 presents the required compressor pressure (including viscous
loss) and the required coolant Mach number at the injection location. The model predicts that a
coolant injection pressure of 3 atm is required (assuming the compressor has a pressure ratio of
2.5). Assuming that the viscous loss is similar to the main flow, the required total pressure at the
compressor exit is 3.5 atm, well beyond what the compressor can deliver. It should also be noted
that the coolant is transonic at injection, a condition which may be difficult to realize in practice
and can lead to high blockage and viscous loss.
The results are however interesting, because they show the conditions needed for high cooling
effectiveness.
The comparison of the cooling effectiveness of the three cases is presented in several figures.
Figures 4-14 to 4-16 show the cooling effectiveness on the rotor, on the disk, and on the blades.
Because coolant injection requires an increase in the main flow temperature to maintain 1,600 K
at inlet, the heat flux on the turbine blades increases when the turbine disk is cooled. So we have
to look at the overall cooling effectiveness on the rotor (figure 4-14), which gives the overall performance of the scheme, as well as at the cooling effectiveness on the disk and on the blades (figures
4-15 and 4-16), which tell us why and where the scheme performs well.
The 77 degree injection scheme performs better than radial injection for coolant fraction below
0.2, mainly because of better disk cooling effectiveness.
75
For coolant fractions above 0.2, radial
1.4
E
+- uoolant total pressure
c
3.2
-1.2
cis
.
.. . . .
3 -
Coolant Mach number
. ..
-o
C:
0
00
0
2.6-
0.6
800
700
1000
900
Coolant total temperature (K)
1100
Figure 4-13: Required compressor pressure to inject coolant at 77 degrees matched to the improved
turbine
injection is preferable. The cooling effectiveness on the blades for both schemes is negative, which
means the heat transfer increases compared to a situation without cooling, but it increases less
quickly for radial injection.
As the coolant is injected with no tangential velocity, the coolant
layer hits the suction side of the blade and provide some residual cooling. In the case of 77 degree
injection, this effect is smaller.
Overall, the improvement due to the 77 degree injection is not persuasive. The main reason
is that even with 77 degree injection, the coolant is not matched to the turbine. We calculated
the relative coolant angle at the rotor inlet. It is equal to -54 degrees for radial injection, and for
-42 degrees for 77 degree injection. Because the total pressure is the same, the coolant has more
tangential velocity but its radial velocity drops, leading to poor cooling.
The turbocharged 77 degree injection performs much better than the other two schemes. The
overall cooling effectiveness can reach 50%, which means all the heat to the turbine disk is removed
(55% of the rotor heat flux occurs on the disk, 45% on the blades, approximately). Because the
disk cooling effectiveness is very good at low coolant fractions, the main flow temperature does not
76
0.
6
0.4C
-
-
)0.3---
0i)
0)
0.2
degrees. injection ............
-0.2 - -+- Tu b ch r e 77....
-0.2Dci-
Turbocharged 77 degrees injection
.....
n
7 e d Regular 77 degrees injection+
-0.3 Regula Irradial injectio'n
0
0.4
0.2
0.3
0.1
Fraction of coolant mass flow over total mass flow
0.5
Figure 4-14: 3-D cooling effectiveness ON THE ROTOR for 3 coolant injection conditions (radial,
77 degrees, 77 degrees high pressure)
increase quickly and the heat flux to the blades remains on the order of the uncooled cases. Thus
a high overall cooling effectiveness can be achieved.
Figure 4-17 shows the impact of coolant injection on the shaft work extracted by the turbine.
The results are compared with a model assuming the coolant is thermally mixed with the main
flow but does not participate in the work extraction process (this model is also used in appendix
B to predict the effect of the flow coming from the journal bearing). Radial injection results are
close to the model, confirming that coolant injection with no swirl has a large detrimental effect
on the turbine performance and should be avoided.
For 77 degree injection, the coolant has a
lower velocity, thus the coolant layer is turned into the blade passage by the pressure gradient and
the detrimental effect is reduced to an acceptable level. The case with 77 degree injection at high
pressure has almost no effect on the shaft work extracted by the turbine because the coolant is
matched to the turbine.
77
1.4
-+--
)
1.2
- +-
-_
Turbocharged 77 degrees injection
Regular 77 degrees injection
Regular radial injection
al)
a0 .8 -........
-..
.. ..
-
80.6c0.4-0.2
Wa
0
0.1
0.3
0.2
0.4
0.5
Fraction of coolant mass flow over total mass flow
Figure 4-15: 3-D cooling effectiveness ON THE DISK for 3 coolant injection conditions (radial, 77
degrees, 77 degrees high pressure)
78
-1k
u-0.1
)
F
0
0
'0
'N-
0
F
U,)
-0.4
-
*Turbocharged 77 degrees injection
Regular 77 degrees injection
-o - Regular radial injection
-+-
'
4
I1
0
0.4
0.3
0.2
0.1
Fraction of coolant mass flow over total mass flow
0.5
Figure 4-16: 3D cooling effectiveness ON THE BLADES for 3 coolant injection conditions (radial,
77 degrees, 77 degrees high pressure)
79
0.1
c
-0.2 -
a) -0.4 -0
-0.5-
-*--
-o
-*-
-0.6
0
Turbocharged 77 degrees injection
Regular 77 degrees injection
Regular radial injection
Model: thermal mixing & no work from coolant
0.3
0.4
0.1
0.2
Fraction of coolant mass flow over total mass flow
0.5
Figure 4-17: 3-D cooling effect on shaft work for 3 coolant injection conditions (radial, 77 degrees,
77 degrees high pressure)
80
So we have demonstrated that high cooling effectiveness can be reached if the coolant and the
main flow have the same velocity triangle when entering the rotor. However, the reason for this is
still unclear. There may be two major factors determining the success of disk cooling with injection
from the static structure. The first is the rate at which thermal mixing of the coolant layer and
the main flow occurs. The faster the coolant, the lower the thermal mixing before the coolant
significantly isolates the turbine disk. The second is the disk coverage, which is maximum when
the coolant is matched to the turbine.
In order to assess the relative importance of those factors, the disk cooling effectiveness for 77
degree injection at three coolant temperatures (700 K, 900 K, and 1,100 K) was compared. As
the coolant temperature increases, the coolant velocity triangles approach that of the main flow,
improving the disk coverage, but at the same time the heat capacity of the coolant decreases,
reducing the potential cooling effectiveness.
The results are presented in figure 4-18.
On one hand, it is shown that disk cooling peak
effectiveness decreases sharply as the coolant temperature increases. On the other hand, the scheme
becomes more robust as the coolant temperature increases, which may be due to a better disk
coverage and lower main flow temperature. So thermal mixing is important and is a limiting factor
of the cooling schemes using coolant injection from the static structure.
The previous remark, suggesting fast thermal mixing may limit the potential effectiveness of
schemes with injection from the static structure, prompts the need for a study of film cooling
schemes with injection directly from the rotating structure. This is the object of the next section.
4.3.3
Disk Cooling with Injection from the Rotor
As explained in table 4.2, coolant injection from the rotor may have a higher cooling effectiveness because it is possible to manufacture the coolant injectors at the chosen location and with
the chosen size. This may balance the fact that normal injection leads to a blow-off effect at high
velocity.
Two variations of cooling slot geometry were studied. The first one is based on the principle
that coolant should be injected at the turbine disk leading edge, where the shear and thus the
heat transfer are the highest. Moreover, the main flow there has a high dynamic head, reducing
81
0.4
Coolant 900 K
-e-
Coolant 1,100
a)S0.3
C)
830 0.2
0 .1.
0
0.1
0.2
0.3
0.4
0.5
Fraction of coolant mass flow over total mass flow (-)
Figure 4-18: 3-D cooling effectiveness ON THE DISK for 77 degree injection, for coolant temperatures equal to 700 K, 900 K, and 1100 K
82
the risk of blow-off. The second slot geometry is based on the results of the first geometry and on
the observation that high cooling effectiveness may be reached by achieving complete disk coverage.
Figures 4-19 and 4-20 show top views of the improved rotor with the first and second generation
cooling slot. In the numerical simulations, the slots have an etch depth of 30 pm, which is long
enough for the boundary layer to fully develop in the slot. The boundary condition imposed at the
base of the slot is the coolant velocity in the relative frame. The coolant static temperature is 950
K, which is the maximum allowable rotor temperature.
The achieved cooling effectiveness and shaft work variation is presented in figure 4-21 to 4-24.
The first observation is that we can achieve a higher cooling effectiveness with the first generation slot and 950 K coolant than with 77 degree injection from the static structure and 700 K
coolant.
We can also note that the second slot geometry does not perform better than the first slot. This
may be due to the fact that a higher disk coverage was not achieved. Plots of the coolant path lines
are not included because Fluent has some difficulty calculating them, but they seem to indicate
the secondary flows prevent the coolant from fully isolating the turbine disk. Thus, compared to
the first slot, coverage was not improved and more coolant flow is wasted by thermal mixing in the
secondary flows.
The main limitation of slot cooling appears to be the blow-off effect. The sharp drop in cooling
effectiveness occurs when the coolant dynamic head is on the same order as the main flow dynamic
head. Because the second slot is partly located near the blade pressure side, where the flow relative dynamic head is small, blow-off occurs earlier at lower coolant velocity than for the first slot.
Surprisingly, when blow-off occurs, the coolant tends to cool not the disk but the rotor blades, as
seen in the simultaneous sharp decrease in disk cooling effectiveness and sharp increase in blade
cooling effectiveness in figures 4-22 and 4-23.
There is still much room for improving coolant injection from the rotor. To suggest future work,
a configuration has been calculated using the first generation slot and reducing its width by one
83
Figure 4-19: Top view of a blade passage with first cooling slot geometry
84
Figure 4-20: Top view of a blade passage with second cooling slot geometry
85
0.16
CD,
2)0. 12
0.1
0)0.08
0
o006
a)0.04
-n
0.02
o
slot
1h
alf width
0
0.05
0.1
0.15
0.2
0.25
0.3
Fraction of coolant mass flow over total mass flow (-)
0.35
Figure 4-21: Disk cooling effectiveness ON THE ROTOR of two cooling configurations with injection from the disk
half. A single cooling effectiveness has been calculated and is represented in figures 4-21 to 4-24 by
a circle. We can see that the cooling effectiveness is reduced, suggesting increasing the slot width
instead of reducing it would lead to a cooling effectiveness improvement. This is consistent with
the fact that normal injection effectiveness decreases when the injection velocity increases. Thus
an efficient normal slot cooling scheme requires a large slot and a low coolant injection velocity.
86
0.45
0
0.25
0.3
0.2
0.15
0.05
0.1
Fraction of coolant mass flow over total mass flow (-)
0.35
Figure 4-22: Disk cooling effectiveness ON THE DISK of two cooling configurations with injection
from the disk
87
0.15
-*-Slot 1
-+Slot 2
o Slot 1 half width
C
C0.
0.05
0
CD,
- 0.05--
-0.1
0
0.3
0.2
0.25
0.1
0.15
0.05
Fraction of coolant mass flow over total mass flow (-)
0.35
Figure 4-23: Disk cooling effectiveness ON THE BLADES of two cooling configurations with injection from the disk
88
0.2
0.15
0.1
C:
0
0.05
-- Slot 1
Slot 2
o Slot 1 ha If width
all
0
-0.05
C/)
-0.1
-0.15
-0.2
0
0.3
0.05
0.1
0.15
0.2
0.25
Fraction of coolant mass flow over total mass flow (-)
0.35
Figure 4-24: Shaft work variation of two cooling configurations with injection from the disk
89
Chapter 5
Conclusion and Recommendations
5.1
Conclusions on Performance Improvements and Film Cooling
The research focused first on performance improvements resulting from a new blade design.
We have formulated and validated a design procedure, using 1-D theoretical analysis and correlations from 3-D CFD. It was shown that significant improvements over the baseline design could
be achieved:
" Improved matching. The design procedure results in an improved matching, between the
NGV and the turbine rotor as well as between the compressor and turbine stage.
" Reduced loss at stage exit. By increasing the turbine exit area and reducing the exit swirl,
the energy lost at the stage exit in the form of viscous loss in the right angle turn or residual
swirl has been reduced.
" Increased work extraction. The design procedure predicted higher turbine efficiency by decreasing the turbine reaction and moving the rotor blades upstream to the turbine disk leading
edge. 3-D simulations confirmed this higher efficiency.
" Exit diffuser shaping not successful. The effort to reduce the viscous loss at exit and increase
the pressure ratio across the turbine blades using an exit diffuser was not successful. Boundary
layer separation sensitivity, the high length of the diffuser, and manufacturing issues make it
difficult to implement.
90
The work on film cooling techniques concluded that:
e Film cooling techniques alone are not sufficient to close the thermodynamic cycle. This was
predicted by Dr. Yifang Gong using current estimates on film cooling effectiveness and coolant
flow requirements.
" Small turbomachinery improvements and film cooling is sufficient to close the cycle. Assuming
the compressor and turbine adiabatic efficiency can be improved by a few points, the current
film cooling effectiveness is sufficient to break even, using coolant injection from the rotor.
" Disk cooling and blade cooling techniques may be efficient. Cooling effectiveness of up to 40%
were reached for disk and blade cooling, each requiring a coolant fraction of 15%.
" Strong secondary flows require careful design of the coolant injectors. It was shown, using 3-D
CFD, that secondary flows did not prevent disk cooling effectiveness from reaching 40%. But
for blade cooling, only 2-D CFD was performed so we have not assessed the effect of those
secondary flows on blade cooling effectiveness.
" Effectiveness drivers are surface coverage and coolant velocity triangle for coolant injection
from the static structure. We have shown that the cooling effectiveness can approach unity
when the coolant has the same velocity triangle as the main flow. However, it is yet unclear
whether the reason for this is the complete disk surface coverage, the reduced thermal mixing
with the main flow, or a combination of both.
e The dual zone combustor exit temperatureprofile can be used for structural cooling. According
to our study, the combustor exit temperature profile may participate in disk cooling, up to
40% disk cooling effectiveness.
A requirement for the combustor would be to produce a
coolant layer of 40 pm ± 10 pm, at a temperature of 700 K, at the NGV exit. Because the
heat transfer coefficient is large on the NGV walls, and because 40 pm is on the order of
magnitude of the thermal boundary layer on the end walls, this requirement is equivalent to a
requirement of 700 K temperature on the inner NGV wall. This requirement may be difficult
to fulfill if we consider the large heat flux occuring to the NGV blades.
" Disk cooling with coolant injection from the static structure has a lower effectiveness than
with injection from the rotor. Injection from the static structure is limited by the available
91
coolant pressure, close to that of the compressor. For coolant injection from the rotor, the
coolant pressure can be increased above the compressor exit pressure. Thus, injection from
the rotating structure has high potential for delivering high cooling effectiveness.
* There is room for cooling techniques improvement. This research is only a preliminary study
of film cooling for a micro turbine. General considerations only lead to the design of several
configurations and it was shown that those configurations are not optimized.
5.2
Future Work
First, improved component efficiency is still a valuable effort. On the turbine side, the goal is
currently to achieve a total to static efficiency of 60%, including the loss due to the journal bearing
flow and the exit right angle turn. Increasing the turbine disk radius may be part of the solution
and is currently under investigation.
On film cooling techniques, more work is required to improve the cooling effectiveness and the
accuracy of the numerical simulations.
" As the dual zone combustor may provide some disk cooling, it is recommended that a coupled
fluid-structure analysis be performed to determine the temperature of the static structure
near the rotor. This temperature is of primary importance to understand the limit of cooling
effectiveness due to the combustor temperature profile.
It may also help to increase the
accuracy of other numerical simulations and analytical models by specifying a static wall
temperature closer to the expected value (currently the uncertainty is very large).
" We recommend actively pursuing work on coolant injection from the rotor. Cooling schemes
based on this would offer the highest degree of freedom to change and optimize the design
as the knowledge base increases.
We also showed that rotor injection can have a cooling
effectiveness similar to schemes based on injection from the static structure.
" Consequently, it is necessary to estimate the loss associated with the transfer of coolant from
the static structure to the rotor.
The study would also have to determine what coolant
pressure can be reached in the rotor.
92
Turbine blade
Thrust
NoMain flow
Turbine disk
Figure 5-1: Disk cooling injection from the rotor, with an additional cover plate to turn the coolant
towards the centerline
" As heat transfer to the blades is larger than heat transfer to the disk, in the current design,
we also recommend to increase the effort on blade cooling.
* As a limiting factor of disk cooling with injection from the rotor is the normal direction of the
coolant, studying concepts like the one presented in figure 5-1 may lead to significant increase
in cooling effectiveness. Issues will be mainly linked with the realization of a complex rotor
structure and must comply with other requirements such as a small rotor imbalance.
93
Appendix A
Validation of Fluent
In this section, the code is presented and validated. It is first validated in 2-D against the code
used to design initially the turbomachinery, MISES (Multiple blade Interacting Stream tube Euler
Solver, Drela et al [2]), developed by Drela and Houngren. Then it is validated in 3-D against experimental data from the macro compressor rig, the only rig at the time of this writting to provide
turbomachinery data1 . The validation in 3-D was performed by Dr. Yifang Gong and showed a
good agreement, both with integrated measures (raw performance) and with local measures (velocity profiles). The result was considered satisfactory enough to pursue computational work using
Fluent until instrumented micro rigs data are available.
A.1
The Fluent Code
Fluent is a commercial package which contains a complete suite of software to build, simulate
and analyze a variety of cases[6). The capabilities include 2-D/3-D, incompressible or compressible
flow, steady-state or time-dependent solution, inviscid, laminar or turbulent flows, with heat transfer (forced or natural convection, radiation, conduction), with chemical reactions, in non-inertial
frames, and others not directly useful to the micro engine project.
Two solvers are available, one called segregated which resolves the momentum and mass'The primary performance concern for a turbojet being the micro compressor, no macro rig was built for the
micro turbine. In this thesis we show, after some work, that this turns out to be also the case in the micro scale but
for a different reason: heat transfer.
94
conservation equations sequentially, the other called coupled which resolves them as a coupled
system. Both use the same finite-volume discretization process and solve the governing integral
equations for the conservation of mass, momentum, energy and other scalars. They differ in the
way to linearize and solve the discretized equations and tailors the range of applications they can
effectively applied at.
A.1.1
The Segregated Solver
The solver uses this particular procedure:
" Assuming a pressure field and face flux fields have been calculated at iteration n-1, the
discretized momentum equations are used to calculate a new velocity field at iteration n.
" This velocity field may not satisfy the continuity equation. A pressure-velocity coupling is
then stated, to transform the continuity equation into a pressure correction equation. This
pressure correction is used to update the pressure field and the velocity field and the mass
flux to ensure that the continuity equation is verified at this step n.
" The other equations (such as turbulence or energy) are solved sequentially.
This solver has been proven to be very effective, in term of speed of convergence and accuracy,
for a large range of cases. So it has consequently been used successfully to simulate the flow in the
nozzle guide vanes in all calculations presented in this thesis. However, two main situations require
the use of another solver:
" Since density is not directly related to pressure in incompressible flows, pressure does not
appear explicitly in the continuity equation. For this reason, this solver reaches its limits
when compressibility effects become dominant. The solver should not be used to model high
subsonic flows.
" This solver also failed significantly in 2-D axisymmetric models with high swirl (60 degrees)
and rotation (above 60,000 RPM), so that we do not recommend the segregated solver for
rotating flows without further investigation in the micro engine project.
95
A.1.2
The Coupled Solver
The coupled solver has a more classic approach, as it tries to solve the continuity and the momentum and the energy equations as a coupled system. It uses a pre-conditioning technique aimed
at improving the convergence rate for low Mach number or incompressible flows.
This solver was preferably used to model the turbine rotor, because of the higher level of accuracy
expected in flows with swirl and strong body forces due to rotation. This choice relies on the code
manual and unphysical results obtained with the other solver as explained above.
A.2
Validation in 2-D (Turbine Geometry)
The goal of this validation is two fold, first to estimate how well Fluent predicts the turbine
flow, second to validate MISES as an assessment of the 2-D design procedure.
To achieve this goal, results were compared using similar cases (Cases. NGV9b and Tdesl4.wb3):
" Identical turbine geometry: baseline geometry designed in September 1998, before modification by Jacobson (top figure 3-8.
* Identical computational domains.
* Identical boundary conditions 2 : Pt and Tt at the domain inlet, P at the domain exit, T on
the blade surface. The values are in the design space for the micro engine.
The results of this comparison for a scalar q are summarized in table A.1 and table A.2 under
the form:
Relative difference
qFluent - qMISES
qMISES
(A.1)
Preliminary conclusions can be drawn from this 2-D evaluation:
* The flow is most probably laminar. The Reynolds number in the micro turbine is in the
low range 1000 to 1500 and Fluent computations, using the same turbulence model as that
2
As MISES and Fluent use different solvers, the boundary conditions in Fluent are the values extracted from
MISES by post processing.
96
MISES
2.21
Fluent relative difference
0.2%
Ttout (K)
Mout (-)
Flow angle (degree)
1600
0.853
73.7
0.7%
-1.1%
-0.8%
rh (g/s)
0.419
2.0%
-19.4
-23.7%
Ptou
1 t (atm)
Q
(W)
Table A.1: Fluent 2-D/MISES comparison for baseline NGV
Ptout (atm)
Ttout (K)
Mout (-)
Flow angle (degree)
rh (g/s)
Q (W)
MISES
1.27
Fluent relative difference
0.05%
1376
0.54
-0.03
0.402
-29.5
0.8%
-1.3%
-0.7%
1.6%
-23.6%
Table A.2: Fluent 2-D/MISES comparison for baseline rotor
used for the compressor, concluded that turbulence production in the near wall region was
negligible compared to the free stream turbulence.
e Fluent 2-D and MISES agree very well, on averaged values, in the design space of interest:
low Reynolds number, laminar flow. This proves that MISES is a suitable 2-D design tool
only when the 2-D assumption is reasonable.
" Fluent predicts a heat flux 25% less than MISES. It is quite acceptable as heat transfer
predictions are usually not accurate. It turns out that the flow pattern is not very sensitive
to the heat transfer, so that adiabatic and isothermal calculations show similar results. The
heat flux itself is at first order proportional to the temperature difference between free stream
and walls, from 1000 K to 1600 K with an error of 5% lower than the overall expected accuracy.
97
Appendix B
Discussion on the Effect of the
Journal Bearing Flow
The journal bearing requires approximately 5% of the compressor flow.
This small flow is
derived from the "cold" compressor exhaust (600K) and exits on the turbine side between the
nozzle guide vanes and the rotor disk. This existing feature may effectively reduce heat transfer
into the turbine rotor; thus its effectiveness has to be addressed.
Several arguments exist in favor of this study:
" The journal bearing flow is a feature of the current and probably future designs. So it is
useful to roughly estimate its effect on the turbine performance and on the heat transfer. The
potential cooling effect is "free" because the flow is required for the bearing.
" As the flow comes from the compressor exhaust through a gap between the static structure
and the rotor, its temperature should be close to that of the rotor, thus providing us with a
large temperature difference with the main flow coming from the combustor.
However, other constraints affect the potential gain:
* The flow from the journal bearing is not matched to the rotor blades. The flow exiting the
bearing gap has an angle of -90 degrees. Only shear with the main hot flow can lower this
value, but we can expect the turbine efficiency to drop as the mass flux of this unmatched
fluid is increased.
98
"
The cold flow is initially normal to the turbine disk, so the fluid may not stick to the disk.
In that case, mixing with the main stream occurs and the heat transfer to the turbine disk is
not decreased.
" As the flow in the turbine is radially inward, the cold flow is more sensitive to centrifugal
forces which where estimated to be higher than the favorable pressure gradient at the rotor
inlet. So even if the cold flow adheres to the turbine disk, reverse flow (and thus mixing with
the hot main stream) may occur early and limit the cooling effectiveness.
Preliminary conclusions:
" The journal bearing flow does not adhere to the turbine stick.
Recirculation at the disk
leading edge is visible when the journal bearing flow reaches 20% of the total flow.
" The performance drop due to the cold unmatched fluid is roughly 1% of efficiency per percent
of flow coming from the journal bearing in the range 0% to 10%. If the journal bearing flow
represents between 10% and 20% of the total flow, the efficiency drop is doubled (figure figure
B-1 ).
" The cooling effectiveness of the journal bearing flow is very low, on the heat transfer to the
turbine disk and to the turbine blades (reduction occurs only at the blade roots). See figure
B-2 . The disk cooling effectiveness is approximately 1% per percent of journal bearing flow.
As heat transfer to the turbine disk is only half of the total heat transfer to the turbine rotor,
the resulting effectiveness on total heat transfer is negligible.
" The assumption that the journal bearing flow temperature is 1000 K may not be valid. A heat
transfer model developed by Simon Evans shows that the journal bearing flow temperature
would be approximately 1200 K, thus reducing even more the cooling effectiveness we can
expect from this flow.
The conclusion of this section is that the journal bearing flow in the baseline geometry does not
provide cooling since it does not adhere sufficiently to the disk, mixes with the hot main stream
and decreases significantly the turbine rotor performance.
99
*
--
a
CFD points for mass-average Tt inlet = 1,600 K
Model: thermal mixing & no work from journal flow
a
0
-0.1 F
Cz
*
0
cz
-0.2 H
C,)
5% design goal
-0.3F
10% achieved on test rig
0
0.05
0.1
0.15
Fraction of journal bearing mass flow over total mass flow
Figure B-1: Impact of the journal bearing flow on the turbine rotor efficiency (Baseline design)
30
0Cn
25
20
(Fz
15
.)
_0
0)
10
(n
E
CD
5
0
0
15
10
5
Flow coming from the journal bearing (%)
20
Figure B-2: Cooling effectiveness of the flow coming from the journal bearing (Baseline design).
100
Appendix C
Discussion on Typical Flow Features
in the Micro Turbine
This appendix presents some details of the results of 3-D calculations using Fluent. They are
presented as contact sheets showing:
" For the NGV: the reversible term of entropy due to heat transfer, the irreversible term of
entropy due to shear and temperature gradient, the total pressure, the total temperature, the
Mach number, and path lines.
" For the rotor: the swirl relative to the inlet, the reversible term of entropy, the irreversible
term of local entropy production, the static pressure, the static temperature, and path lines
in the relative frame.
The baseline design is always presented on the left column and the improved design on the right
column. Each quantity is presented at three different span locations: at 2.5% span from the blade
tip at the top of the page, at 50% span in the middle, and at 97.5% span at the bottom of the
page. The scale is the same for all six figures on each page.
The last contact sheet shows the baseline and improved rotor at the predicted matched operating point (pressure, temperature and mass flow are matched, but the turbine still provides less
power than that required by the compressor). Contours of swirl relative to the inlet swirl, local
entropy production, and static pressure are presented at mid span only.
101
All calculations shown here use the following boundary conditions:
* Exit pressure of 1 atm at the stage exit
* Static structure wall temperature of 1,100 K (NGV blades and all end walls)
" Rotating wall temperature of 950 K (Rotor blades and rotor disk)
" Rotation speed of 1.2 MRPM
The following remarks will help the reader interpret correctly the metrics presented:
* Swirl relative to inlet. By swirl relative to the inlet, we mean the ratio of the local tangential
velocity in the absolute frame to the average tangential velocity of the flow at the rotor inlet
(3 mm). The average is an area average at the specified fraction of the blade span: for each
span location, the swirl reference is different, so that the normalized swirl is always 1 at the
rotor inlet. It must also be noted that the values have been clipped between 0 and 1, so that
a normalized swirl higher than 1 appears in red and a negative normalized swirl appears in
blue. The normalized swirl may be higher than unity, for example, on the blade suction side
where the flow accelerates.
* Reversible term of entropy. The reversible term of entropy is the entropy due to heat transfer
between the fluid and the outside world. It is computed by Fluent using the following formula:
Sreversible
=
CV ( PPref
(P/Pref)?
(C.1)
1
In our case, heat flux is generally from the flow to the walls, so that the reversible term of
entropy decreases.
" Irreversible term of entropy production. This term is of great interest, because it represents
the production rate of entropy due to shear and temperature gradient. This term is always
positive and measures the irreversibility of a process. It is user-defined in Fluent (requires
the coupled solver) using the following formula given by A. Bonnet [1, p. 36]:
d
p T -(S
dt
-
Sreversible) =
102
D
+ A
(V T)2
T
(C.2)
where 4)D is the dissipation function and Ac the thermal conductivity.
The dissipation function of a Newtonian fluid is defined as:
9u
uD
S
av )
2
D
y
1
Dv
Ou
-
3 Dx
8x
m2 +
Dy
Dwm2
+
u
)
z
ay
ov
2
)
DX
(C.3)
a)2
In this equation, p is the molecular viscosity, and u, v, and w are the components of the
velocity vector.
It must be noted that we obtain a rate of entropy production, which is
a local value. To know how this entropy is convected by the flow, it would be necessary to
integrate this rate of production along a streamline. Fluent is not capable of such integrations
streamline integration.
9 Path lines. Path lines are 3-D lines, but the starting point of each line at the inlet of the blade
passage is at the specified span location. It must also be noted that Fluent does not properly
calculate the path lines exiting the rotor blade passage, so the lines end approximately at the
exit of the blade passage. This problem does not exist with the NGV calculations which use
a single non rotating frame. Also, because of the 3-D nature of path lines, they are difficult
to interpret. Essentially the goal is to show that end wall effects are large
C.1
Flow in the NGV for an Inlet Pressure of 2.1 atm
Generally, for the NGV and the rotor, the reversible term of entropy is large compared to the
irreversible term. Figure C-1 presents the reversible term of entropy due to heat transfer which is
very close to the plots of entropy (both reversible and irreversible) and so was thus not included.
In figure C-2, the local irreversible term of entropy production is presented. This is a local rate of
production, so no information is provided as to how it is convected by the flow. It can be noted
that the irreversible production seems to increase from the baseline to the improved design, which
is consistent with the increase of viscous loss due to a higher turning in the improved design.
103
The plots of total pressure, in figure C-3, show the wake of the NGV blade at mid span. On the
end walls, the total pressure is equal to the static pressure so we can see there is no difference due to
the combustor step, on the side of the NGV blade root (0% span). The plots of total temperature
in figure C-4 confirm that there is more heat transfer in the improved NGV design. At mid span,
the mass averaged total temperature of the flow is 50 K lower in the improved design compared to
the baseline. This is due to the higher shear.
Figure C-5 shows the Mach number contours.
They clearly show that the NGV exit Mach
number is far from uniform. It is difficult to visually estimate if the non uniformity has increased
from one design to another, but it is surely close to 40% in the angular direction at mid span. The
plots also show that it has been difficult to increase the NGV Mach number significantly above 0.6.
Despite the strong favorable pressure gradient, the average Mach number in 3-D calculations was
lower than that predicted in 2-D calculations, and never reached values above 0.8.
In figure C-6, the path lines indicate the presence of strong secondary flows. Unlike the static
pressure, there is a significant difference between the two end walls. This difference is not yet
explained, but may be linked with the combustor step and the difference in boundary thickness on
the end walls at the NGV inlet. We can also note the separation on the blade surface is not on
the same side at mid span and near the end walls. This suggests the existence of counter rotating
vortices near the blade surface, which has been confirmed by plots of velocity vectors in vertical
planes normal to the blade surface.
C.2
Flow in the Rotor for an Inlet Pressure of 1.8 atm
The first plot of flow in the rotor, figure C-7, presents the normalized swirl. This shows how
effectively the blade can remove this swirl and extract power from the fluid. We can see that
the improved turbine rotor extracts a larger fraction of the swirl before the flow exits the blade
passage. After the blade passage, the residual swirl is considered a loss, because it cannot produce
power or thrust. We can also note a large non uniformity from hub to tip, which is common in
centrifugal turbomachines, and which is unavoidable in the case of the micro engine because of the
manufacturing restriction to 2-D etching.
104
Similarly to the NGV, we present in figures C-8 and C-9 the reversible term of entropy and
the local irreversible production. Here also heat transfer is large and the associated entropy drop
could hide the irreversible production due to shear and temperature gradient if the two terms were
summed. We can see that the entropy production is large in the wake of the blades and also in the
middle of the blade passage, far away from secondary flows, but where the temperature gradient is
the highest (as observed on both figures). The improved rotor design, like the NGV, seems to have
also a larger irreversible entropy production on the blade surface than the baseline design, when
the designs are compared at the same inlet pressure. However, at the predicted operating point,
the improved design has a lower viscous loss (relative to the inlet enthalpy).
Figures C-10 and C-11 show contours of static pressure and temperature. On the first one, we
note that the static pressure is higher for the baseline design than for the improved design, at both
the rotor inlet and the rotor exit, while the total to static pressure ratio is the same (1.8 atm from
rotor inlet to stage exit).
The fact that the static pressure is higher at the rotor inlet only shows that the absolute inlet
Mach number is lower. But the fact that the static pressure is higher at the blade passage exit
shows that the exhaust diffuser requires a significant pressure gradient, leading to a flow acceleration
and viscous loss. The improved rotor exhaust does not require this pressure gradient, so that the
pressure drop across the exhaust diffuser can be minimized and more work extracted (this is the
result of our analysis, the static pressure plot alone is not sufficient to draw this conclusion). The
redesign effort showed that reducing the turbine reaction would increase the stage efficiency, so that
the pressure ratio accross the improved rotor is lower than that of the baseline rotor (the turbine
reaction is presented in figure 3.2)
On the baseline rotor design, near the blade tip, it is possible to see a small region where the
static pressure is approximately 1 atm. It is a sign of the flow separation at the right angle turn
lip.
On the static temperature plot, the average flow temperature at mid span seems to be lower
for the improved rotor design. But the heat transfer analysis showed that the disk Stanton number
was lower in the improved design but that the blade Stanton number was approximately the same.
Figure C-12 shows some path lines in the turbine rotor. As for the NGV, the presence of strong
105
secondary flows can be recognized at the blade root in the top figures. The pattern of secondary
flows seems to have changed from one design to the other, although we don't know what lead to
this change. The separation on the mid span suction side was also reduced by the redesign effort.
C.3
Flow in the Rotor Matched to the Compressor
Finally, the last contact sheet, figure C-13, presents similar contour plots but at the predicted
matched operating point, as specified in table 3.2.
The baseline rotor and improved rotor are
matched to different compressors, so that the inlet pressure and mass flows are different on the
plots.
106
Co2r E20
-100
-100
18180
?20
-220
-20
-260
-300
-300
a340
-340-
380
-380
-420
420
-460
-140
-460
-140
-50500A
Contoursof Entropy
Apr 30,2001
FLUENT5.3(3d,segregated,
lam)
ContoursofEntropy
-20
20
-60
-60-
Apr 30,2001
FLUENT5.3 (3d,segregated,
lam)
-100
-0
-140
-180
180
-220
220
4260
-460
-500
-300
Apr30, 2001
FLUENT5.3(3d,segregated,
lam)
Contoursof Entropy
Contoursof Entropy
Apr30,2001
FLUENT5.3(3d,segregated,
lam)
-340
E
20
-20
:60
-60
-100
-140
-140
-180
-18
220
|
.
--
2
260
-260
300
-300
-3-0
-340
-390
-380
-420
-420
-480
-460
-500
-500
Contours of Entropy
Contours of Entropy
Apr 30, 2001
FLUENT 5.3 (3d, segregated, lam) iFLUENT
Apr30,2001
5,3 (3d, segregated,
lam)
Figure C-1: Reversible term of entropy in the NGV, for the baseline design (left) and improved
design (right), at 2.5% span (top), 50% span (middle), and 97.5% span (bottom), for an inlet
pressure of 2.1 atm
107
8.3e+06
5.8e+06
6
8+06
t'6e+06
4.4+06
4e+06
2.8e+06
39+06
1.9e+06
20+06
1G+06
1+30+06
9. 1t+05
_90+05
6.3e+05
68+05
4 4e+05
4e+05
3.0e+05
.u3e+05
2.1e+05
28+05
- 1.+05
1.4e+05
1.0e+05
c
Contours of entropy-production
10+05
Apr30,2001
FLUENT
5.3 (3d,coupledImp,lam)
Contours of entropy-production
8G+06
8.3e+06
5
Apr30, 2001
FLUENT5.3(3d, coupledImp,lam)
8e+06
6&+06
4.0G+06
4e+06
2.80+06
3e+06
1.9e+06
2e+06
1.3e+06
10+06
9. 1e+05
9e+05
6e+05
4.4e+05
4e+05
3.4e+05
3e+05
2.1--+05
2e+05
1.4e+05
18+05
1.0e+05
1 e+05
Contours of entropy-production
Apr30,2001
FLUENT
5.3 (3d,coupledImp,lam)
Contours of entropy-production
Apr30, 2001
FLUENT5.3(3d, coupledimp,lam)
8e+06
8.3e+06
e+06
5.88+06
4e+06
2.89+06
3e+06
1.9e+06
20+06
1.3e+06
1%+06
9.
1e+05
9&+05
6s+05
414e+05
4e+05
13.08+05
3e+05
2.t4e+05
2e+05
21e+05
10+05
1.404+05
Contours of entropy-production
1 e+05
Apr30,2001
imp,lam)
5.3 (3d,coupled
FLUENT
Contours of entropy-production
Apr30,2001
FLUENT
5.3 (3d,coupled Imp,lam)
Figure C-2: Irreversible term of local entropy production in the NGV, for the baseline design (left)
and improved design (right), at 2.5% span (top), 50% span (middle), and 97.5% span (bottom),
for an inlet pressure of 2.1 atm
108
~208400
/
208400
205200
205200
202000
202000
198800
198800
195600
195600
192400
192400
189200
189200
186000
186000
182800
182800
179600
179600
176400
173200
176400
173200
1170000
170000
Contours of Total Pressure (pasca)
Apr 30, 2001
FLUENT5.3 (3d, segregated, lam)
A,
P208400
'205200
Contours of Total Pressure (pascal)
F-
Apr30, 2001
FLUENT5.3 (3d,segregated,
[am)
7208400
205200
202000
202000
198800
198800
195600
195600
192400
192400
189200
189200
186000
186000
182800
182800
179600
179600
176400
173200
173200
170000
170000
Contours of Total Pressure (pascal)
Apr 30, 2001
.FLUENT 5.3 (3d, segregated, lam)
Contours of Total Pressure (pascal)
7208400
208400
205200
205200
202000
202000
198800
198800
195600
195600
192400
192400
189200
189200
186000
186000
"182800
182800
, 179600
179600
176400
176400
173200
Apr30, 2001
FLUENT5.3 (3d,segregated,
lam)
P
173200
170000
1170000
Contours of Total Pressure (pascal)
Apr30,2001
lam)
FLUENT
5.3(3d,segregated,
Contours of Total Pressure (pascal)
Apr30,2001
FLUENT5.3 (3d, segregated,
lam)
Figure C-3: Total pressure in the NGV, for the baseline design (left) and improved design (right),
at 2.5% span (top), 50% span (middle), and 97.5% span (bottom), for an inlet pressure of 2.1 atm
109
16806W
1680
1640
1640
1600
1600
1560
1560
1520
1520
1480
1480
1440
1440
1400
1400
1360
1360
1320
1320
1280
1240
1200
Apr30, 2001
FLUENT5.3(3d,segregated,
lam)
ContoursofTotalTemperature
(k)
71680
1680
/
1640
1600
1600
1560
11560
1520
1520
1480
1440
1480
4
1440
1400
1400
1360
1360
1320
1320
1280
1280
1240
1240
1200
1200
Apr30,2001
FLUENT5.3(3d,segregated,
(am)
Contours of Total Temperature (k)
17"1680
I
1640
1640
1600
1600
1560
1560
1520
1520
1480
1480
41440
1440
S1400
1400
1360
1360
1320
1320
1280
1280
1240
1240
1200
1200
ofTotalTemperature
(k)
Apr30,2001
FLUENT5.3(3d,segregated,lam)
Contours of Total Temperature (k)
PF
1680
Contours
Apr30, 2001
lam)
FLUENT5.3(3d, segregated,
Contours of Total Tempe rature (k)
Apr30, 2001
FLUENT5.3(3d,segregated,
tam)
Contoursof Total Temperature (k)
I
-1
Apr30, 2001
FLUENT5.3(3d, segregated,
lam)
Figure C-4: Total temperature in the NGV, for the baseline design (left) and improved design
(right), at 2.5% span (top), 50% span (middle), and 97.5% span (bottom), for an inlet pressure of
2.1 atm
110
0.4
F.'---
"M7:711
0.5
0.4
0.4
0.4
0.4
0.4
0.3
0.3
0.32
0.3
0.2
0.2
0.2
0.2
0.2
0.1
0.1
0.1
0.0
0.0
0.0
Contoursof MachNumber
0.0
Apr 30,2001
FLUENT5.3(3d,segregated,lam)
0.5
Contoursof MachNumber
Apr 30, 2001
FLUENT5.3(3d,segregated,
lam)
70.5
0.4
0.4
0.4
0.4
0.4
0.3
0.3
03
0.3
0.2
0.2
0.2
0.2
0.2
0.2
0.1
0.1
"0.1
0.1
0.0
Contours of Mach Number
0.0
Apr30, 2001
FLUENT5.3 (3d.segregated,
lam)
Contours of Mach Number
0.5
0.5
0.4
"0.4
0.4
0.4
3.4
0.4
0.3
0.3
0.3
0.3
0.2
0.2
0.2
3.2
0.2
0.2
0.1
0.1
0.1
0.1
0.0
0.0
0.0
Contours of Mach Number
Apr 30,2001
FLUENT 5.3 (3d, segregated, lam)
0.0o
Apr 30,2001
FLUENT
5.3 (3d,segregated,
lam)
Contours of Mach Number
Apr30,2001
FLUENT5.3(3d,segregated,
lam)
Figure C-5: Mach number in the NGV, for the baseline design (left) and improved design (right),
at 2.5% span (top), 50% span (middle), and 97.5% span (bottom), for an inlet pressure of 2.1 atm
111
-----..
;il
Figure C-6: Path lines in the NGV, for the baseline design (left) and improved design (right),
starting at 2.5% span (top), starting at 50% span (middle), and starting at 97.5% span (bottom),
for an inlet pressure of 2.1 atm
112
P1.0
.10.9
0.6
0.7
0.6
0.6
04
0.4
0.3
0.3
n.2
0.2
0.2
0.2
0.1
0.1
0.0
Contours of swirl-re ative-to-In et
0.0
Apr27, 2001
imp, lam)
FLUENT5.3 (3d,coupled
05
Contoursof relative-swirl-10um
Apr24, 2001
FLUENT
5.3 (3d,coupledimp,lam)
11.0
09
07
0.6
06
0.4
0.3
0-2
0.2
10.1
Apr 24, 2001
FLUENT5.3(3d,coupledimp.lam)
Contours of swirl-relative-to-inlet
Apr24.2001
FLUENT5.3(3d,coupledImp,lam)
1.0
0.9
0.9
0.8
0.7
0.8
0.7
0.0
0.6,
o6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.2
0.2
0.1
0.0
Contours of relative-swirl-390um
0.0
Apr24, 2001
FLUENT5.3(3d,coupledimp,lam)
Contours of relative-swirl-390im
Apr24, 2001
FLUENT5.3 (3d,coupledImp,lam)
Figure C-7: Normalized absolute swirl in the rotor, for the baseline design (left) and improved
design (right), at 2.5% span (top), 50% span (middle), and 97.5% span (bottom), for an inlet
pressure of 1.8 atm
113
-20
fM
-100
-100
-140
-140
-180
-180
-220
-22w
~-260
-260
-300
-340
-380
-380
%
-420
-420
-460
-460
-500
-500
Contours of Entropy
Apr 27 2001
FLUENT53 (3d, coupledimp,lam)
-20
-60
Apr24, 2001
FLUENT5.3(3d,coupledImp,lam)
-20
-60
100
--100
-140
-180
Contours of Entropy
-140
.
-180
-220
-220
-260
-260
-300
-380
I-420
-420
-460
-460
-500
-500
Contours of Entropy
Apr 27 2001
FLUENT5.3(3d,coupledImp,lam)
Contours of Entropy
Apr 24, 2001
FLUENT5.3(.3d,coupledImp,lam)
20
-7 20
-60
60
100
-100
-140
-140
-180
-180
-220
-220
-260
-260
-300
"'1-300
-340
-340
-380
-420
-420
-460
-460
1-500
-500
Contours of Entropy
FLUENT5.3(3d,coupledImp,lam)
Contours of Entropy
Apr 24, 2001
FLUENT&3 (3d,coupledImp,lam)
Figure C-8: Reversible term of entropy in the rotor, for the baseline design (left) and improved
design (right), at 2.5% span (top), 50% span (middle), and 97.5% span (bottom), for an inlet
pressure of 1.8 atm
114
7@+08
7e+08
3e+08
3e+0826+08
Be+07
8e+07
4e+07
26+07
20-07
j.,Be+08
W8e+06
2e+06
2e+06
9e+05
9e+05
4e+05
48+05
2e+05
2e+05
I e+05
1e+05
Contours of entropy-production
Apr27,2001
FLUENT5.3(3d,coupledimp,lam)
Contours of entropy-production
Apr 24,2001
FLUENT5.3(3d,coupledimp,lam)
7e+08
2e+08
87
3e+06
07
2e+08-
3e+07
40+07
48+07
2e+07
2e+07
e+06
4e+06
+2
%+06
e+06
+06
9e+05
40+05
2e405
a
e+05
\
104+05
Contours of entropy-production
Apr27,2001
FLUENT
5.3 (3d,coupledimp,lam)
4e+05
Apr 24, 2001
FLUENT
5.3 (3d,coupledImp,tam)
1,3+05
30+08
382+08
3e+08
80+07
4e+087
e+07
4e+0/72e+075
80+06
4e+06
4e+06
2e+06
29+06
9+05
9@+05
4e+05
4e+05
2e+05
28+05
ie+05
1e+05
Contours of entropy-production
Apr27, 2001
FLUENT5.3(3d,coupledimp,lam)
Contours of entropy-production
Apr24,2001
FLUENT5.3(3d,coupledimp,lam)
Figure C-9: Irreversible term of local entropy production in the rotor, for the baseline design (left)
and improved design (right), at 2.5% span (top), 50% span (middle), and 97.5% span (bottom),
for an inlet pressure of 1.8 atm
115
160000
MW
.
155000
155000
140000
150000
145000
145000
140000
140000
135000
135000
130000
13000r
125000
125400
120000
1200006
115000
115000
11-0000
110000
1 05000D
105000
100000
100000
Contours of Static Pressure (pascal)
Apr24, 2001
FLUENT5.3(3d,coupledImp,lam)
Contours of Static Pressure (pascal)
160000
Apr24,2001
FLUENT5.3 (3d,coupled Imp,lam)
160000
7 155000
155000
150000
150000
145000
145000
140000
140000
135000
135000
130000
130000
125000
125000
120000
120000
115000
110000
110000
105000
100000
105000
100000
\
Contours of Static Pressure (pascal)
Apr 24, 2001
FLUENT
5.3 (3d,coupled
imp tam)
Contours of Static Pressure (pascal)
160000
160000
155000
k*l155000
150000
y4
45000
Apr24, 2001
FLUENT5.3(3d,coupledImp,lam)
150000
S145000
140000
140000
135000
130000
125000
13D000
-125000
n
120100
115000
115000
110000
110000
105000
105000
100000
100000
Contours of Static Pressure (pascal)
Apr 24, 2001I
Contours of Static Pressure (pascal)
FLUENT 5.3 (3d, coupled
||FLUENT
Imp,lam)
Apr 24, 2001
5.3 (3d, coupled imp, [am)
Figure C-10: Static pressure in the rotor, for the baseline design (left) and improved design (right),
at 2.5% span (top), 50% span (middle), and 97.5% span (bottom), for an inlet pressure of 1.8 atm
116
1575
$ 500
1425
1350
1275
1050
975
900
S900
Contoursof Static Temperature
(k)
Apr24, 2001
FLUENT5.3(3d,coupledImp,lam)
Con tou rs o f Stati c Tem pe rat ure (k)
Apr 24, 2001
FLUENT5.3 (3d,coupledImp,lam)
1575
11575
1500
1425
-1425
1350
1350
1275
1275
1200
1200
1125
1125
1050
975
1050
\
975
'900
Contours of Static Temperature (k)
900
Apr24,2001
FLUENT5.3(3d,coupledimp,lam)
Contours of Static Temperature (k)
Apr24,2001
FLUENT
5.3 (3d,coupledImp,lam)
1600
1575
1500
1460
1 425
1390
1350
1320
1 275
1250
1180
1 125
1110
1050
1040
975
970
Contours of Static Temperature (k)
Apr24, 2001
FLUENT5.3(3d,coupled
Imp,lam)
Contours of Static Temperature (k)
Apr24,2001
FLUENT5.3(3d,coupledImp,lam)
Figure C-11: Static temperature in the rotor, for the baseline design (left) and improved design
(right), at 2.5% span (top), 50% span (middle), and 97.5% span (bottom), for an inlet pressure of
1.8 atm
117
00
-I
tzC
w oi
(D
(D~
C0
0.7
0.7
0.6
0.6
0.4
0.3
0.2
Conour
ofsilrtAr2,20
0.2
0.1
0.0
Apr27, 2001
Contours of swirl-rel
of swirl-ret
Contours
FLUENT5.3 (3d, coupled imp, [am)
79+08
7&+08
:3@+08
3&+08
Apr 24, 2001
FLUENT 5.3 (3d, coupled
lam)
Imp,
Apr24,2001
2&+08
8e+07
8e+07
4e+07
4e+07
2+07
2e+07
80+06
4@+06
4e+06
29+06
2e+08
90+05
4e+05
9e+05
\
4e+05
28+05
1e+05
2e+05
1 e+05
\
Contoursof entropy-production
Contoursof entropy-production
Apr27 2001
FLUENT
5.3(3d,coupledImp,lam)
147587
147587
142876
142876
138316
138316
133902
133902
129628
129628
,X125491
125491
121485
121485......
117808
117608\
113854
113854
110220
110220
106702
1067D2\
103297
103297
100000
100000
Contours of Static Pressue (pascal)
Apr24, 2001
FLUENT
5.3 (3d,coupledimp,lam)
Apr 27,2001
FLUENT
5.3(3d,coupledimp,lam)
Cntours of Static Pressure (pascal)
Apr24,2001
FLUENT
5.3 (3d,coupled imp,lam)
Figure C-13: Swirl relative to inlet (top), local irreversible entropy production (middle), and static
pressure contours (bottom) for the baseline rotor (left) and the improved rotor (right) at their
respective matched operating point (see table 3.2)
119
Bibliography
[1] A. Bonnet and J. Luneau. Theories de la dynamique des fluides. Cepadues Editions, 1989.
[2] M. Drela and H. Youngren. A User's Guide to MISES 2.1, June 1995.
[3] A.H. Epstein and S.D. Senturia. Macro power from micro machinery. Science, 276, May 1997.
[4] A.H. Epstein et al. Power mems and microengines. In IEEE Conference on Solid State Sensors
and Actuators, June 1997.
[5] S. Evans. cycle analysis of the micro engine with heat flux matching. personnal communications, 2000-2001.
[6] Fluent Inc. Fluent 5 User's Guide.
[7] R.J. Goldstein. literature review on heat transfer for laminar and turbulent flows.
[8] Y. Gong.
cycle analysis of the micro engine turbomachinery.
personnal communications,
1999-2001.
[9] J.L. Kerrebrock. Aircraft engines and gas turbines. The MIT Press, 1977.
[10] E.S. Piekos, D.J. Orr, S.A. Jacobson, F.F. Ehrich, and K.S. Breuer. Design and analysis
of microfabricated high speed gas journal bearings. 28th AIAA Fluid Dynamic Conference,
1997(1966), July 1997.
[11] R.A. Seban. Effects of initial boundary layer thickness on a tangential injection system. Journal
of heat transfer, page 392, November 1960.
[12] E.R.G. Eckert S.G. Schwarz, R.J. Goldstein. The influence of curvature on film cooling performance. The American Society of Mechanical Engineers, June 1990.
120