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dissertation entitled

INTEGRATION OF A WAVE ROTOR TO AN ULTRA-MICRO
GAS TURBINE (UpGT)

presented by

FLORIN IANCU

has been accepted towards fulfillment
of the requirements for the

 

PhD. degree in __MECHAN|CAL ENGINEERING__

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INTEGRATION OF A WAVE ROTOR TO AN
ULTRA-MICRO GAS TURBINE (quT)

BY

Florin Iancu

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment Of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Mechanical Engineering

2005

ABSTRACT
INTEGRATION OF A WAVE ROTOR TO AN ULTRA-MICRO GAS TURBINE (UuGT)
BY

Florin Iancu

Wave rotor technology has shown a significant potential for performance
improvement of thermodynamic cycles. The wave rotor is an unsteady flow madtine
that utilizes shod< waves to transfer energy from a high energy fluid to a low energy
fluid, increasing both the temperature and the pressure of the low energy fluid.
Used initially as a high pressure stage for a gas turbine locomotive engine, me wave
rotor was commercialized only as a supercharging device for intemal combustion
engines, but reoenfly there is a stronger researd'i effort on implementing wave
rotors as topping units or pressure gain oombustors for gas turbines.

At the same time, Ultra Micro Gas Turbines (UpGT) are expected to be a next
generation Of power source for applications from propulsion to power generation,
from aerospace industry to electronic industry. Starting in 1995, with the MIT
“Micro Gas Turbine” project, the mechanical engineering research world has
explored more and more the idea of “Power MEMS”. Microfabricated
turbomachinery like turbines, compressors, pumps, but also electric generators,
heat exchangers, internal combustion engines and rocket engines have been on
the focus list of researchers for the past 10 years. The reason is simple: the

output power is proportional to the mass flow rate of the working fluid through

the engine, or the cross-sectional area while the mass or volume of the engine is
proportional to the cube of the characteristic length, thus the power density
tends to increase at small scales (PoweI/Mass=L"). This is the so-called “cube
square law”.

This work investigates the possibilities of incorporating a wave rotor to an UpGT
and discusses the advantages of wave rotor as topping units for gas turbines,
especially at microscale. Based on documented wave rotor efficiencies at larger
scale and subsidized by both, a gasdynamic model that includes wall friction, and
a CFD model, the wave rotor compression efficiency at microfabrication scale
could be estimated at about 70%, whid1 is much higher than the Obtained
efficiency Obtained for centrifugal compressors in a microfabricated gas turbine.
This dissertation also proposes several designs of ultra-micro wave rotors,
including the novel concept of a radial-flow configuration. It describes a new and
simplified design procedure as well as numerical simulations Of these wave rotors.
Results are Obtained using FLUENT, a Computational Fluid Dynamies (CFD)
commercial code. The vast information about the unsteady processes occurring
during simulation is visualized. Last, two designs for experimental tests have been
created, one for a micro shock tube and one for the ultra-micro wave rotor.
Theoretical and numerical results encourage the idea that at microscale,
compression by shock waves may be more efficient than by conventional
centrifugal compressors, thus making the ultra-micro wave rotor (UpWR) a

feasible idea for enhancing (upgrading) UuGT.

to my father

who has inspired me to pursue a carrier in mechanical engineering

Acknowledgments

I offer my sincerest appreciation to Dr. Norbert Miiller for introducing me to the
topic of wave rotors and giving me the opportunity to work on this subject, as
well as for his continuous advice and support. His guidance extended to all
aspects of my life as a Ph.D. student and was not limited to the research
problems. I think of him as a great advisor and a friend.

I also thank Dr. Janusz Piechna for all the support and help he offered during my
struggles with research queries. Without some of his great suggestions and
ideas, I would not have been able to finish this work.

I was lucky to choose a committee that believed in me and my work and offered
continuous and valuable guidance and advice. Dr. Dean Aslam, Dr. André
Bénard, Dr. Abraham Engeda and Dr. Luc Fréchette, all contributed significantly
to the value of this dissertation.

All my colleagues in the Turbomachinery laboratory have been extremely
supportive and helpful. I would like to mention particularly Dr. Pejman Akbari, for
helping me tackle the challenging subject of wave rotors, James Bellefeuille and
Emmett Dempsey, for helping me untangle some difficult problems. I also
appreciate the friendship and help Of Nathan Holden and Amir Kharazi. I thank
Changgu Lee, Xiangwei Zhu and Yuxing Tang for their help with the

experimental part of the dissertation. I am grateful for having such friends

around me for helping me and making my life as a Ph.D. student more
enjoyable.

Last but not least, I would like to thank my sister, my parents, and my girlfriend
for their encouragement and for tolerating me during the last months of writing

this dissertation.

vi

Preface

The purpose of this research is to combine two development trends in the
turbomachinery world (enhancing efficiency by wave rotor topping and
increasing power density by miniaturization) by introducing a new concept, the
Ultra-Micro Wave Rotor (UuWR). This dissertation proposes several designs for
integrating the wave rotor to a miniaturized gas turbine as well as shows
introductory investigations regarding the feasibility of the ultra-micro wave
rotors. The structure of the study is as follows.

Chapter 1 is a short introduction of MEMS turbomachinery and wave rotors. The
history of the micro gas turbine project at MIT (the starting point of present
research study), section reviewed by Dr. Stuart Jacobson from the Massachusetts
Institute of Technology - Gas Turbine Laboratory. Next, a literature review
survey of the wave rotor investigations is presented, starting in 1950 until
present, including numerical studies of the gas dynamic process inside the wave
rotor channels.

Chapter 2 describes the initial concepts of ultra-micro wave rotors. Ideas
presented here are part of the “Wave Rotors for Ultra-Micro Gas Turbines"
permanent patent that was filed in July 2005. The material was partly presented
at the Michigan Space Grant Consortium in October 2003.

Chapter 3 is a theoretical and numerical study of the efficiency of the

compression process by shock waves in microchannels. The material was

vii

presented at the 40th AIAA Joint Propulsion Conference and Exhibit in July 2004
and was published in Journal of Microfluidics and Nanofluidics in August 2005.
This chapter also introduces the optimum design space for the ultra-micro wave
rotor, material that will be presented at the PowerMEMS Conference in Tokyo,
November 2005.

Chapter 4 presents preliminary stress investigations of a rotating disc subjected
to mechanical and thermal loads. Material presented at the NASA Michigan Space
Grant Consortium in October 2004.

Chapter 5 describes a simple procedure of designing ultra-micro wave rotors.
The procedure partially has been presented at the 35th AIAA Fluid Dynamic
Conference in July 2005.

OrapIer 6 introduces the concept of radial wave rotor as well as the capability of
FLUENT to simulate unsteady flow behavior in ultra-micro wave rotors. Two papers
covering these subjects have been presented at the 2004 Intemational Med'lanical
Engineering Conference in November 2004. The radial wave rotor is also the subject
of a paper submitted to AIAA Journal that is currently still under review.

Chapter 7 presents a brief description of the final design of UpGT including the
integration of the wave rotor.

Chapter 8 describes the manufacturing procedure for a UuWR and a simpler
single channel test rig.

Chapter 9 outlines directions for future work, provides the summary and

conclusions.

viii

TABLE OF CONTENTS

List of Tables ................................................................................................ xi
List of Figures .............................................................................................. xii
Key to Symbols and Abbreviations .............................................................. >o<iii
Chapter I INTRODUCTION ............................................................................. 1
1.1 Micro and Ultra-Micro Power Systems ................................................ 1
1.1.1 MIT Micro Gas Turbine Engine Project ......................................... 3
1.1.2 Other Therrno-Mechanical MEMS Devices .................................. 11

1.2 Wave Rotor Technology and Its Applications .................................... 19
I.2.1 Wave Rotor Investigations and Products ................................... 23
1.2.2 Numerical Investigations .......................................................... 34

13 Wave Rotor Enhanced Ultra Micro Gas Turbines ............................... 43
Chapter II PROPOSED INITIAL DESIGNS OF A WAVE ROTOR TOPPING AN UuGT
................................................................................................................. 44
11.1 Axial Wave Rotor Configuration ....................................................... 44
11.2 Radial Wave Rotor Configuration ..................................................... 47
Chapter III PERFORMANCE CHARACTERISTICS OF ULTRA—MICRO WAVE
ROTORS ..................................................................................................... 49
NM One Dimensional Flow with Friction ................................................. 58
111.2 Flow Across a Moving Shock ........................................................... 61
1113 Numerical Model ............................................................................ 74
III.4 Comparison of Results .................................................................... 79
1115 Design Space of Wave Rotor Topped Gas Turbines at Microscale ............... 81
Chapter IV STRESS INVESTIGATIONS .......................................................... 89
Ni Materials Used and Properties ......................................................... 89
IV.2 Radial and Tangential Stresses with and without Thermal Effects ....... 90
IV.2.1 No thermal effects ................................................................... 90
IV.2.2 Thermal effects ....................................................................... 92
IV.2.3 Summary and conclusions ........................................................ 93
Chapter V DESIGN OF ULTRA-MICRO WAVE ROTORS (UpWR) ....................... 96
v.1 Gasdynamics of Compressible Flow ................................................. 97
V2 Modeling of Unsteady Compressible Flow ......................................... 97
V21 Explicit vs. Implicit .................................................................. 97

v.3 Design Methodology ...................................................................... 100
V.3.1 Through - Flow Solution ......................................................... 101
V.3.2 Reverse - Flow Solution .......................................................... 117

Chapter VI NUMERICAL SIMULATIONS OF upwa ......................................... 119

V1.1 Setting up GAMBIT ....................................................................... 119
V1.2 Setting up FLUENT ........................................................................ 125
V1.3 Heat Transfer Simulations ............................................................. 132
V1.4 Axial UpWR... ............................................................................... 144
V1.5 Radial UuWR ................................................................................ 156
V1.5.1 Through—Flow Radial Wave Rotor ............................................. 157
V1.5.2 Reverse-Flow Radial Wave Rotor ............................................. 171
V1.5.3 Comparison of Radial Configurations ........................................ 183
Chapter VII FINAL DESIGN OF THE UpWAVE ROTOR .................................... 191
Chapter VIII EXPERIMENTAL INVESTIGATIONS ........................................... 196
VIII.1 Axial Ultra-Micro Wave Rotor ...................................................... 196
VIII.2 Radial Ultra-Micro Wave Rotor .................................................... 200
VIII.2.1 Fabrication of the Radial Wave Rotor Test Rig ....................... 203
VIII.3 Single Channel Experiment ......................................................... 208
VIII.4 End Plates and Ducting .............................................................. 216
Chapter IX SUMMARY AND CONCLUSIONS ................................................... 217
D(.1 Summary ..................................................................................... 217
1X.2 Conclusions .................................................................................. 218
D(.3 Suggestions for Future Work .......................................................... 221
D(.3.1 Wave Disc with Curved Channels ............................................. 221
D(.3.2 Optimization of the Thermodynamic Parameters ....................... 222
D(.3.3 Experimental Testing .............................................................. 222
IX.3.4 3D CFD Investigations ............................................................ 223
Appendices ................................................................................................ 225
Appendix 1 - Material Properties .............................................................. 225
Appendix 2 — UpWR Fabrication Drawings ................................................ 227
Appendix 3 — Microfabrication Details ....................................................... 235
References ................................................................................................ 240

List of Tables

Table 111.1: Wave rotor compression and expansion efficiency and only

compression efficiency. Data found in extant literature ............................ 52
Table 111.2: Entry data for the mathematical model ....................................... 64
Table 111.3: Efficiencies of compression process function of shock pressure ratio,

entrance temperature and direction of moving shock ............................... 70
Table IV.1: Radial and tangential stresses in a rotating disc ............................ 94
Table V1.1: Comparison of numerical results between the three models. ........ 137

Table V1.2: Comparison of contour plots between the three models: pressure,
temperature, velocity, heat flux and heat transfer coefficient. ................. 138

Table V1.3: Thermodynamic parameters of the ultra-micro wave rotor — set one.
.......................................................................................................... 144

Table V1.4: Thermodynamic parameters of the ultra-micro wave rotor - set two.
.......................................................................................................... 145

Table V1.5: General thermodynamic parameters of the ultra-micro wave rotor.

.......................................................................................................... 145
Table V1.6: Details of the full model. ........................................................... 145
Table V1.7: Details of the reduced model. .................................................... 146

Table V1.8: Wave rotor operating conditions adjusted for higher pressures in the
high-pressure region and lower pressures for the low-pressure region. ....162

Table V1.9: Wave rotor operating conditions adjusted for higher pressures in the
high-pressure region and lower pressures for the low-pressure region. ....180

xi

List of Figures

Figure 1.1: MIT Micro gas turbine generator: cross-section (adapted from
(Epstein, Ayén et al. 1997)). ................................................................... 4

Figure 1.2: Microcompressor and microturbine of the MIT project in the first
design stage, (reproduced from (Lin, Ghodssi et al. 1999)). ....................... 5

Figure 1.3: MIT combustor structure (adapted from (Mehra, Zhang et al. 2000)).6

Figure 1.:4 MIT Three-wafer structure for microcombustion study (reproduced
from (Mehra, Zhang et al. 2000)). ...........................................................

Figure 1.5: MIT H2 Demo Engine with conduction-cooled turbine constructed from
six silicon wafers (adapted from (Epstein, Jacobson et al. 2000)). .............. 8

Figure 1.6: MIT bearing testing structure (reproduced from (Frechette 2001)).... 9

Figure 1.7: Single-zone and Dual-zone combustor, part of the MIT micro gas
turbine engine (adapted from (Spadaccini, Zhang et al. 2003) - left and
(Spadaccini, Mehra et al. 2003) - right). ................................................ 10

Figure 1.8: MIT turbocharger test structure (adapted from (Epstein 2003)). ..... 10

Figure 1.9: Stanford’s micro turbo-compressor with bearing cartridge (reproduced
from (Kang, Johnston et al. 2004)). ....................................................... 12

Figure 1.10: Schematic cross-section of a Rankine steam turbine device
(reproduced from (Frechette, Lee et al. 2004)). ...................................... 13

Figure 1.11: “Palm top” model of microturbines (reproduced from (Matsuura,
Kato et al. 2003)). ................................................................................ 14

Figure 1.12: ONERA alternative to the MIT combustion chamber (reproduced
from (Ribaud 2003)). ............................................................................ 16

Figure 1.13: Berkeley’s steel piston and combustion chamber for a micro Wankel
engine (reproduced from (Walther and Pisano 2003)). ............................ 17

"Images in this dissertation are presented in color."

xii

Figure 1.14: Berkeley's silicon piston chamber for a micro Wankel engine

(reproduced from (Walther and Pisano 2003)). ....................................... 18
Figure 1.15: Axial wave rotor drum and end plates ......................................... 19
Figure 1.16: Comprex® wave rotor drum. ..................................................... 20

Figure 1.17: Four-port wave rotor schematic. a) Through-flow configuration; b)
Reverse-flow configuration (C - compressor, CC — combustion chamber, WR
- wave rotor, T - turbine). .................................................................... 21

Figure 1.18: Flow trajectories in a Through-flow axial wave rotor. ................... 22

Figure 1.19: Temperature -Entropy Diagram for a gas turbine engine with and
without wave rotor topping. ....................................... 25

Figure 1.20: NASA four port wave rotor. Left — the rotor, Right — the test system.

........................................................................................................... 28
Figure 1.21: Comparison between the Comprex® supercharged engine (CX) and

the turbocharged engine (TC) performances (Heisler 1995). .................... 29
Figure 1.22: Comprex® system: 1 - ICE; 2 — HPG port; 3 - HPA port; 4 - LPG

port; 5 -LPA port; 6 - rotor; 7 - drive system. ......................................... 30
Figure 1.23: Comprex® rotor and a Mazda 626 supercharging system cut-vie;
Figure 11.1: Conceptual design of UuGT — “Classic” design .............................. 45
Figure 11.2: Conceptual design of UuGT - “Two-layer" design. ........................ 46
Figure 11.3 Conceptual design of UpGT - “Extemal” design ............................. 46
Figure 11.4: Conceptual design of UpGT — “Radial" design. ............................. 47

Figure 111.1: Temperature — Entropy diagram for ultra-micro gas turbines, with
and without wave rotor. ........................................................................ 50

Figure [11.2: Efl‘iciency trend of the compression process. Solid line — wave rotor
efficiency; Dashed line - compressor efliciency. References: 1 - (Miiller and

xiii

Frédwette 2002), 2 - (Johnston, Kang et al. 2003), 3 - (Okamoto and Nagashima
2003), 4 - (Moritz 1985), 5 - (AldJari and Miiller 2003), 6 - (Mathur 1985), 7 -
(Thayer 1985). ...................................................................................... 54

Figure 111.3: 1D model of a microchannel. a) Single channel; b) Shock traveling
in direction opposite to the flow; c) Shock traveling in direction of the flow.
........................................................................................................... 56

Figure 111.4: Pressure and temperature distributions for a single channel model
with heat transfer calculations and without. Flow moving from left to right.
The results were obtained using FLUENT 6.1. ......................................... 60

Figure 111.5: Variation of friction factor with respect to Reynolds number
assuming laminar flow: solid line - calculation using classic theory
(f=64/Re); doted line - experimental results for microscale flow. ............. 64

Figure 111.6: Efficiency of compression process as function of position of shock
inside the microchannel for different shock strengths, inlet temperature of
1465K, and a shock traveling in direction opposite to the flow. Results
obtained using analytical 10 code. ......................................................... 66

Figure 111.7: Efficiency of compression process function of position of shock
inside the microchannel for different shock strengths, inlet temperature of
750K, and a shock traveling in direction opposite to the flow. Results
obtained using analytical 1D code. ......................................................... 66

Figure 111.8: Efficiency of compression process as function of position of shock
inside the microchannel for different shock strengths, inlet temperature of
1465 K, and a shock traveling in the direction of the flow. Results obtained
using analytical 10 code. ...................................................................... 67

Figure 111.9: Schematic of pressure distribution along the microchannel. a) With
shock close to entrance; b) With shock close to exit. Pressure p1 and ratio
p3/p2 are the same in both cases. .......................................................... 69

Figure 111.10: Efficiency of compression process as function of entry temperature
for different shock strengths, and for a shock traveling in the direction
opposite to the flow. Results obtained using analytical 1D code ................ 72

Figure 111.11: Efficiency of compression process function of microchannel
length/diameter ratio for different shock strengths, and for a shock traveling
in the direction of the flow. ................................................................... 73

xiv

Figure 111.12: Mesh models of a microchannel, inlet and outlet ports ............... 76

Figure 111.13: Static pressure inside a microchannel at two different time steps.
Trme =1 is when pressure wave reached the end of the channel. Flow
moving from left to right. Results obtained using CFD code FLUENT 6.1. .77

Figure 111.14: Density contours inside a microchannel. Trme=1 is when pressure
wave reached the end of the channel. Flow moving from left to right. Results
have been obtained using CFD code FLUENT 6.1. ................................... 78

Figure 111.15: Wave rotor compression efficiency as function of channel length
for constant length/diameter ratio of 6.67. References: 1 — CFD model, 2 -
(lender and Mayer 1984), 3 — (Okamoto and Nagashima 2003), 4 - (Mathur

1985), 5 — (T aussig 1984). .................................................................... 80
Figure 111.16: Optimum points for all performance evaluation parameters
function of polytropic compressor efficiency ............................................ 82
Figure 111.17: Optimum points for all performance evaluation parameters
function of polytropic turbine efficiency. ................................................. 83
Figure 111.18: Optimum points for all performance evaluation parameters
function of turbine inlet temperature (TIT). ............................................ 84
Figure 111.19: Optimum points for specific work for variation of turbine inlet
temperature (TIT). ............................................................................... 85
Figure 111.20: Optimum points for specific fuel consumption for variation of
turbine inlet temperature (TII ). ............................................................. 86
Figure 111.21: Optimum points for thermal efficiency for variation of turbine inlet
temperature (TIT). ............................................................................... 87
Figure IV.1: Model of a single compressor/turbine disc ................................... 90

Frgure IV.2: Radial and tangential stresses without thermal effects along the
radius of the disk (compressor/turbine rotor). ......................................... 91

Figure IV.3: Temperature distribution in the three sub-cases: linear, quadratic
and logarithmic. ................................................................................... 93

Frgure 1V.4: Radial and tangential stresses with thermal effects along the radius

of the disk (compressor/turbine rotor) .................................................... 94
Figure v.1: Wave pattern for a four port wave rotor (adapted after Resler et al.).
.......................................................................................................... 100
Frgure V.2: NASA wave patterns for the four port wave rotor. Left — through-flow
configuration, right - reverse-flow configuration. ................................... 101
Frgure v.3: Wave pattern for a four port through-flow wave rotor. ................. 102

Frgure v.4: Comparison between analytical results and numerical results for an
initial port prediction of a through-flow wave rotor (first number is
analytically obtained, the second one — numerically). ............................. 115

Frgure v.5: Mass flow rate through the boundaries of a wave rotor channel in
through-flow configuration, [kg/s]. ....................................................... 116

Frgure v.6: Wave pattern for a four port reverse-flow wave rotor ................... 117

Figure v.7: Comparison between analytical results and numerical results for an
initial port prediction of a reverse-flow wave rotor (first number is
analytically obtained, the second one - numerically). ............................. 118

Frgure V.8: Mass flow rate through the boundaries of a wave rotor channel in
reverse-flow configuration, (kg/s]. ........................................................ 118

Figure V1.1: Axial wave rotor in 20 developed view: a) through-flow
configuration; b) reverse-flow configuration (values in um) ..................... 120

Figure V1.2: Mesh and interfaces setup for 2D axial wave rotor investigations: a)
single port - multiple channel interface, b) single port - multiple channel
interface with additional gap, c) multiple port - multiple channel interface with

gap. ................................................................................................... 121
Frgure V1.3: Radial wave rotor cross-sectional view [dimensions in um]. ......... 122
Frgure V1.4: Radial wave rotor cross-sectional view — reduced model. ............ 123

Frgure V1.5: Radial waver rotor in a through flow (TF) configuration: reduced
model and zoom in of the mesh ............................................................ 124

xvi

figure V1.6: 2D simulation of axial wave rotor: a) pressure distribution, b)

temperature distribution. ..................................................................... 130
figure V1.7: 2D simulation of axial wave rotor: a) pressure distribution, b)
temperature distribution. ..................................................................... 131
figure V1.8: Mesh of radial wave rotor with adiabatic walls - zoom-in view ..... 134
figure V1.9: Wall boundary conditions - set up window ................................. 135
figure V1.10: Mesh of radial wave rotor with solid walls - zoom-in view. ........ 136

figure V1.11: 3D model of axial wave rotor: a) full model with 12 cycles per

revolution, b) reduced model with 1 cycle per revolution. ....................... 147
figure V1.12: Pressure distribution for a single channel mode: a) 2pm gap, b)
20pm gap. .......................................................................................... 148
figure V1.13: Pressure distribution for 2D simulation of axial wave rotor: a) TF
model, b) RF model, [Pa]. .................................................................... 150
figure V1.14: Temperature distribution for 2D simulation of axial wave rotor: a)
TF model, b) RF model, [K]. ................................................................. 150
figure V1.15: Low temperature distribution. ................................................. 151

figure V1.16: Velocity distribution in an axial wave rotor: a) TF — positive
direction flow, a) RF — negative direction flow, c) RF — positive direction

flow, [m/s] .......................................................................................... 152
figure V1.17: Reynolds number distribution for axial wave rotor. ................... 153
figure V1.18: Flow Mach number distribution for axial wave rotor. ................. 154
figure V1.19: Pressure distribution in the channels of the 3D reduced axial wave

rotor model ......................................................................................... 155
figure V1.20: Through-flow wave disc - porting schematic. ........................... 157

figure V1.21: Pressure distribution for the through-flow configuration (first
iteration), [Pa]. ................................................................................... 158

xvii

figure V1.22: Radial velocity distribution for the through-flow configuration (first
iteration), [m/s]. ................................................................................. 159

figure V1.23: Comparison between initial and updated models. ..................... 159

figure V1.24: Through-flow wave disc— static pressure distribution, [Pa], left: full
pressure spectrum, right: pressure values form 2510 5 to 3.9310 5 Pa. .160

figure V1.25: Through-flow wave disc - static temperature distribution, [K]....161

figure V1.26: Through-flow wave disc - static temperature distribution, [K] a)
lower port pressures, b) boosted port pressures ..................................... 162

figure V1.27: Through-flow wave disc - velocity vectors distribution, [m/s]. ...163

figure V1.28: Radial velocity distribution for the through-flow configuration (third

iteration), [m/s]. ................................................................................. 164
figure V1.29: Comparison of radial and axial flow wave rotors - static
temperature distribution, [K]. ............................................................... 165
figure V1.30: Temperature boundary conditions for the external heat transfer
investigations, [K]. .............................................................................. 166
figure V1.31: Comparison of temperature distributions without and with external
heat transfer, [K]. ............................................................................... 166
figure V1.32: Comparison of pressure distributions without and with external
heat transfer, [Pa]. .............................................................................. 167
figure V1.33: Comparison of Nusselt number distributions along the rotor walls
without and with external heat transfer. ................................................ 168
Figure V1.34: Schematic of flow entry into a channel ..................................... 169
figure V1.35: Reverse-flow wave disc — possible port arrangements. .............. 172

figure V1.36: Reverse—flow wave disc - static pressure distribution, [Pa]. ...... 173

figure V1.37: Reverse-flow wave disc — static temperature distribution, [K]. .. 173

xviii

figure V1.38: Reverse-flow wave disc — density distribution, [kg/m3]. ............ 174
figure V1.39 Reverse-flow wave disc - radial velocity distribution, [m/s] ........ 175

figure V1.40: Reverse-flow wave disc with air ports on inner diameter —
temperature distribution, [K]: a) results after first cycle, b) results after
several cycles ...................................................................................... 176

figure V1.41: Reverse-flow wave disc with gas ports on inner diameter —
temperature distribution, [K]: a) results after first cycle, b) results after
several cycles. ..................................................................................... 177

figure V1.42: Reverse-flow wave disc - static pressure distribution: left — air ports
located on inner diameter, right - gas ports located on inner diameter, [Pa].
.......................................................................................................... 178

figure V1.43: Reverse-flow wave disc - static pressure distribution: left - air ports
located on inner diameter, right - gas ports located on inner diameter, [Pa].
.......................................................................................................... 178

figure V1.44: Reverse-flow wave disc -— Mach number distribution: left - air
ports located on inner diameter, right — gas ports located on inner diameter.
.......................................................................................................... 179

figure V1.45: Reverse-flow wave disc - Reynolds number distribution: left — air
ports located on inner diameter, right — gas ports located on inner diameter.

.......................................................................................................... 180
figure V1.46: Static pressure distribution for the RFAI models, [Pa]. ............. 181
figure V1.47: Static temperature distribution for the RFAI models, [K] ........... 182
figure V1.48: Mach number distribution for the RFAI models. ....................... 183

figure V1.49: Pressure diagram for inner and outer circumference for the three
configurations, [Pa]. ............................................................................ 184

Figure V1.50: Pressure diagram for inner and outer circumference displayed for
one cycle only, [Pa]. ............................................................................ 185

xix

figure V1.51: Pressure diagram for high and low pressure gas for the three

configurations, [Pa]. ............................................................................ 186
figure V1.52: Pressure diagram for high and low pressure air for the three
configurations, [Pa]. ............................................................................ 187
figure V1.53: Temperature diagram for inner and outer circumference displayed
for one cycle only, [K] .......................................................................... 188
Figure V1.54: Temperature diagram for high and low pressure gas for the three
configurations, [K]. .............................................................................. 189
figure V1.55: Temperature diagram for high and low pressure air, [K]. .......... 190
Figure V1.56: Mach number diagram for inner and outer circumference. ......... 190

figure VII.1: Full assembly of the wave rotor topped ultra-micro gas turbine. .192

figure VII.2: Cross-sectional views of the UuGT unit. .................................... 193
figure V11.3: Partial assembly views of the UuGT, showing different components.

.......................................................................................................... 194
figure V11.4: Top and bottom view of the UpGT, showing also flow paths. ..... 195
Figure VIII.1: Axial ultra-micro wave rotor. .................................................. 196

figure V111.2: Axial ultra-micro wave rotor: left — top view; right - cross-section.
.......................................................................................................... 197

Figure V111.3: Schematic process flow for microfabrication of axial wave rotor.198
figure VIII.4: Positive mask used in step 5 of axial wave rotor fabrication. ..... 199

figure VIII.5: Radial ultra-micro wave rotor: a) 3D view; b) side view; c) top
view. .................................................................................................. 200

figure V111.6: Radial wave rotor: left - A-A cross-section (from Fig.5); right - B-B
cross-section. ...................................................................................... 201

figure VIII.7: Process flow for radial ultra-micro wave rotor fabrication. ......... 202
figure V111.8: Radial wave rotor with rounded cross-sectional channels. ......... 202

figure V111.9: Positive mask used in step 5 of radial wave rotor fabrication. ....203

figure VIII.10: Wafers used for rotor fabrication. ......................................... 204
figure VIII.11: Wafers used for ports and plenums fabrication. ..................... 205
figure V111.12: Cut-view of the rotor wafers' assembly. ................................. 206
figure V111.13: Cut-view of the ports’ and plenums’ wafer assembly ............... 206
figure V111.14: Full wave rotor assembly ...................................................... 207
figure VIII.15: Alignment marks - example. ................................................ 207

figure V111.16: Process flow for microfabrication of single channel test rig. ..... 208
figure VIII.17: Masks used for etching single channels. ................................ 209

figure VIII.18: Silicon microchannels: a) array of silicon dies; b) single die -
front view; c) single die- back view. ...................................................... 210

figure V111.19: Different size channels visualized with optical microscope. ...... 211

figure V111.20: Light reflection interference when visualizing silicon channels with
optical microscope. .............................................................................. 212

figure V111.21: Different size channels visualized with SEM: a) 90pm and 180 pm

wide channels; b) 360 pm and 720 um wide channels. ........................... 212
Figure V111.22: Details of microfabrication of the silicon channel. ................... 213
figure V111.23: Bond between silicon and glass wafers. ................................. 214

figure V111.24: Mounting bracket for the silicon chip: a) assembly; b) middle
aluminum plate; c) bottom plate with access holes ................................. 215

figure IX.1: Wave disc with curved channels — ports schematic. ................... 221
figure D(.2: Wave disc with curved channels - 3D rendering. ....................... 222
figure 1X.3: Simplified ultra-micro wave rotor test rig. ................................. 223
figure IX.4: Quasi 30 mesh model for 3D CFD investigations. ...................... 224
Figure A.5: Technical drawing of the ultra-micro wave rotor in a through-flow

configuration ....................................................................................... 227
figure A.6: Technical drawing of the ultra-micro wave rotor in a reverse-flow

configuration with air ports placed on the inside region. ......................... 227
figure A.7: Mask used for first etch step of rotor wafer 1. ............................. 230
figure A.8: Mask used for second etch step of rotor wafer 1 .......................... 230
figure A.9: Mask used for first etch step of rotor wafer 2. ............................. 231
figure A.10: Mask used for second etch step of rotor wafer 2. ....................... 231
figure A.11: Mask used for first etch step of plenum wafer 1. ........................ 232
figure A.12: Mask used for second etch step of plenum wafer 1. ................... 232
figure A. 13: Mask used for first etch step of plenum wafer 2 ......................... 233
figure A. 14: Mask used for second etch step of plenum wafer 2. ................... 233
figure A.15: Mask used for third etch step of plenum wafer 2. ...................... 234
figure A. 16: MA6/BA6 Mask Aligner - mask trey. .......................................... 236
figure A.17: Wafer holder for etching. ......................................................... 237

Figure A.18:

Wafer dicing saw. ................................................................... 239

xxii

CP

DH

:nxrqm

3V‘Q

UP

Key to Symbols and Abbreviations

speed of sound [m/s]

coefficient of thermal expansion [1/K]
cross-sectional area [m2]

specific heat [J/kg'K]

diameter [m]

hydraulic diameter [m]

boundary layer thickness [m]

thermal boundary layer thickness [m]
internal energy [J]

expansion wave; elastic modulus [GPa]
friction factor

body forces [N]

gravitational acceleration [m/sz]
specific heat ratio; specific weight
coefficient of convective heat transfer [W/mZ'K]
pressure drop [Pa]

polytropic efficiency [%]

isentropic efficiency [°/o]

channel length [m]

distance to sonic conditions [m]
velocity entry length [m]

thermal entry length [m]

mean free path [m]

characteristic length [m]

entrance loss coefficient; coefficient of thermal conductivity [W/m'K]
Knudsen number

Mach number

xxiii

 

p kinematic viscosity [St]
Nu Nusselt number
v Poisson’s ration
17 pressure ratio
p pressure [Pa]
Pr Prandtl number
PRw wave rotor compression ratio
(7 heat flux [W/mz]
radius [m]
specific gas constant [J/kg'K], compressor pressure ratio
density [kg/m3]
Re Reynolds number
5 shock wave
5t Stanton number
0' stress [Pa]
t time [5]
temperature [K]
u flow velocity [m/s]
up induced flow velocity behind shock wave [m/s]
v tangential velocity [m/s]
w shock wave velocity [m/s], specific work [kJ/kg]
x coordinate along the x—axis (usually along the channel)
Subscript:
0 inlet port
1 entry of the microchannel
2 location before shock (relative to fixed reference frame)
3 location after shock (relative to fixed reference frame)
4 exit of the microchannel

)odv

 

Chapter 1

INTRODUCTION

1.1 Micro and Ultra-Micro Power Systems

The second half of the 20‘" century was dominated by a boom in the electronic
industry and the semiconductor manufacturing technology associated with it. As this
technology of creating smaller and smaller devices evolved, more and more
complicated aesemblies were created and also medianical parts were included. These
assemblies grouped together generamd systems leading to the concept of Mice
E7ectn’ca/ Mechanical Systems (MEMS), whidi appeared at the end of 20th century.
Early work includes sensors and actuators; followed by valves; and recenfly complete
fluid microsystems.

As the systems become more complex, the need for a more efficient power source as
an alternative to batteries emerged. Scientists have started to investigate the
possibility of reducing the scale of high efficiency power sources that are currently
used (internal combustion engines, gas turbines, steam turbines) down to millimeter
and micrometer dimensions. A new research field was born: Power MEMS (Epstein,
Ayc'rn et al. 1997).

The most investigated power sources are gas turbines. Since there is a discrepancy
between what researchers all a microturbine, whid'r are gas turbines with structures

of micrometer size, and what industry calls microturbine, fire gas turbines in the

range of about 10-100kW. This work refers to first one - the microscale gas turbines -
as Ultra-Mica Gas Turbine (UpGD.

Due to their high power density, ultra-micro gas turbines (UpGT) are appropriate
solutions for powering unmanned air-vehicles (UAV) and the electronically
equipment associated with them (sensors, probes, or cameras). A typical size of
a microfabricated (on-the-chip) UpGT is 10mmx10mmx3mm with a power output
between 1 and 100W. These microfabricated gas turbines are also suitable for
high-density, distributed power generation onboard larger aircrafts. Applied in
batches they yield high redundancy and reduce the vulnerability of the system.
The power density of turbomachinery increases while their size decreases
because the output power is proportional to the mass flow rate of working fluid
through the engine. While this scales with the through-flow area, which is
proportional to the square of the characteristic length, the mass or volume of the
engine is proportional to the cube of the characteristic length. Thus, the power
density, which is Power/Volume will be proportional to the inverse of the
characteristic length. This is the so-called “cube square law", which suggests that
power density of turbomachinery will increase while the dimensions decrease
(Frechette 2000).

Today, the Power MEMS community comprises a few research groups, and some of
these and their results are going to be presented in this sub-diapter: Massad'rusetts
Institute of Tedwnology, Stanford University, University of Califomia at Berkeley,

Georgia Institute of Tedwnology, Washington State University, Midiigan State

University in United States, Sherbrooke University in Canada, ONERA in France,
Warsaw University of Technology in Poland, The University of Tokyo, Tokyo Institute
of Tedinology and Kanagawa Institute of Ted'rnology in Japan, Katholieke
Universiteit Leuven in Belgium, Birmingham University in United Kingdom, and
Korea Advanced Institute of Science and Ted'rnology in Korea. An “informal survey"
was presented by Epstein and Jacobson in 2003 and summarizes some of the results
obtained at that time in Power MEMS (Jacobson and Epstein 2003).

The first publication appeared about the Micro Gas Turbine Engine project at MIT
(Epstein, Ayén et al. 1997). It appears that there so far the most extensive work
has been performed in investigating Power MEMS. Their latest design (Jacobson,
Das et al. 2004) provides the basis of the research done and presented in this

thesis.

1.1.1 MIT Micro Gas Turbine Engine Project

In 1995 MIT initiated a project of miniaturizing gas turbines with the scape of
using them for power generation and small aerial vehicle propulsion. It was the
beginning of the Micro Gas Turbine Engine iject.

In 1997, the first information about the project is released. The baseline engine
design consisted of a supersonic radial compressor and turbine connected by a

hollow shaft (figure 1.1).

Slurter,
Gerrerulor
Flame

UGI Fuel p S
Holders Manifold lniecturs ,nniiire.snr

Diffuser Rotor

Gas
Varies Blades Inlet Path

 

 

 

 

 

 

 

 

 

l urbine Turbine Exhaug[
Nozzle Rotor Nnyzlp
Vanes B'BGBS (Lenterline m Rotor

of Rotation

_ Figure 1.1: MIT Micro gas turbine generator: cross-section (adapted from
(Epstein, Ayén et al. 1997)).

The combustor wraps the compressor-turbine unit as an annular ring. The
material used initially for fabrication was silicon. Extensive information for silicon
microfabrication was available; but part of the research process was to develop
new techniques for microfabrication, which allows for higher precision and better
manufacturing capabilities. Later, silicon carbide was incorporated to strengthen
the silicon substrate. This was done by the deposition of a SiC layer into 50pm
deep channels etched into a 100 pm thick Si wafer. At the same time silicon
carbide, which can withstand temperature up to 1900K (Keith 2004) without
cooling or a more advanced design having cooled Si as material for
compressor/turbine unit was introduced. Gas bearings were selected for the
rotating parts: journal bearings support the radial load and thrust bearings the
axial one. A motor/generator starts the gas turbine and produces electrical
power. It has been assumed to produce 20-40W (Epstein, Ayén et al. 1997;

Epstein, Senturia et al. 1997).

Initially, journal bearings were designed to be hydrodynamic (HD). But they
proved to be unstable at low speeds, creating problems at start-up (Jacobson
1998). Although they proved to be efficient, the design was modified to
incorporate hydrostatic (HS) thrust bearings for ease of operation, since they are
stable even with no rotation (Uu, Teo et al. 2005).

The first Microturbine/Bearing Rig fabricated was presented, including the
manufacturing process and initial test results, in the paper presented at the 13th
IEEE International MEMS Conference (Lin, Ghodssi et al. 1999). Initial tests
focused on the stability of the rotor and the potential of the hydrostatic bearings.
Results were shown after continuous operation up to 60,000rpm, but it was

noticed that the bearings were not constructed in the design parameters. The

compressor and turbine are displayed in Figure 1.2.

 

figure 1.2: Microcompressor and microturbine of the MIT project in the first
design stage, (reproduced from (Lin, Ghodssi et al. 1999)).

The microscale combustion process was studied in more detailed by creating a
three-wafer static structure that incorporated an annular combustion chamber.

figure 1.3 is a schematic of the structure, while Figure 1.4 shows an SEM

photography of the structure‘s cross-section. Preliminary hydrogen-air
combustion tests proved the resistance of the system to temperatures up to
1725K without degradation after continuous operation for 6 hours (Mehra, Waltz
et al. 1999). The structure was further advanced with compressor and turbine
airfoils, flame holders, and a recirculation jacket, all designed in a six-wafer
structure. The jacket aimed to recover the lost energy of the combustion
chamber to preheat the incoming reactants, while allowing the compressor
discharge air to cool the hot walls of the chamber. The flame holders were
incorporated for increasing combustion stability by creating some reservoirs for
hot products to serve as igniters for fresh reactants (Mehra, Zhang et al. 2000).
The tests showed a combustion efficiency ranging from 90—98% for a fuel-air
equivalence ratio of 0.6-0.4 and a mass flow rate of 0.04—0.06g/s. Hydrocarbon
fuels were tested but a sustained combustion reaction was not obtained.

Fuel Manifold
1 .

 

 

    

 

 

 

 

Swrrl Varies Combustion Chamber

Figure 1.3: MIT combustor structure (adapted from (Mehra, Zhang et al. 2000)).

 

luel plenum

 

combustion chamber

Figure 1.4: MIT Three—wafer structure for microcombustion study (reproduced
from (Mehra, Zhang et al. 2000)).

A new design for the micro gas turbine engine was proposed in 2000, called the
H2 Demo Engine. (Epstein, Jacobson et al. 2000). The main change was to
structurally connect the compressor directly to the turbine back to back without a
shaft connecting them. The turbine is then cooled by conduction to the
compressor, thus keeping the overall temperature lower than the maximum
admissible temperature of the material. This way, the air coming to the
compressor would be used to cool down the turbine. The disadvantage is that
the pressure ratio in the compressor would drop from 4:1 to 2:1. The
compressor diameter was increased from 4mm to 8mm, and the turbine
diameter to 6 mm. The airfoils were heightened from 200pm to 400nm; thus,
the mass flow rate increased to 0.3Gg/s. The cross-sectional diagram of the H2

Demo Engine is presented in Figure 1.5.

Starting
in Thrust

Compressor Diffuser
rotor vane Combustor

  

3.7 mm

guide vane

JOU'Va' Turbine
l beanng 21 mm rotor :

 

Figure 1.5: MIT H2 Demo Engine with conduction-cooled turbine constructed from
six silicon wafers (adapted from (Epstein, Jacobson et al. 2000)).

More work was done on enhancing the gas bearing system. Since the project ‘5
main part is a rotating disk, the problem of free rotation is crucial. A microsystem
(Figure 1.6) was developed to study the performance of a turbine and
compressor unit supported by gas lubricated bearings (Frechette, Jacobson et al.
2000; Frechette, Jacobson et al. 2005; Liu, Teo et al. 2005). The device was
tested to rotational speeds above 1 million RPM, which would convert into a tip
speed of 300m/s, similar to the ones obtained in conventional scale
turbomachinery.

The igniters for the combustion chamber were investigated next (Zhang, Mehra
et al. 2002; Zhang, Mehra et al. 2003). The MIT research group concluded that
thin-film polysilicon resistive elements should be used as igniters for the
microengine combustor, showing that it is possible to locally heat an isolated

element up to 600K and ignite the hydrogen-air mixture used as combustible.

Iiirhiric Hydrostatic Jorrnml

 

Stator Rotor llrnrst Bearings Bearing
.,
i
l s
I wafer
i slack
7%
...l
Journal “mist Art Journal
Pressiuualiou Daliuice Exhaust Press'iuunlion
l’lcmim l Plcnirm Plenum 2

Figure 1.6: MIT bearing testing structure (reproduced from (Frechette 2001)).

The research efforts were once again focused on the combustion system of the
micro gas turbine engine. An intermediate step in developing the final concept of
combustion chamber was to fit platinum-coated nickel foam inserts and use them
as on initial catalytic combustor test-bed. Thus hydrocarbon fuels could be
ignited and burned with a sustained rate at efficiencies of about 40%
(Spadaccini, Zhang et al. 2003). A new approach was taken for the combustion
system: to have a dual-zone combustor, basically delivering fuel-air mixture to
the combustion chamber by two paths (Spadaccini, Lee et al. 2002; Spadaccini,
Mehra et al. 2003). This allowed hydrogen fuel to burn with efficiencies above
90% and hydrocarbon fuels at 60%. The difference between the older design

and the new one is illustrated in Figure 1.7.

Fuel Pressure Compressor
enurn port vanes

   

 

Combustor
inlet slots

10.6 mm

 

Figure 1.7: Single-zone and Dual-zone combustor, part of the MIT micro gas
turbine engine (adapted from (Spadaccini, Zhang et al. 2003) - left and
(Spadaccini, Mehra et al. 2003) — right).

In 2003 the design was modified by reintroducing the shaft between the
compressor and the turbine. This was possible by strengthening the turbine disc
with silicon carbide (Epstein 2003). The new generation turbocharger (shown in
Figure 1.8) was tested to rotational speeds of 480,000RPM. The turbocharger
had a compressor and turbine and was basically the H2 Demo Engine with the
compressor exhaust disconnected from the turbine inlet. The pressure ratio

measured across the compressor was 1.21 (Jacobson, Das et al. 2004).

Compressor Compressor

Tutu". Compfugof Inlet out.“

rln

       
  
 
 
   

  
 
 

 
 

    

 
    

é. f-

i, firearm trim

Ear:- .~:~e.s~.~..‘1:¢mrrwlimm mm can“
Turbine

 

Exhaust

Figure 1.8: MIT turbocharger test structure (adapted from (Epstein 2003)).

10

Although many of the initial problems and challenges were overcome in the past
10 years and the micro gas turbine engine project is closer to reality than in
1995, a problem is still to be solved: the efficiency of the overall process is low,
making the system unfeasible. This is due to physical effects that have more
influence on the process at microscale compared to regular scale fluid dynamics:
wall shear stresses and friction, viscous forces, usable strength of materials, and
chemical reaction times. Also, the manufacturing processes are still constraining
the design to an approximate 2D layered design, which is restricting the flow and
affecting the mass flow rate.

The low efficiency (below 50%) of the turbo compression system (Miiller and
Fréchette 2002) has been isolated as a major problem for the feasible design
space of the project. In this thesis, a solution is proposed which will increase the
efficiency of the compressor and/or increase the pressure boost of fresh air
delivered to the combustion chamber, thus increasing the efficiency of

combustion.

1.1.2 gher Thermg-Mechanical MEMS Devices

1. 1.2.1 Stanford University

The Rapid Prototyping Laboratory at Stanford University built a micro compressor
impeller and tested it at rotational speeds up to 420,000RPM. The impeller was

molded from silicon nitride using a Mold Shape Deposition Manufacturing (SDM)

11

process. In the same time a numerical model was developed using an in-house made
Computational Fluid Dynamics (CFD) code. The results from experiments were
compared to the CFD results, and good matching has been obtained. The adiabatic
efficiency of the compressor was calculated as 70% at 400,000RPM with numerical
and experimental values, and predicted 65% at 800,000RPM which would convert to
500m/s tangential tip velocity (Kang 2001; Johnston, Kang et al. 2003; Kang,

Johnston et al. 2004). figure 1.9 presents the micro compressor-turbine unit.

mass for
balancing

     

compresso ‘

Figure 1.9: Stanford’s micro turbo—compressor with bearing cartridge (reproduced
from (Kang, Johnston et al. 2004)).

1. 1.2.2 Sherbrooke University

Efforts for developing a Rankine Cycle Microturbine are underway in Canada. The
research group led by Dr. Luc Fréchette proposes the concept of a miniaturized
complete micro Rankine power source, consisting of a heat source (burner with

fuel tank or waste heat), a cooling mechanism (cooling fan or other heat removal

12

approach), the MEMS-based micro Rankine device and power electronics. The
Rankine device itself consists of a steam-driven turbine that entrains a liquid
pump and an integrated generator, along with a compact evaporator and a
condenser (Frechette, Lee et al. 2004). A schematic cross-section of this device

is shown in Figure 1.10.

  
 
   
 
   
 

HOT m WOGKING ‘LUID EVAPORAlOfl

l URBlNE
Nut Input STAYDR DDTOR

lH£'~‘MAL
ISOLADON

(OLD SIDE
Hut Rejection BEARINGS CONDENSER PUP/i? GENERATDR CONTACT PADS

 

Figure 1.10: Schematic cross-section of a Rankine steam turbine device
(reproduced from (Frechette, Lee et al. 2004)).

1.1.2.3 University of Tokyo

The University of Tokyo has been investigating a device similar to the MIT one,
having initially built a “palm top” model with an outer diameter of 180mm and
length of 335mm, which will generate 2-3kW at 235,000RPM. Also a microscale
model is proposed, the “finger top" gas turbine with a diameter of 23mm and
length of 32mm producing tens of Watts at 1,170,000RPM. The predicted
thermal efficiency of the micro gas turbine would be 7% for a simple cycle and

15% in a regenerative cycle (Matsuo, Yoshiki et al. 2003). Several other models
13

of 2D and 3D radial microturbines were designed and fabricated, efficiencies of
the 2D ones being reported as 15% lower than the ones of 3D for the same

generic dimensions (Matsuura, Kato et al. 2003).

""I‘T—T “T-“ ‘l

 

Figure 1.11: “Palm top” model of microturbines (reproduced from (Matsuura,
Kato et al. 2003)).

1. 1.2.4 Tokyo Institute of Techno/ogy

The design of a recuperator is proposed by the Tokyo Institute of Technology for
microturbines similar to the ones designed at the University of Tokyo: one with
an output of nearly 3kW and another with 15W output. In the case of 3kW class
turbine an offset-strip-fin recuperator was employed. For the smaller size turbine
a microchannel recuperator was designed. Although the effectiveness of
microchannel recuperator is larger than that of offset-strip—fin recuperator, it
suffers from a deterioration of effectiveness clue to the axial heat conduction of
the wall. The reported thermal efficiencies of the cycles topped at 35%

(Nagasaki, Tokue et al. 2003).

14

1. 1.2.5 777e French Aeronautics and Space Research Center (ONERA)

Ribaud and his team at ONERA have extensively investigated the heat transfer
phenomena in a ultra-micro gas turbine (Dessornes, Dumand et al. 2003; Ribaud
2003). Based on theoretical and numerical models developed, several
conclusions were stated: a non adiabatic operation of the turbomachines leads to
a strong penalty in performances, doubling the size of the microturbine allows
the recovery of a suitable power, so is heat insulation. The use of a low
conductivity material for the stator would improve performances by a large
amount. The external radiation heat losses are estimated to 10% of the nominal
power for the 20mm diameter microturbine. A thermal shield of 2mm thickness is
a good way to enhance the performances and is certainly a necessity for
integration. Starting from the MIT micro gas turbine engine, an alternative

combustion chamber was designed (Figure 1.12).

15

rim ..

 

 

      
 

’////l '

’l//////l/l/l/l/I/I/I/l/l/I/II/ " ‘
/// //// 'l/l. //

compressor
fresh air

Figure 1.12: ONERA alternative to the MIT combustion chamber (reproduced
from (Ribaud 2003)).

L/V

  

1. 1.2.6 Catholic University of Leuven

Peirs, Reynaerts, and Verplaetsen have developed a single-stage axial
microturbine generator with a rotor diameter of 10 mm (Peirs, Reynaers et al.
2004; Peirs, Verplaesten et al. 2004). This turbine is a first step in the
development of a microgenerator that produces electrical energy from fuel. The
turbine, made of stainless steel, was manufactured using die-sinking electro-
discharge machining (EDM). The turbomachinery is connected by a shaft that is
supported by ball bearings. It has been tested to speeds up to 160,000rpm and

generates a maximum mechanical power of 28W with an efficiency of 18%.

16

When coupled to a small generator, it generates 16W of electrical power, which

corresponds to 10.5% efficiency for the total system.

1. 1.2.7 University of California at Berkeley

The Berkeley Sensor and Actuator Center has developed the micro Wankel
Engine. Initially, a 12.9mm rotor engine was manufactured out of steel, spinning
at 9,300RPM and producing 4W (Figure 1.13). The next step was a 2.4mm silicon
rotor (Figure 1.14), aiming to produce up to 0.1W (Walther and Pisano 2003).
Also, a Viscous Rotary Engine Power System (VREPS) is proposed, which will
extract mechanical power from the surface viscous shearing forces developed by
a pressure driven flow present between a rotating disk or annulus and a

stationary housing (Cauley, Rosario-Rosario et al. 2004).

 

Figure 1.13: Berkeley’s steel piston and combustion chamber for a micro Wankel
engine (reproduced from (Walther and Pisano 2003)).

17

 

figure 1.14: Berkeley’s silicon piston d'iamber for a micro Wankel engine
(reproduced from (Walther and Pisano 2003)).

18

1.2 Wave Rotor Technology and Its Applications

The wave rotor is a pressure exchanger that uses the concept of direct pressure
transfer between fluids by waves. A basic wave rotor consists of a rotating drum
with straight channels arranged around its axis. The drum lies between two end
plates, each of which has a few ports or manifolds controlling the fluid flow
through the channels. Figure 1.15 presents a schematic axial wave rotor drum
and its end plates.

End Plates

  
  

 

Channels

 

Pods

Figure 1.15: Axial wave rotor drum and end plates.

Figure 1.16 presents a wave rotor drum from a Comprex®. The number of ports
and their positions vary for different applications. T'hrough rotation, the channel
ends are periodically exposed to the ports located on the stationary end plates
initiating compression and expansion waves within the wave rotor channels.

Therefore, unlike a steady-flow turbomachine, which either compresses or

19

expands the gas, both compression and expansion are accomplished within a

single component.

 

Figure 1.16: Comprex® wave rotor drum.

The gap between the end plates and the channel assembly has to be relatively
small to minimize leakage losses. This may be ensured by a passive or active gap
control or by contacting surfaces that are made of an appropriate sealing
material. While in most applications the channel assembly rotates and the end
plates are stationary, the opposite configuration has been suggested in which the
channels are stationary and the end plates with port openings rotate, ensuring
the same flow control mechanism. Such a configuration has more than one
rotating part and usually doubles the number of interfaces that need to be sealed
between rotating and stationary parts. However, it may be preferred for
laboratory investigations because it easily enables flow measurement in the

stationary channels where the important dynamic interactions take place.

20

Two four-port wave rotor schematics for gas turbine topping are presented in
Figure 1.17: In a through flow (TF) configuration all flows travel in the same
direction. In a reverse flow configuration (RF), each flow (gas or air) exits the
same side at which it enters. For the TF wave rotor, the channels of the wave
rotor are initially filled with air coming from the compressor (“fresh air"), through
the low pressure air port (LPA/ 1). When they come in contact with the gases
coming from the combustion chamber, which have high pressure and
temperature (HPG/3), a shock wave is formed, which compresses the fresh air.
This high pressure air (HPA/2) is then evacuated to the combustion chamber,
while the remaining gases, which now have a lower pressure than at the
entrance are scavenged towards the turbine. They are called pre-expanded

gases or low pressure gases (LPG/4).

a)

 

 

 

 

bl

    

Wk

Figure 1.17: Four-port wave rotor schematic. a) Through-flow configuration; b)
Reverse-flow configuration (C — compressor, CC — combustion chamber, WR —
wave rotor, T — turbine).

21

The active components of an axial wave rotor in a through-flow configuration as

well as the trajectories of the flow are displayed in Figure 1.18.

 

Figure 1.18: Flow trajectories in a Through—flow axial wave rotor.

The rotating parts may be gear or belt driven or preferably direct driven by an
electric motor. The power required to keep them at correctly designed speed is
negligible. It only needs to overcome rotor windage and friction in the bearings
and contact sealing if used. Alternatively, rotors can be made self—driving. This
configuration, known as the “free-running rotor”, can drive itself by using the
momentum of the flow to rotate the rotor.

The periodic exposure of the channels to both fluids between which the pressure
is exchanged, assures a channel wall temperature between the temperatures of
both fluids, which gives the wave rotor an inherently self-cooling feature.
Further, the velocity of the working fluid in the channels is about one-third of
values within turbomachines. Therefore, the rotor channels are less prone to
erosion damage than the blades of turbomachines and viscous loses are less

seve re .

22

From the manufacturing point of view, adding a wave rotor is much easier at
microscale than at macroscale. The fabrication processes at microscale are
mainly two-dimensional (etching, deposition, oxidation, and bonding), heavily
constraining the geometry of the components. The wave rotor can easily be
etched in silicon due to its common extruded 2D shape; moreover it can be done
in the same process step with creating the turbine or compressor blades.
Additionally, in a regenerative way the wave rotor allows to harvest some of the
heat conducted away from the combustor through the structure, which is a
severe problem for microfabricated gas turbines and also reduces the efficiency

of the spool compressor.

I.2.1 Wave Rotor Investigations and Produfi

A very useful and well documented review of the wave rotor technology is
offered by Akbari, Nalim, and Miiller (Akbari, Nalim et al. 2004). The most
important applications and research results in the field are presented next.

As a combined expansion and compression device, the wave rotor can be used
as a supercharging device for IC engines, a topping component for gas turbines,
or in refrigeration cycles. 1n advanced configurations, the high energy fluid may
be generated by combustion occurring internally in the wave rotor channels
allowing extremely short residence times at high temperature, hence potentially
reducing emissions. A condensing wave rotor may be viewed as a similarly
advanced configuration that enhances the performance of refrigeration cycles.

23

Recently, wave rotor technology has been envisioned to enhance the
performance of ultra-micro gas turbines manufactured using today’s and future
microfabrication technologies (Okamoto, Nagashima et al. 2003; Iancu, Akbari et

al. 2004).

Gas Turbine Applications

For gas turbine applications, in a conventional arrangement, a wave rotor is
embedded between the compressor and turbine “parallel" to the combustion
chamber. Figure 1.17 illustrates how a four-port wave rotor is used to top a gas
turbine cycle. In the wave rotor channels, the hot gas leaving the combustion
chamber compresses the air coming out of the compressor. After the additional
compression of the air in the wave rotor, it is discharged into the combustion
chamber. The burned gas expands during the compression of the air and is
aftenivards scavenged toward the turbine. The channels are then reconnected to
the compressor outlet, allowing fresh pre-compressed air to flow into the wave
rotor channels; and the cycle starts again. Due to the pre-expansion in the wave
rotor, the burned gas enters the turbine with a temperature less than the
combustor exit temperature. However, the gas pressure is higher than the
compressor exit pressure by the pressure gain obtained in the wave rotor. This is
in contrast to the untopped engine, where the turbine inlet pressure is always
less than the compressor discharge pressure due to the pressure loss occurring

in the combustion chamber.

24

The general advantage of using a wave rotor becomes obvious when comparing
the thermodynamic cycles of baseline and wave-rotor-enhanced engines. Since
the wave rotor application was first envisioned and tried for gas turbines (Meyer
1947), this is demonstrated in a schematic temperature-entropy diagram for a
gas turbine baseline engine (dashed line) and the corresponding wave-rotor-

topped engine (solid line) in Figure 1.19.

0 - 1b — 4y, - 5b baseline engine

Temperature

 

 

 

Entropy

Figure 1.19: Temperature -Entropy Diagram for a gas turbine engine with and
without wave rotor topping.

While many other advantageous implementation cases of the wave rotor into a
given baseline engine are possible (Akbari and Mijller 2003; Akbari and Miiller
2003). The diagram shows that both the baseline and the enhanced cycle gas

turbine are operating with the same turbine inlet temperature and compressor

25

pressure ratio. However, the output work of the topped engine is higher than
that of the baseline engine due to the pressure gain across the wave rotor. In
the shown case the amount of heat addition is the same for both cycles.
Therefore, the thermal efficiency for the topped engine is higher than that of the
baseline engine, which is indicated by the lower entropy production in the wave-
rotor- enhanced cycle.

Wave rotors as topping devices for gas turbine cycles have been studied
extensively. Since the early 19605, General Electric Company (GE), General
Power Corporation (GPC), and Rolls Royce have been involved in the
development of wave rotor prototypes for propulsion applications (T aussig and
Hertzberg 1984; Shreeve and Mathur 1985). Mathematical Science Northwest
(MSNW) also studied various aspects of wave energy exchange and proposed a
wave rotor design for an aircraft turbofan engine (T aussig and Hertzberg 1984).
In the 19805, different US agencies like Defense Advanced Research Program
Projects Agency (DARPA) and the US Navy expressed interest and sponsored
programs to develop an understanding of wave rotor science and technology.
Many developments were presented in the 1985 ONR/NAVAIR Wave Rotor
Research and Technology Workshop (Shreeve and Mathur 1985).

Since the late 19805, A large research program at NASA Glenn Research Center
(GRC) collaborated by the US Army Research Laboratory (ARL) and Rolls-Royce
Allison has aimed to develop and demonstrate the benefits of wave rotor

technology for future aircraft propulsion systems (Paxson 1992; Paxson 1996;

26

Wilson and Paxson 1996; Welch 1997; Welch 1997; Welch, Jones et al. 1997;
Welch 2000). Experimental studies at NASA on four-port (Wilson 1997) and
three-port (Wilson and Fronek 1993; Wilson 1997; Wilson 1998) wave rotors
enabled the estimation of loss budgets (Paxson 1993; Paxson 1995) and
simulation code validation (Paxson and Wilson 1995). The experimental work
consisted of two phases. Initially, a simple three-port flow divider wave rotor was
built and tested to evaluate loss mechanisms and calibrate the simulation code.
Next, a four-port pressure exchanger was built and was tested to evaluate the
pressure-gain performance for application to a small gas turbine (Allison 250).
However, a study by Rolls-Royce Allison indicated that thermal loads on the rotor
and ducting predicted for the NASA wave rotor cycle in real engine conditions
may be difficult to manage. The rotor used in testing, as well as the test stand
for a four port configuration are displayed in Figure 1.20. In response, Nalim and
Paxson (Nalim and Paxson 1999; Paxson and Nalim 1999) proposed an alterative
cycle with a combustor bypass significantly lowering thermal loads. Sealing and
mechanical design issues are being addressed in current NASA tests.

NASA's wave rotor research was later extended to the concept of internal
combustion wave rotors (Nalim 1995; Nalim and Paxson 1997; Nalim and Paxson
1997; Nalim 1999) in which both pressure exchange and combustion take place
within the wave channels, and further to pulse detonation engines (PDE) taking

advantage of constant-volume combustion for higher performance and better

27

efficiency (Paxson 2001; Schauer, Stutrud et al. 2001 ; Shimo, Meyer et al. 2002;

Wilson and Paxson 2002).

 

Figure 1.20: NASA four port wave rotor. Left - the rotor, Right - the test system.

In a recent study, Akbari and Mueller have performed a thermodynamic analysis
to calculate the thermal efficiency and specific work of two unrecuperated
microturbines (30 and 60kW) topped with a four-port wave rotor. The engines
manufactured by Capstone Turbine Corporation have been widely used recently,
and efforts are currently being instituted to increase their performance
considerably. The results have predicted overall thermal efficiency and specific
work enhancement up to 34% for the smaller engine and 25% for the larger
engine, using a four-port wave rotor with a compression ratio of 1.8 (Akbari and
Miiller 2003). The general performance maps obtained by the authors clearly
have demonstrated the considerable performance enhancements of small gas
turbines through the use of wave rotors. A similar approach has predicted an

improvement up to 15% of overall efficiency and specific thrust in a turbojet

28

engine using the wave-rotor-topping cycle of the 30kW microturbine flying at an
altitude of 10,000m at Mach 0.8 (Akbari and Miiller 2003).

Car Engine Supercharging

Wave rotors have been commercially used for internal combustion engines (ICE)
as a replacement for conventional superchargers or turbochargers. Compared to
the turbocharger, the wave rotor has the advantage of a better response time to
engine acceleration (no turbo-lag), and its efficiency does not decrease with the
size reduction of the device. These characteristics make the wave rotor more
suitable for small displacement engines than the TC, as it can be seen in Figure
11.21. The wave rotor has also self-cooling capability, due to the continuous

circulation of the air through the rotor.

 

 

 

 

 

100 '
80 "
H .
I: 50 - 100
b L
3 o\°
8. 40 ' 80 3
s - 3
c:
20 r 60 “
. . E
O 1 1 1 1 4O
20 4O 60 80 100
%cnginc speed

Figure 11.21: Comparison between the Comprex® supercharged engine (CX) and
the turbocharged engine (TC) performances (Heisler 1995).

Figure 11.22di5plays the main components of the ICE-wave rotor system. The
channels are placed axially at the periphery of a cylindrical rotor. In the Comprex®

case, it is a RF wave rotor, which determines the rotor to have a “hot” side and a

29

“cold” one. The hot side contains the engine exhaust gases ports, while the air
ports are placed on the cold side, as well as the rotor bearings. The engine
crankshaft drives the rotor via a belt drive (Doerfler 1975). The wave rotor does
not use mechanical work from the engine to compress the air like a mechanical
supercharger. Instead, the rotor is driven in order to match the wave

phenomena with the load and speed requirements of the engine.

 

. (
Figure 1.22: Comprex® system: 1 - ICE; 2 - HPG port; 3 — HPA port; 4 - LPG
port; 5 -LPA port; 6 - rotor; 7 - drive system.

The wave rotor is more suitable for a steady-state function, but the ICE works on
a wide range of speeds and loads; so there are mismatched working conditions
between the two systems. In order to smooth out these problems, so called
“pocke ” were built inside the stator casing. There are two pockets on the cold
side of the stator, the Compression Pocket (CP) and the Expansion Pocket (EP)
and a Gas Pocket (GP) on the stator’s hot side. The CP deals with the unmatched
processes when the engine works at low revs, and the EP and GP help the
exhaust gas rotor scavenging process on all loads and speeds range of the

engine (Gyarmathy 1983).
30

The exhaust gas scavenging of the rotor is very problematic, such being the case
at low engine loads, like start-up or idling. For these specific conditions, the wave
rotor has a starting-valve, which blocks the exhaust gas from entering into the
engine cylinders. When the wave rotor is cut-off from the inlet manifolds, the ICE
works in a natural-aspired mode. For a better control of the boost-pressure, the
Comprex® incorporates a “wastegate valve”, similar to that used on modern
turbochargers.

The wave rotor can be driven by a belt drive system or by the exhaust gas, like
the turbocharger. This type of Comprex® is called the “free-running” Comprex®.
In this case, the speed of the rotor does not have the same importance like it
has for the turbocharger because the compression process is not influenced by
it. The speed of the wave rotor has only a distribution role, so even if there is a
turbo lag, it has little effect on the performance of the free-running Comprex®.
This type of wave rotor has a ceramic rotor in order to reduce the inertia and to
improve the overall efficiency, unlike the original Comprex®, which had a metal
rotor (Zehnder, Mayer et al. 1989).

Brown Boveri Company (BBC), later Asea Brown Boveri (ABB) and now Alston, in
Switzerland has a long history in wave rotor technology. As reported by Meyer
(Meyer 1947), the first successful wave rotor was tested in the beginning of
19405 as a topping stage for a locomotive gas turbine engine based on patents
by Claude Seippel (Seippel 1940; Seippel 1942; Seippel 1946; Seippel 1949). The

first wave rotor was not used commercially, mainly because of its inefficient

31

design and crude integration (Azoury 1992). Later, BBC decided to concentrate
on the development of pressure wave superchargers for diesel engines, due to
their greater payoff compared to other applications (Taussig and Hertzberg
1984). By 1987, the first wide application of the Comprex® in passenger cars
occurred in the Mazda 626 Capella(Mayer, Oda et al. 1989; Zehnder, Mayer et al.
1989). The Comprex rotor and a cut-view of the supercharging system from a
Mazda 626 is presented in Figure 1.23. Since then, ABB’s Comprex® pressure
wave supercharger has been commercialized for several passenger cars and
heavy diesel engines. The Comprex® has also tested successfully on vehicles
such as Mercedes-Benz diesel car (Hiereth 1989), Peugeot, and Ferrari (Taussig
and Hertzberg 1984). The main advantage of the Comprex® compared to a
conventional turbocharger is its rapid response to changes in engine operating
conditions. Furthermore, as the efficiency of the Comprex® is independent of
scale, its light weight and compact size make this device attractive for
supercharging small engines (below about 75kW or 100HP) (Azoury 1965;

Guzzella, Wenger et al. 2000).

32

  

‘\
Figure 1.23: Comprex® rotor and a Mazda 626 supercharging system cut-view.
Another interesting approach in the wave rotor for ICE area was made in the late
905 by the Swiss Federal Institute of Technology Zurich, Switzerland in
collaboration with Swissauto Wenko AG. Their version of Comprex®, called the
Hyprex®, is driven by an electrical motor, which is controlled by the engine’s
Electronic Control Unit (ECU). The Hyprex® does not have pockets in its stator
and rely on a Gas Pocket Valve (GPV) to regulate the boost-pressure and the
rotor’s scavenging process. The GPV is also controlled by the ECU and has a very
important role because the Hyprex® is designed to work on small gasoline
engines, where the boost pressure and the EGR rate have a major influence on

the energetic and pollution performances of the SI engine (Weber 2001).

Refrigeration Applications
Wave rotors also have been used for air-cycle refrigeration systems (Azoury
1992; Kentfield 1993; Kentfield 1998). Power Jets Ltd in the U.K. utilized wave

rotor technology in the design and development of two prototype air-cycle

33

refrigerators used for environmental cooling purposes. The prototypes were
installed and employed in gold mines in India and South Africa and performed
the same duty as equivalent vapor-cycle machines but with lower weight and
bulk.

Recently, a unique and cutting-edge application of wave rotors in refrigeration
cycles using water (R718) as a refrigerant has been studied (Akbari, Miiller et al.
2003; Kharazi, Akbari et al. 2004; Kharazi, Akbari et al. 2004; Kharazi, Akbari et
al. 2004). In fact, the wave rotor implementation can increase efficiency and
reduce the size and cost of R718 units. A three-port wave rotor has been
introduced as a condensing wave rotor that employs pressurized water to
pressurize, desuperheat, and condense the refrigerant vapor - all in one dynamic
process. Besides, giving the possibility of an additional rise of the vapor pressure,
the condensing wave rotor eliminates the need of a bulky condenser because full
condensation occurs inside the rotor channels. Furthermore, adding a
condensing wave rotor to a water refrigeration cycle allows for a lower pressure

ratio of the compressor, which is crucial for the R718 chiller technology.

1.2.2 Numerical Investigatigns

Among the processes taking place inside the wave rotor cells the main one is the
development of compression and expansion waves between gases having
different pressures and temperatures. This will constitute the primary energy

exchange that takes place inside the cells. Other forms of energy exchanges are:

34

heat transfer between fluids traveling through the channels and walls and friction
losses due to the high viscous aspect of the flow at microscale.

Some assumptions are taken into consideration when writing the governing
equations of the flow inside the wave rotor channels. Since the ratio of cell
length over the cell width or height is greater than 10, this problem is accepted
as being one-dimensional and will be treated as such. The gases involved in the
process are considered to be ideal and compressible. Since the perfect gas
constant and specific heat ratio are almost equal for air and exhaust gas, it will
be assumed in this chapter that all gases have the same properties: R=287
J/kg'K and 7:1.4.

Considering all the presented assumptions, unsteady flow of compressible gas in

a one dimensional process is described by the following equations (Shapiro 1953;

Anderson 2003).
Continuity equation
g; + 6(_6/:(Q = 0 (L1)
Navier-Stokes equation
%+U§%z—Z+g—g—v:—z—pfl=0 (1.2)

where h} are the body forces and v is the kinematic viscosity.

For frictionless flow, the Navier-Stokes equation is reduced to Euler equation.

35

Energy equation

a [,{e + LCD + £031]? + flag] + am") — pa — ,0fo = o (1.3)

 

5t 2 2 6x

where q is the heat flux between fluid and walls.

Several variations of these equations are found in the wave rotor literature since
each paper deals with certain aspects of the flow investigations.

Spalding at Imperial College in the United Kingdom is one of the pioneers using a
1D method to investigate unsteady flows inside wave rotors in the early 19705.
He formulated a numerical procedure for wave rotors considering the effects of
heat transfer and friction. 1t utilized novel features to ensure solutions free from
instabilities and physical improbabilities, as reported by Azoury (Azoury 1992).
Based on this numerical model, a computer program was developed by Jonsson
(Jonsson, Matthews et al. 1973), and it was successfully applied to pressure
exchangers (Matthews 1969; Azim 1974; Azoury and Hai 1975).

In 1981, Turbopropulsion Laboratory (TPL) at the Naval Postgraduate School
(NPS), directed by Shreeve, started an extensive numerical and analytical wave
rotor program to evaluate the wave rotor concept and its potential application in
propulsion systems (Shreeve, Mathur et al. 1982). For numerical simulations, two
different approaches to the solution of the unsteady Euler equations were
examined in the overall program. First, Eidelman developed a ZD code based on
the Godunov Method to analyze the flow in wave rotor channels (Eidelman 1984;

Eidelman, Mathur et al. 1984; Eidelman 1985; Eidelman 1986). Unlike

36

contemporary one-dimensional approaches (Mathur, Shreeve et al. 1984), the 2D
code showed the effect of gradual opening of the channels. The main conclusion
of these studies is that if the channels are straight, the flow remains nearly 1D,
which in turn leads to minimal mixing losses caused by rotational flow in the
Channels (Eidelman 1996). However, when the channel of the wave rotor is
curved, even an instantaneous opening of the channel does not lead to the
development of a 1D flow pattern with small losses. Computation time of such a
2D code has been reported to be quite long. Therefore, interest was given to
development of a 1D code introduced by Mathur based on the Random Choice
Method solving the Euler equations (Mathur 1985; Mathur and Shreeve 1987).
The code which is called WRCOMP (wave rotor component) is first-order
accurate in time and it was unconditionally stable. WRCOMP calculated the
unsteady process inside the wave rotor, inlet and outlet opening times, and other
useful design parameters required for a preliminary design. The outputs from
WRCOMP are used in a second program, called ENGINE, performing a
performance calculation for a turbofan jet engine (Mathur 1986; Mathur 1986;
Roberts 1990). The results have also confirmed the significant performance
improvement that could be expected integrating a wave rotor into a turbofan
engine. Work was planned toward incorporating the effects of friction and heat
transfer into WRCOMP and also including other engine configurations in ENGINE

code. Some modifications to WRCOMP code was later started (Salacka 1985;

37

Johnston 1987), but further development was not pursued after the wave rotor
research at TPL-NPS was terminated around 1986.

During 19905, a few numerical investigations of pressure wave superchargers are
reported. Eldin and his associates in Germany developed a fast and accurate
numerical method for predicting unsteady flow field in pressure wave machines,
using the theory of characteristics (Eldin, Oberhem et al. 1987; Oberhem and
Eldin 1990; Oberhem and Eldin 1991; Eldin and Oberhem 1993; Makarious, Eldin
et al. 1995; Oberhem and Eldin 1995; Makarious, Eldin et al. 1997). Piechna and
his research group at Warsaw University of Technology in Poland have developed
experimentally validated 1D and 2D numerical codes to analyze the flow field
inside the Comprex® (Piechna 1998; Piechna 1998; Piechna 1998; Piechna and
Lisewski 1998; Elloye and Piechna 1999; Piechna 1999; Selerowicz and Piechna
1999). Piechna has also proposed a hybrid of the pressure exchanger with
internal combustion wave rotor presenting the idea of the autonomous pressure
wave compressor (Piechna 2003).

By initiating wave rotor research at NASA Lewis Research Center (now Glenn
Research Center) in the late 19805, Paxson developed a quasi-one-dimensional
gasdynamic model by analogy with a shock tube to calculate design geometry
and off-design wave rotor performance (Paxson 1992; Paxson and Wilson 1993).
The code uses an explicit, second-order, Lax-Wendroff type TVD scheme based
on the method of Roe to solve the unsteady flow field in an axial passage for

time-varying inlet and outlet port conditions. It employs simplified models to

38

account for losses due to gradual passage opening and closing, viscous and heat
transfer effects, leakage, flow incidence mismatch, and non-uniform port flow
field mixing. Recent improvement and validations have completed it as a
preliminary and general design tool (Paxson 1995; Paxson 1995; Paxson and
Wilson 1995; Paxson 1996; Paxson 1997; Paxson and Lindau 1997; Paxson
1998; Welch, Paxson et al. 1999). Welch has also established 1D and 2D analysis
models to estimate the performance enhancements of wave rotors (Welch 1993;
Welch and Chima 1993; Welch 1997). Larosiliere has also established a multi-
dimensional code to investigate the effect of gradual opening and losses
(Larosiliere 1993; Larosiliere 1995; Larosiliere and Mawid 1995).

In 1995, Weber published a book about designing a shock wave engine (Weber
1995). His preliminary design procedures include solving the Riemann problem
for a 1D, gasdynamic process. His method is adapted from Shapiro and Rudinger
(Shapiro 1953; Rudinger 1969).

Lear at the University of Florida started investigating different configurations of
wave rotors by means of analytical and numerical methods. His team developed
an unsteady, two-dimensional, numerical code using a direct boundary value
method for the Euler equations to analyze the flow in wave rotors and their
adjoining ducts, treating the straight or curved channel walls as constraints
imposed via a body force term (Lear and Candler 1993). The code was later used
to simulate the flow filed of the three-port NASA (Wilson and Fronek 1993;

Wilson 1997; Wilson 1998) wave rotor A parametric study of gradual opening

39

effects on wave rotor compression processes is reported, too (Hoxie, Lear et al.
1998).

Fatsis and Ribaud at the French National Aerospace Research Establishment
(ONERA) have also developed a 10, numerical code based on an approximate
Riemann solver taking into account viscous, thermal, and leakage losses (Fatsis
and Ribaud 1997; Fatsis and Ribaud 1998). The code has been applied to three-
port, through-flow, and reverse-flow configurations.

Nagashima, at the University of Tokyo, has developed 1D (Okamoto and
Nagashima 2003) and 2D (Okamoto, Nagashima et al. 2001) CFD codes to
simulate the flow fields inside through-flow four port wave rotors, including the
efl‘ects of passage-to-passage leakage. The codes have been validated with
experimental data obtained by a single-channel wave rotor experiment.

A simple but very descriptive set of equations is provided by Piechna in this
book, Wave Machines, Models and Numerical Simulation (Piech na 2005). He
takes into consideration wall friction, leakage between rotor and ports, heat
transfer, and variation of cross-sectional area and ignores body forces.

Continuity equation

6p 6(pu) d(/n A) + If?
—— —— —— _ — = 1.4
at + 6x + p” dx A 0 ( )

Momentum equation

arpu) arpuZ) gr: .dflnA) 3H _n;z __
at +0 ax +ax+pu dx +prDiUA—O (1.5)

40

Energy equation

6(pe) +26%th Walt/pi,” pe+p)d_(__/”A)_.‘Zie fl=o (1.6)

at 6x A

where

A: Channel local cross-sectional area

q': heat flux to cell walls

m: mass flow rate of leaks

d(/n A)

dx : variation of cross-sectional area along the length of channel

2
- e = -U— + 1 — :internal energy of the flow
2 y— 1 p

:D

 

Wave Rotor Simulations with Commercial CFD Packages

Some attempts at simulating pressure wave superchargers with the help of
commercial codes already have been undertaken. One such code is GT -POWER
in which pipe elements have been divided into a series of objects for which the
conservation equations have been solved. By dividing variables into primary
(density, total internal energy) and secondary variables (pressure, temperature)
a staggered grid has been the result of discretization. Sets of elementary
elements can be connected into one net, controlling the flow between them. The
pipe elements can also include wall friction and heat transfer. Proper modules

can represent local changes of pipe cross—section or valve system. An interesting

41

description of techniques for optimization of timing, shaping, and control of
pressure wave changers using GT -POWER has been described by Podhorelsky et
al. (Podhorelsky, Macek et al. 2004).

For the preliminary tests results generated here the commonly available CFD
software FLUENT has been used. The present work shows 2D results of
simulating complete operation of a novel radial wave rotor (wave disc) with
straight channels and curved channels. Details of the operation of an
aerodynamic speed control and the oblique opening of curved channels are
described as well. Furthermore, 3D results of a complete conventional axial wave
rotor are presented proving the capability of this software. For most of the
results investigated here, no experimental data exist for possible verification. The
only concept for which data are available is the conventional axial wave rotor. It
seems that such types of models are useful for the final tests of devices for
which the geometry has been already optimized by the use of specialized, but
much simpler, 1D codes. The presented results shall not be interpreted as a
proposition of a particular geometry for practical applications. While they can be
a base for further investigations, they rather present some illustrations of
physical phenomena generated in different configurations and phases of

operation and showing the capability of the code.

42

1.3 Wave Rotor Enhanced Ultra Micro Gas Turbines

The concept of adding a wave rotor to an ultra-micro gas turbine was addressed
by several research groups from all over the world. With great experience
gathered in the wave rotor field, Ribaud at ONERA was attracted by this idea and
at begin studying the possibilities of incorporating a wave rotor to an ultra-micro
gas turbine. A more extensive work was done by the University of Tokyo
research group directed by Nagashima. An initial test stand with a single
stationary channel was built. The length of the channel was 180mm. The results
were compared with 2D CFD simulations (Okamoto, Nagashima et al. 2003).
Further, a numerical model was designed for a wave rotor with channel length of
6.9mm (Okamoto and Nagashima 2003).

Recently, Michigan State University in collaboration with the Warsaw University
of Technology is intensively searching for a feasible method of topping an ultra-
micro gas turbine with a wave rotor. The new proposed design of wave rotors,
which have the Channels placed radial instead of axial with respect to the axis of
rotation, appears to be the solution to the problem (Piechna, Akbari et al. 2004).
Several proposed designs of Ultra — Micro Wave Rotors (UpGD are presented

next.

43

Chapter II
PROPOSED INITIAL DESIGNS OF A WAVE ROTOR

TOPPING AN UuGT

11.1 Axial Wave Rotor Configuration

Starting from a baseline engine similar to the one developed by the MIT research
group, several wave rotor topped, ultra-micro gas turbine configurations are
proposed (Iancu, Akbari et al. 2004). The wave rotor works on a four-port
configuration, namely each cycle is completed once the wave rotor Channels
make contact at one end or the other with all four ports. The overall aspect of
the wave rotor may include a larger number of ports depending on the number
of cycles per revolution.

figure 11.1 shows a wave rotor added at the outer diameter of the disk formed
by compressor/turbine unit. The end plates with the ports at either side of the
wave rotor can be etched in the same wafer as the stationary guide vanes. The
second possible design implies using additional wafers allowing a multi-layer
rotor, as shown in Figure 11.2. The major challenge with this design is the perfect
axial alignment of the compressor/turbine unit with the wave rotor (may be
achieved with the common laser aligning method). The flow connection from the
compressor to the wave rotor may be viewed as a Challenge in respect to

keeping the pressure loss small. However, the equivalent diameter of this

44

connection may be designed sufficiently large. Further, this may aid in isolating
the compressor case from the combustor heat, especially with the counter flow
of the compressed air, where a regenerative effect is seen again. The third
design concept introduces a new idea in respect of having free spinning wave
rotors located Circumferentially around the compressor/turbine unit, as shown in
Figure 11.3. Similar to the first classic design, this design requires less wavers
then the second design, which translates into lower fabrication cost. The
challenge associated with this design is driving the wave rotors at the
appropriate speed, which may be achieved by arranging the wave rotor ports in

proper angles so that the impulse of the fluid streams can be utilized.

 
 
   

Rotating Disk
Air Intake
! i

 

 

 

 

 

 

 

 

 

 

Combustor 4 cycle] revolution
(16 port wave rotor)

Figure 11.1: Conceptual design of UuGT — “Classic" design.

45

Air Intake

    

Wave Rotor

Figure 11.2: Conceptual design of UpGT— “Two-layer” design.

mum

Routi‘ng Disk A], Intake Compressor \
\

ll|[ !

Turblne

 

  

  

l ‘.
//iw"‘

 

 

 

-Exhlu‘

figure 11.3 Conceptual design of UuGT —- “External” design.

46

1.1 Radial Wave Rotor Configuration

A new and innovative design is proposed next (Piechna, Akbari et al. 2004).
Instead of the traditional axial wave rotor, a radial one seems to be far more
suitable for ultra-micro gas turbines. Its Shape and overall surface to height ratio
is ideal for microfabrication processes, most of them being 2D processes. Plus,
the variable cross-sectional area has been proven to provide a more efficient
shock wave compression (Pfeifer and Garlich 1990). The radial wave rotor (wave
disc) will be incorporated, as the axial one, in parallel with the combustor;
schematics are shown in Figure 11.4. Unlike the axial configurations, the Channel

shape along its length can be tailored in width and angle.

Wave Rotor

   
 

Rotating Disk
End Plates
/\ I Air Intake Compressor

 

 

 

 

 

 

Figure 11.4: Conceptual design of UuGT — “Radial” design.

For most thermodynamic applications, axial-flow wave rotors have mostly been
used and investigated. Pure scavenging is a challenging task in the axial-flow

configurations. In gas turbine applications, through-flow configurations

47

recirculate a fraction (30 to 50%) of combustor products to the combustion
chamber (Welch, Jones et al. 1997). Even though reverse-flow configurations
can deliver pure compressed air to the combustion chamber, a buffer layer can
remain in the channels. This residuum can remain permanently in the channels.
Repeated compression waves increase the temperature of this buffer layer. This
leads to high wall temperatures in the center of the Channels (Nalim and Paxson
1999). It is possible to achieve a full scavenging process for both through and
reverse-flow configurations using bypassing or bleeding of certain mass flows
(Zauner, Chyou et al. 1993; Nalim and Paxson 1999; Paxson and Nalim 1999).
However, all of this leads to more complex configurations.

Jenny and Bulaty (Jenny and Bulaty 1973) have introduced a conical wave rotor
with oblique Channels in which a radial component is added to the axial flow.
However, the flow still enters and leaves at the front and rear end respectively
and predominantly in axial direction. They have noticed the positive influence of
centrifugal forces on the scavenging process. The idea was not pursued further
due to restrictions in computational power. These extensive calculations of
unsteady flow with the effect of centrifugal forces proved to be impossible.

The radial-flow wave (wave disc) concept employs the flow in radial and
Circumferential directions. This can substantially improve the scavenging process
by using centrifugal forces. Figure 11.4 shows schematically a simple radial-flow

wave rotor with straight channels and a rectangular cross-sectional area.

48

Chapter 111
PERFORMANCE CHARACTERISTICS OF

ULTRA-MICRO WAVE ROTORS1

The way in which the wave-rotor topping enhances the cycle at micro scale often
differs from that at larger scales. At a large scale, the goal is mostly either to
increase the cycle overall pressure ratio or to substitute the wave rotor for costly
high pressure turbomachinery stages. The most significant performance gain has
been found for engines with low compressor pressure ratio and high turbine inlet
temperature (Wilson and Paxson 1993; Fatsis and Ribaud 1999). At the ultra-
micro scale, the optimum cycle pressure ratio is very small, e.g. around 2, due to
the low component efficiencies (Miiller and Fréchette 2002). Thus, a single-stage
centrifugal compressor can easily generate the low optimum overall pressure
ratio, and a further increase with the same efficiency actually decreases the
desired performance. Therefore, the wave rotor integration is most effective if its
compression and expansion efficiencies are greater than those of the
turbomachinery components of the baseline engine. This enhances not only the
overall compression and expansion efficiencies, but it also increases the optimum
cycle pressure ratio to a greater value, allowing for additional performance
improvements. In such a case where the wave rotor compression efficiency is

higher than that of the spool compressor, a wave rotor can enhance the

 

‘ Part of the material presented in this chapter was published in the Journal of Microfluidics and
Nanofluidlcs(1ancu and Miiller 2005)

49

performance of an UuGT that was already designed for an optimum pressure
ratio. Then while the Optimum overall compression ratio increases with the wave
rotor integration, the pressure ratio of the Spool compressor can he usually
decreased. This can additionally enhance the isentropic efficiency of the spool
compressor, provided its polytropic efficiency (aerodynamic quality) stays the

same. These effects are schematically shown in Figure 111.1.

04,-4.6, baselineengine
0-1,-2,-3‘-4‘-5, toppedengine

Temperature

 

 

 

 

 

 

5mm

Figure 111.1: Temperature - Entropy diagram for ultra-micro gas turbines, with
and without wave rotor.

The turbine inlet temperature may stay the same while the combustion takes
place at a higher temperature. Alternately, the turbine inlet temperature may be
lowered. An additional pressure gain to that provided by the compressor is also

Obtained by the wave rotor. Therefore, the performance enhancement is

50

achieved by increasing both the overall efficiency and specific power, hence
reducing the specific fuel consumption considerably.

An initial study on the efficiency of the compression process in a wave rotor
channel has shown that values around 70% can be achieved at microscale
(Iancu, Akbari et al. 2004). For large scale wave rotors the value of 83% is
consistent throughout the literature.

While the wave rotor efficiency is based on the efficiency of the shock wave
compression inside each channel, the influence of external losses can be at a
minimum since the wave rotor itself is the only moving part. External losses are
leakage, windage, and friction in the bearings of the rotor. At micro scale losses
due to sharp bends in the flow path to the rotor since rounded corners are very
difficult to obtain in the etching direction. All these losses also occur in
turbomachinery, but in a wave rotor they can be lower, since the compression
process is only controlled but not accomplished by the rotational speed of the
rotor. Therefore, high efficiency can be obtained even at relatively low rotational
speed, which implies less friction.

As explained above, the implementation of a wave rotor at ultra-micro scale
appears most effective if its compression efficiency is greater than that of the
baseline spool compressor. Whereas the latter ranges low around 50% at ultra-
micro scale compared to about 70 - 90% at large scale, the compression
efficiency of wave rotors (nwc) has been found to be in the range of 70 - 86%,

assuming that the wave rotor expansion efficiency is equal to its compression

51

efficiency (my;- = 27,95). This may be considered as matching the efficiency of
large scale compressors or turbines and almost double of that achieved with
ultra-micro scale compressors. The favorable wave rotor efficiencies are

subsidized by the following.

Table 111.1: Wave rotor compression and expansion efficiency and only
compression efficiency. Data found in extant literature

 

 

Source nwr ' um um:
Taussig (T aussig 1984) 0.70 — 0.74 0.83 — 0.186
Rolls-Royce, Moritz (Moritz, 1985) 0.6 0.77
Kollbrunner (Kollbrunner 1981) 0.36 - 0.46 0.60 — 0.68
Wilson and Paxson (Wilson and Paxson 1993) 0.69 0.83

Fatsis and Ribaud (Fatsis and Ribaud 1999) 0.64 - 0.70 0.80- 0.86

 

(Italic figures are calculated assuming nwc= 27m)

Thus, it appears that rm: = 27m = 0.83 is a reasonable assumption for a large
scale wave rotor with a cell length of about 100-300mm (Zehnder and Mayer
1984). For the smallest documented wave rotor with a channel length of 69mm
(Okamoto, Nagashima et al. 2003), using the wave-rotor characteristic equation
(Eq. 111.1 below) introduced by Wilson and Paxson (Wilson and Paxson 1993)

and nwc'nm; the authors calculated an isentropic compression efficiency of

 

 

 

 

 

about 79%.
‘ 7935
Cpair 1 Tu fair '1 1 7 gas '1
P C as riwr 'UWC 7:4 W 7"" —
1 + C 7- RW 7317' -
pgas ”WC t4

 

 

52

Exploring the application of even smaller wave rotors suitable for ultra-micro gas
turbines, the question arises if such wave rotor efficiencies can be maintained at
ultra-micro scale. No values are available at this scale. However, the above
results Show no or only a small decrease in efficiency with reduced size, which
encourages investigations at the ultra-micro scale.

Using the available wave rotor efficiencies above versus the corresponding wave
rotor channel length, a trend can be generated as shown as a solid green line in
Figure 111.2. The simple linear extrapolation predicts wave rotor efficiency at
ultra-micro scale (about 1mm Channel length) that is greater than 70%. Such a
compression efficiency of a microfabricated wave rotor is much better than the
Obtained efficiencies of around 50% for microfabricated compressors (Miiller and
Fréchette 2002). Furthermore, efficiency values of compressors suitable for or
corresponding to the reported wave rotor topped cycle are shown red in Figure
111.2. This allows showing the red broken trend line for the compressor efficiency
corresponding to the wave rotor length. Both trends for the wave rotor efficiency
and for the compressor efficiency coincide at larger scale. However, towards
smaller wave rotor size for UpGT, the compressor efficiency trend falls far below
the wave rotor efficiency trend. This clearly suggests an advantage of using a

wave rotor for UpGT.

53

 

100
90
80
70
60
50

40 L - I - - Compressor
30 '"W Pkflrnflfialti --‘F--' VVBVEBRKNIN'
20 r sti-scale ~~ , . <>< ------- extrapolated

10 D — _ .. .-. _‘. -_.. .._. ..,-C.._. ._..._.._. .......s........ _. .
0 r r r r
0 100 200 300 400 500

Wave rotor cell length (mm)

  

 

Efficiency (%)

 

 

 

 

 

 

 

 

 

 

figure 111.2: Efficiency trend of the compression process. Solid line — wave rotor
efficiency; Dashed line — compressor efficiency. References: 1 — (Miiller and Fréchette
2002), 2 — (Johnston, Kang et al. 2003), 3 — (Okamoto and Nagashima 2003), 4 -
(Moritz 1985), 5 — (Akbari and Miiller 2003), 6 - (Mathur 1985), 7 — (Thayer 1985).

The trend line in Figure 111.2 suggests a wave rotor compression-efficiency of
about 75% at micro scale. TO investigate the practical relevance Of this simply
extrapolated trend line of the wave rotor compression-efficiency a mathematical
model was created based on a physical background. The model considers the
entropy production by a single normal shock that runs through the wave rotor
Channel and the wall friction generated by the gas flowing through the Channel.
Entry losses due to ducting are also taken into considerabon. The only effects
neglected were those of heat transfer.

Focusing on the phenomenon occurring inside a Single Channel, the one-
dimensional mathematical model is based on the gas dynamics of normal shock

waves for one-dimensional flow as described by Anderson (Anderson 2003). The

54

model assumes air as a working fluid that is modeled as an ideal gas, and a
friction coefficient along the Channel to be a variable function of gasdynamic
conditions. The wave rotor Channel is simulated as a tube with an equivalent
hydraulic diameter DH as shown in Figure 11.2-a. The model relates the efficiency
of the compression process to the velocity, pressure, and temperature of the gas
at the entrance of the Channel (station 1: U1, p1, T1), the pressure ratio across
the shock [75, the friction coefficient 6 and tube dimensions 21 and DH. In Figure
11.2-b, a shock wave is shown that moves in the opposite direction of the flow
that is positioned in the middle of the channel. Later, it will be proved that a
snap shot evaluation at the mid position is a good representation of the overall
results and does not affect the accuracy of the model. Friction is considered

along the lengths 1 before and after the shock.

 

a) ,_ .7 01$ _.

 

 

 

 

 

“I: 91: T1: 31

) I 3’ v. - . . . Y S, J .
uzr p2! T2! a2 U]! D}! T3! a3

0021 T02, 9031 T03,

 

 

 

 

 

 

55

“1: p1: T1: 31
pair Tor
<1) <23 <29 e
”41 p4: T4! 34
Dow T04

.) :3 *

”2: pp T2: a2 “3: p3! T3! 33
9021 T02, 903: T03,

 

 

 

 

 

 

 

Figure 11.2: ID model of a microchannel. a) Single Channel; b) Shock traveling in
direction Opposite to the flow; c) Shock traveling in direction of the flow.

From the equations of a one-dimensional, compressible flow with friction,
starting with the conditions at station 1 we can deduce the conditions at station
.2, just before the arrival of the shock wave. The frictional effect is modeled as
shear stress at the wall acting on a fluid with uniform properties over the cross
section. Although the wave rotor Channels have a rectangular or trapezoidal

shape, the calculations are performed using the equivalent hydraulic diameter DH
A
D = 4— 111.2
H p ( )

In the case of a one-dimensional model, the flow is studied based on the infinite
parallel plates case, where

DH = 2 D (111.3)

Since the port will have a dimension larger than that of the channel, the entry
losses are treated as losses due to variation Of diameter in a pipe. The pressure

drop is

U2
Ap = k - p - 7 (111.4)

56

Where the entry loss coefficient, k is considered to be 0.5 for a contraction with

sharp 90 degree corners (Sabersky et al. 1998).

57

 

111.1 One Dimensional Flow with Friction

Knowing the temperature and velocity at station 1, we can compute the speed of

sound using Eq. 111.5 and in turn the Mach number with Eq. 111.6.

a: y-R-T (111.5)

U
M = — III.6
a ( r

In order to find the Mach number at station 2, we use the sonic condition as it
develops due to friction, through station 2, from the flow in station 1. The virtual
distance from station 1 that is needed for the flow to reach sonic conditions is

denoted with L} and can be calculated using Eq. 111.7, which is derived from the

momentum equation, expressing the shear stress in terms of friction coefficient

and integrating between station 1 and the point where M=1 (Anderson 2003).

 

 

.. D 1-M12 y+1 (y+1)-M2
= -/n 1 111.7

The classical theory of laminar flow relates the friction coefficient to be

proportional to the Reynolds number.

r =_ 111.8
Re ( )

58

But the Reynolds number is dependent on density, viscosity, velocity, and
hydraulic diameter (Eq. 111.9). The first two are related to the temperature, one

by ideal gas law, the second by Sutherland law (Eq. 111.10).

Re = M (111.9)
,u
1.5
T T , + 5
= _ ————’P III.1O

where pm; = 1.789105 kg/ms is the reference viscosity, 77?’ = 273.11 K is the
reference temperature, and S = 110.56 K is the effective temperature in the
three coefficients Sutherland law (Sutherland 1893).
Since the same sonic condition develops from the flow in station 1 and 2, the
difference between the two virtual distances to sonic condition is the distance
between stations L.

i=1; -4 (111.11)
By applying Eq. 111.7 to the station 2 and substituting 1; from the Eq. 111.11 we

can solve Eq. 111.7 for the Mach number M2. Knowing the Mach number at
station 2 and all the conditions at station 1, and applying the continuity equation
in adiabatic conditions, the pressure and temperature at station 2 can be

calculated with Eqs. 111.12 and 111.13:

 

M1 J2+(7‘1)'M12 (111.12)

”2:97"? 2+(r-u-M:

59

— n 2
7'2 =7;.2_+_(_7’_l)_."’7_17
2+(,_1).M,

(111.13)

Adiabatic conditions were assumed for the analytical one-dimensional model,

justified by numerical results Obtained for relevant cases as Shown further below.

Using a CFD code, a 2D model was investigated with and without adiabatic walls.

Comparing the pressure and temperature distributions revealed errors below 1%,

as displayed in Figure 111.4. The set-up conditions for the model are described in

the following section.

2.00:005
r1: 1.95905
1 ' l.90e~05
1.85c605
1.80.:405
1.75005
1.70005
1.65005
1.60005
‘ 1.55c005
«' Lsocros
1.651305
1.60905
1.35005
1.30:005
1.35c005
1.30.905
1.15c005
1.10c005
1.05005
1.00005

 

with heat transfer

! Static pressure (Pa)

without heat transfer

n l Static pressure (Pa)

with heat transfer

I -. Static temperature (K)

without heat transfer

; -- Static temperature (K)

    

:2]

«iterature (K)

1.93003
7.67:003
711:003
1.16:503
6.90c902
6.“c~02
6.39M
6.13c002
5.87c002
5.62003
5.36902
5.10003
4.85c903
4.59002
$.33c003
4.082002
3.82c002
3.56:002
3.31903
3.05003
2.79:003

Figure III.4: Pressure and temperature distributions for a single channel model
with heat transfer calculations and without. Flow moving from left to right. The

results were obtained using FLUENT 6.1.

60

111.2 Flow Across a Moving Shock

Knowing 7'2, the speed of sound a2, can be calculated with Eq. 111.5 and then the
velocity of the flow u2. Assuming that the distance between stations 2 and 3 is
negligible and knowing the pressure ratio across the shock, 175 =p3/p2, conditions
at 3 can be obtained employing the normal shock relations (Eqs. III.14 and

111.15).

 

 

(111.14)

From the three basic Euler equations, the Mach number of the shock wave, M5,

can be evaluated as follows:

 

M5 = \llzfl-(ns —1)+1 (111.15)
7

Knowing that M5 = w/az, it results that the velocity of the shock wave, w is

 

 

w=a2‘[y2:1-(H5—1)+1 (111.16)

and the induced velocity of the flow behind the wave up is

61

 

u =—-(115—1)- ——Zil—— (111.1)

 

The velocity of the flow at station 3 is a vector sum of the initial velocity of the
flow and the velocity induced by the moving shock wave.

(73 = (72 + (7 (III.2)
From station 3 to station 4, the same algorithm is applied as for the flow
traveling from 1 to 2.
Since this is an unsteady process the total properties behind the shock at station
3 are different from the ones in front of the shock (station 2). The total pressure
is calculated using the known properties of the induced mass motion instead of
being directly calculated from the equation of state (Anderson 2003).
The isentropic efficiency of the compression process is defined as the
temperature difference for an isentropic process versus a real process (Dixon
1998):

77 __ATS
C AT

 

(111.3)

For the model presented here it can be calculated by

73/7 "1

[fi] lair _ 1
’01 (111.4)

”C: Zl—J.
7'1

 

62

The model described in this dissertation is applied to compressible air flow with
Reynolds numbers in the range of 500 to 1500. These values were obtained
using Eq. 111.9, which is also valid for shock wave propagation in a narrow
channel (Sun, Ogawa et al. 2001). Further, based on the analysis of gas flow
characteristics in silicon microchannels by Ying-Tao and his research group (Ying-
Tao, Zhao-Hui et al. 2002), the friction coefficient f has been found to be
approximately 0.04 for a Reynolds number of 500, while for Reynolds numbers
greater than 1000, the friction coefficient becomes less than 0.005. In the paper,
Ylng-Tao and his group concluded that the discrepancy between the theoretical
friction factor and the experimentally found one is due to the gas compressibility
effect. They describe the analysis that leads to the conclusion that the density in
the streamwise direction is not constant, since the relation between pressure
ratio and mass flow rate is not constant. Next, the friction coefficient is plotted
with respect to the Reynolds number for the theoretical calculations and

experimental values (Figure I115).

63

1.000

 

 

 

 

 

|__._ fclassic'
i'__?_'f_e§P*_ 1'

0100

~

~ Q

0.010 4 ‘ ~ . _

*Ding Ying-Tao et al. (2002)
0.001 _____

 

 

100 200 300 400 500 600 700 800 900 1000
Re

Figure 111.5: Variation of friction factor with respect to Reynolds number
assuming laminar flow: solid line — calculation using classic theory (f=64/Re);
doted line — experimental results for microscale flow.

Table III.2: Entry data for the mathematical model
Property Value

 

 

Static inlet pressure, pa 2.57 ' 105 Pa
Static inlet temperature, To 1465 K
Inlet velocity, Up 350 m/s
air specific heat ratio, 73,-, 1.4
air specific gas constant, Ra; 287 J/kg'K
channel length, L 10'3 m
channel diameter, D 76 ' 10'6 m

 

The entry data for the model have been introduced based on preliminary
thermodynamic calculations of a wave rotor suitable for an ultra-micro gas

turbine (Iancu, Akbari et al. 2004) and initial thermodynamic parameters used by

64

the MIT Micro Gas Turbine group (Kang 2001 ; Epstein 2004; Frechette, Jacobson
et al. 2005), as well as micro turbomachinery design space calculations of Miiller
and Fréchette (Miiller and Fréchette 2002) . The data are found in Table III.2.
Since the shock is moving through the channel, the calculations were made on
discrete time steps (snapshots), at which the shock was found in discrete
positions with respect to the channel length.

Finding afterwards, average values of compression efficiency by integrating the
values of efficiency obtained at the discrete time steps with respect to channel
length, it was found that these integral efficiencies are well represented by the
discrete efficiency value calculated for the moment (snapshot) when the shock
wave moves through the center position of the tube. The error introduced by this
approximation is in the range of 0 to 5% and considered negligible. This is due
to an almost linear dependence of the discrete efficiencies of the compression
process on the momentary position of the moving shock in the channel. This is
shown in Figures III.6 and UN for different pressure ratios across the shock.
The efficiency values averaged over the channel length are shown by horizontal
lines for each shock pressure ratio. It is seen that the average values for each
pressure ratio correspond very well to the respective discrete efficiency values
found at the half channel length position, which justifies the use of the snapshot
value at the half channel position as a representative value for the entire
compression process during which the shock wave moves through the full length

of the channel.

65

 

 

 

 

 

    

 

 

 

 

 

 

1 1 ........s.... I -—-~ v}

0.95 4 i
3 l +n=i.5
: 09 1 avg. for n=1.7-2.0 g -—I'l-1 7
o _ .
5 avg. for n=1.5 —I]=1.8
'5 - -—-n=i.9
E 0.85
“‘ '_—U=2-0

0.8 .
x/L =0.5—>
0.75 T f I l I V T T T r r r V i r f 4'

 

 

 

<o b <o b 63 <0 ‘0 <0 <0
99 Q5 Qty 9"!) Q?‘ Q6“) 0%) 0’3 Q?) 09

Distance to the shock/channel length

Figure III.6: Efficiency of compression process as function of position of shock
inside the microchannel for different shock strengths, inlet temperature of
1465K, and a shock traveling in direction opposite to the flow. Results obtained
using analytical 1D code.

 

 

 

 

 
    
 

 

 

 

 

 

 

 

 

 

 

 

0.954

_ 0'9 avg.forn=1.9,2.0
.\° ‘ angfor n=1.7.1.8 —n=1,5
E avg. for l‘l=1.S \ — ”=1-7
,5 03* -—I'I=l.8
E 0.75 _ ——n=1.9
—I'l=2.0
0,7. -

0.65~ i

x/L =0.5—>‘ ;

0.6 l T T 1 1 7 i 1 I . l r ‘r 1 1 ,r A

‘0 ‘3 ‘0 <0 ‘0 (0 <0 ‘0
99 05 g.» Q?» Q!» Q?» 09 Q.) (3‘? 54°

Distance to the shock/channel length

Figure III.7: Efficiency of compression process function of position of shock
inside the microchannel for different shock strengths, inlet temperature of 750K,
and a shock traveling in direction opposite to the flow. Results obtained using
analytical 1D code.

66

Results in Figure III.6 have been obtained for an entry temperature of 1465K,
while for Figure III.7 a temperature of 750K has been used. Figure III.8 presents

the results for a shock traveling in the direction of the flow for an entrance

 

 

 

 

 

   
  
      

 

 

 

 

 

 

 

 

   

 

temperature of 1465K.
1 ~-r--~--——--—~—~—‘—~~-——-— ..-- I 3.
avg. for n=1.7
0'95 6 avg. for n=1.5 7___ g 7
7 l— [H 5
\
2 a . for n=1.9 . — 11:1.7
3 avg. for n=2.o —n=1.8
é; ---n=1 9
in ‘—‘__”=?-_0.
,_ 33%-; y r r '
0.75 f r r T T T L T T T I T T f I l
‘3 ('3 ‘3 ‘3 ‘3 ‘3 ‘3 ‘3 ‘3 ‘3

Distance to the shocklchannel length

Figure III.8: Efficiency of compression process as function of position of shock
inside the microchannel for different shock strengths, inlet temperature of 1465
K, and a shock traveling in the direction of the flow. Results obtained using
analytical 1D code.

Comparing results of efficiency for both directions of the shock wave, a small
difference between the averaged values of both cases is noticed. When the flow
travels along the tube, its pressure drops due to the friction losses (Eqs. III.7 to
III.13). Assuming the flow moves from station 1 to station 4 and there is a
constant pressure ratio across the shock, the following scenarios can be seen.

If the flow meets the shock close to station 1, the pressure loss from 1 to 2 is
very small due to the short length traveled. Then, the shock increases the

pressure to a high [23, while it afterwards gradually reduces to p4, resulting in a
67

relative high average pressure throughout the tube. Therefore, the average
density is relatively high, the average flow velocity relative low, and the losses
are relative small. If the flow meets the shock close to station 4, the pressure in
front of the shock p; is already considerably lower than in the previous case due
to the pressure loss incurred by now traveling the much longer distance between
station 1 and 2. The shock brings then the pressure up to p3 that is only a little
more than p4, since there is only a small pressure loss from 3 to 4 due to the
short distance. The pressure behind the shock will be much less than in the
previous case, even though the pressure ratio is the same in both cases.
Consequently, the average pressure throughout the tube is relatively low; and,
therefore, the average density is relatively low too, requiring high average flow
velocity that causes greater frictional losses reducing the efficiency of the
compression process as seen in Figures III.6 and III.8. A schematic of this

process with snapshots for both cases is presented in Figure I119.

68

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

i
1’ l
933‘; 1 j; : 1L T _ f
p."""""": .' """"""""""""""""""""""""""""""" —?
l x , Pressure i
3 l Average pressure Increase l

p1‘ """ "fl'.'"""“"‘""""""“"‘"'"""“""""" """"""’"""""f'""
I ' s

(3) ., g

x
plr : ' I
l i 3
- s
i 2
I l i
l ;
p4 “ .......................................................... :---_--------------‘: d----
p1 . ......................................... Ifiressurenncrease .......... . “up---
\
pevg 1k I
Average pressure ‘ i
ll’
'x

(99

 

Figure III.9: Schematic of pressure distribution along the microchannel. a) With
shock close to entrance; b) With shock close to exit. Pressure p1 and ratio p3/pz

are the same in both cases.

The effect is reversed when the shock wave is moving in the same direction as

the flow since the higher pressure is behind the shock and the highest pressure

is at the entrance of the flow and not at the exit. The efficiency is higher if the

shock is closer to station 4, as Figure III.9 shows. Also, if the shock wave and

flow have the same direction, it is seen that the efficiency increases with

decreasing pressure ratio.

Thus, for obtaining a maximum efficiency, for a primary shock wave that travels

in the same direction a lower pressure ratio would be preferred and a higher

69

pressure ratio for a reflected shock wave traveling in opposite direction. But
since the reflected shock cannot be stronger than the primary one, a
compromise has to be made in order to choose the optimum pair of pressure
ratios for both shocks. The results presented above are summarized in Table
III.3. The table reveals a maximum efficiency for the opposite direction of flow
and shock wave. Such a maximum is not found for same direction of flow and
shock wave, since pressure ratios lower than 1.5 are too small to compensate

the friction losses.

Table III.3: Efficiencies of compression process function of shock pressure ratio,
entrance temperature and direction of moving shock

 

ns = 1.5 [15 = 1.7 Us = 1.8 Us = 1.9 1'15 = 2.0 ['15 = 2.1

 

 

 

To=1465K
same direction 092?? 0.921 0.908 0.893 0.877 0.855
To=1465K
reverse direction 0.865 0.890 0.893 0.894 0.892 0.890
To=750K
reverse direction 0.801 0.849 0.858 0.863 0.865 0.864

 

For further investigations, the following justified approximation will be employed:
discrete efficiencies values obtained for the moving shock at the half channel
length position approximate an average value for the entire shock wave
compression. The variation of the efficiency with the inlet temperature is
presented next.

A variable friction coefficient is introduced for these simulations. The friction
coefficient is dependent on the Reynolds number and indirectly on viscosity and

70

temperature. Using Eq. 111.20, the efficiency results for various entry
temperatures and shock strengths were calculated. Since according to Ying-Tao
(Ying-Tao, Zhao-Hui et al. 2002), for a laminar flow at microscale, the friction
coefficient does not depend linearly on the Reynolds number, therefore a second
set of efficiencies for the same range of inlet temperatures were generated using
their experimentally obtained dependence of the friction coefficient on the
Reynolds number. These two sets of efficiency are presented in Figure 111.10. As
noticed, the efficiencies obtained with the experimentally determined friction
coefficient are about 10% higher than the ones obtained using the theoretical
friction coefficient. For each pressure ratio across the shock, an optimum entry
temperature can be found, which will lead to highest efficiency. Another
observation that can be made is that the values of efficiency vary only a little
with entry temperature, justifying the use of a constant friction coefficient
determined for the inlet temperature. This effect is caused by the dual influence
of the temperature: higher temperature leads to a lower Mach number for the
same inlet velocity but lower Reynolds number, thus higher friction coefficient.
The effect of lower Mach number and higher friction coefficient are opposite

when calculating the characteristic length in Eq. 111.7.

71

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

fdetermined
experimentally
'0' 11=l.6
A '9' 11=l.7
5. optima line -e— 11:20
c
o
:F: 0.85 - 71 x R r: 64/Re
In a — l'l=l.6
/" \ _ 11:1,?
0.8 - —— 11:1.8
optima line “=20
0.75 T l T T
Q6 Q6 06 06 o o o o o o
e ’\ ‘b ‘3 .99 (9 .39 45° .39 .350
Entry temperature (K)

Figure 111.10: Efficiency of compression process as function of entry temperature
for different shock strengths, and for a shock traveling in the direction opposite
to the flow. Results obtained using analytical 1D code.

An important parameter in wave rotor design as well as shock tube design is the
length/diameter ratio. In the relevant case of an ultra-micro wave rotor, the ratio
was chosen to be 6.67, due to microfabrication constraints. But a variation of this
parameter over a wider range showed that the efficiency does not vary
significantly, variation being more considerable for lower pressure ratios. For a
shock strength, [75 = 1.8 the variation is only 3.3% for a diameter from 0,, =
30pm up to 100pm and a 1mm channel length. According to the above findings
in these calculations the friction coefficient is based on the inlet temperature and
the experimental graph shown in Figure 111.5. Efficiency results are plotted in
Figure 111.11. The left graphs present the results versus length/diameter ratio

with shock pressure ratio as parameter, while the graph on the right side is like a

72

side view with the length/diameter ratio as parameter. On the right side the solid

line connects the optimum pressure ratios for maximum efficiency for each

length/diameter ratio.

  
  
  

0.% ‘rfim' 7" " "M -‘_‘_"‘ "‘_ _ i
:‘— ”-1.8 35
l—-—- 13
l“ Ila-1.6 :{
f—llelfi ii
0.94 ~ 1 1 ii
{—11:14 it

Efllclency [as]
_o o
8 8

.0
<0
4

 

0.9 Y t —1 —Y Y 1— 7 U
5 6 7 8 9 1O 11 12 13 14 15

 

Dimensionless lenng nmeter ratio

.. --ufimmw ._.- ~-.._-~ ‘.- ,....-~-..._-_.-..

1
.
—_._..-. ._.. ‘_ .._. .l

 

uo=53

1.10:5.9

LID=67

,’—_ _::‘~_ uo=7.7

/’ /’ “~“-uo=91
I I’l’..—-" “-~‘~::uo=100 j
’l / ',_ ...... ' uo=111 i
I ,’ ' uo=125 l
/ / ,’ 'uo=143 l
I /’ ,
/ 2
/ ’ l
/ l
’ l
/ optimaline .
/ i
l

1.4 1.5 1.6 1.7 1.8
Shock pressure ratio

Figure 111.11: Efficiency of compression process function of microchannel

length/diameter ratio for different shock strengths, and for a shock traveling in

the direction of the flow.

73

111.3 Numerical Model

Several researchers have investigated compressible flow in microchannels. Some
have focused on recovering the characteristics of the flow (Xue and Chen 2003),
others studied the behavior of compressible flow at microscale and the
differences in relation to large scale (Papautsky, Ameel et al. 2001). In the
present work a numerical model was created to validate the analytical model
described in section 3 and to explore the flow behavior at microscale.

A 2D numerical model was designed to simulate the best possible the real life
conditions in a wave rotor channel. The channel modeled is 1mm long and 76pm
wide and has a larger inlet duct (port) and opens into a larger outlet port (Figure
111.12). GAMBIT 2.0 was used to create the mesh and set up the interface, initial
conditions, and boundary zones for the given geometry. The mesh size in
channels and inlet and outlet ports was carefully selected to provide accurate
and fast solutions. Tetrahedral mesh was used with a 2pm cell size for the
channel and a paved 10pm cells for the inflow and outflow ports. Tests showed
that finer meshes would not provide more accurate results but only cause
additional computational time. For the mesh, standard quad elements were used
in a map and pave type distribution. The pave distribution was used to connect
the finer mesh of the channel with the coarser mesh of the ports. Once the grid
was generated in GAMBIT, the mesh was imported into FLUENT 6.1. Boundary
conditions, solving method, working fluids type, convergence criterion, and

several other functions (parameters) were defined prior to the simulation.

74

The fluid material used in modeling the flow was air, treated as a compressible
ideal gas. The specific heat and thermal conductivity were kept constant, while
the viscosity varies with temperature, according to Sutherland’s law.

For the model including heat transfer, the solid walls were modeled out of
silicon, assuming constant density and specific heat, and thermal conductivity
modeled as temperature dependent. Values of the material's constants can be
found in the Appendix 1.

An implicit solver model of FLUENT was used, coupling the conservation and
momentum equations with the energy equation and the flow was treated as
laminar, viscous and unsteady (Iancu, Piechna et al. 2005).

Boundary conditions at inlet and outlet ports play important roles in flow field
simulations, since a specific pressure jump across the shock cannot be defined. A
pressure inlet was set up on the left edge (side) of the inlet duct, and similarly a
pressure outlet was set up at the far right side of the outlet duct. The channel
and the duct (ports) were initially assumed to be filled with fluid at constant
pressure and temperature. A high pressure, high temperature fluid was supplied
through the pressure inlet zone. To the entire fluid region, an axial motion was
induced with the velocity u). These boundary conditions (pressures,
temperatures and velocities) are presented in Table 111.2. The meshed model is
presented in Figure 111.12. The conditions were specified via “patch” option for
the left side reservoir similar with conditions in the table 111.2. The rest of

surfaces (channel and right side reservoir) were initialized at ambient conditions.

75

     

pressure outlet

pressure inlet
edge

edge

 

inlet port

outlet port

Figure 111.12: Mesh models of a microchannel, inlet and outlet ports.

Using the results obtained with the CFD model described above, efficiency values
can be established for the compression process, based on the values of pressure
and temperature across the shock and using Eq. 111.20. This is simplified by the
fact that the properties in front of the shock (right side) are constant up to the
end of the channel. Further, it can be seen in the CFD results that for the initial
part of the process, the pressure drop is confined over a short distance (between
stations 2 and 3 in Figure 111.13 above. As the shock wave travels further from
the left to the right, the pressure gradient dissipates more and more
continuously over a longer range. Instead of a well defined shock wave, it then
can be seen as a set of compression waves distributed over more than a half of

the length of the channel (Figure 111.13 below).

76

4 119005
3 95905
3 809-05
3 65e~05
3 496‘05
3 336’05
3 188‘05
3 02505 @ time = 0.25
2 87905
2 71905
2 56905
2 408‘05
2 24e~05
2 099-05
1 939-05
1 789.05
_ ‘i 628~05
' ‘i Aie+05
l 31e‘05
i 16er05
1 00905

f :l

 

v3 ~ssure (Pa)

         

 

@ time = 1.00

Figure 111.13: Static pressure inside a microchannel at two different time steps.
Time =1 is when pressure wave reached the end of the channel. Flow moving
from left to right. Results obtained using CFD code FLUENT 6.1.

This effect has already been noted by Brouillette in his experiments with
microscale shock tubes (Brouillette 2003), and it originates from the stronger
influence of the viscous forces at low Reynolds numbers. In the density contour
plot (Figure 111.14), the existence of the boundary layer can be seen clearly,
behind the shock wave as soon as it has traveled about 20% of the channel

length.

77

3.980000
3.8?000
. 3.?6e000
2.65c000
3.5412900
3131:900
3.33c000
3.311300
3.104900
1.991900
1.88c900
131‘ch0
1.66¢000
1.56: ~00
1.4511900
1.34c000
1.313e-00
1.13coOO
1.016000
8.99c-01
7.90c-01

“‘l
.11

 

 

@ time = 0.35 U

Boundary layer influence

   

Figure 11.1: Density contours inside a microchannel. Time=1 is when pressure
wave reached the end of the channel. Flow moving from left to right. Results
have been obtained using CFD code FLUENT 6.1.

78

111.4 Comparison of Results

Keeping a constant L/DH ratio of 6.67, a scale influence on the efficiency of the
shock wave compression process was investigated. The upper continuous line in
Figure 111.15 presents this effect based on the presented analytical one-
dimensional model. Two sets of data points are shown along with this graph.
Using the CFD model, the efficiencies of compression process for two cell lengths
were calculated (for 1mm and 2mm). At the same time the literature results
initially presented in Figure 111.2 are placed on the graph. It is observed that the
analytical 10 model over predicts the efficiency of the compression process
mainly because it represents only the gasdynamic process inside the wave rotor
cells, while the literature results present the efficiencies of wave rotor systems as
a whole. It can be concluded that the analytical model over predicts the
efficiency by approximately 10% to 15%. This difference is attributed to
additional losses not considered in the presented model. These are mainly due to
leakage between the channel ends and the end plates, but also some due to
heat transfer and slight off-design operation. Accounting for these losses
additionally to the results of the analytical model, a real compression efficiency of
65 — 70% can be predicted for microscale ultra-micro wave rotors with channel
lengths in the order of 1mm. The results have been obtained using Eq. 111.20,

the formula of the isentropic compression efficiency.

79

100

$7"

I

0

C

2

0

E 50

NJ
40
30
20
10
0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Losses unaccounted
in the model: heat
transfer, leakage, _
off-design timing. ' Literature resu'ts
—— Analytical model
& Translated graph
0.1 1 10 100

Wave rotor cell length (mm)

1000

Figure 111.15: Wave rotor compression efficiency as function of channel length
for constant length/diameter ratio of 6.67. References: 1 - CFD model, 2 -
(Zender and Mayer 1984), 3 - (Okamoto and Nagashima 2003), 4 - (Mathur

1985), 5 - (T aussig 1984).

80

111.5 Design SpaoeofWave RotorToppedGasTurbinesatMia'oscale‘

The following graphs try to identify optimum design points from the point of view
of Specific Fuel Consumption (SFC), specific work or thermal efficiency. Several
parameters are taken into consideration as variables, one by one, while the rest
are kept constant for finding these optimum points of wave rotor enhanced gas
turbines, from which initial operating conditions can be determined in the initial
phase of the design process (Akbari 2004; Dempsey, Akbari et al. 2005).

The performance maps below are generated using for the first the first time
variable wave rotor efficiency as described in the sections 111.1 to 111.4. This way
the efficiency of the compression due to shock waves, thus the inner wave rotor
gasdynamic process, is linked to the overall thermodynamic turbomachinery
cycle.

The design points used for input to the CFD simulations in this work may not be
found in the above shown optimum design maps, since these were not available
until very recently. However they represent viable design solutions to the
integration of a wave rotor to an ultra-micro gas turbine. The focus of the
present work in terms of optimization is on the geometry and port timing of the
wave rotor, not to the overall turbomachinery cycle as it has been in the cited
works of Akbari and Dempsey. The recommendations for future work will include

updating the UpWR design for the new optimum design points.

 

2 The results presented in this section were obtained with the indispensable help of Emmett
Dempsey, MS student at MSU - Turbomachinery Laboratory.

81

Figure 111.16 presents the optimum points found for a range of polytropic
compressor efficiency of 0.41 to 0.81. The procedure uses fixed rm and 17m and
variable R for finding one optimum point, then we is incremented to the next
value. It was observed that as type increases, thermal efficiency (77”,), specific
work (w) and baseline compressor pressure ratio (R) increase, while SFC
decreases. Optimum thermal efficiency lines are shown as bold light green lines,
specific work lines of are shown as bold blue lines and SFC lines in red. All lines

of constant 17m; are shown as thin dashed orange lines.

Variation of Polytropic Compressor Efficiency

 

. nm=03
I “FFOJ
TIT=1500 K

    

src (kglkJ.s)
N

0
Thermal Efficiency

Specific Work (kJIkg)

 

 

 

 

 

 

ripe-0M Compressor Pressure Ratio

Figure 111.16: Optimum points for all performance evaluation parameters
function of polytropic compressor efficiency.

82

Next, the optimum points for polytropic turbine efficiency variation are presented
in Figure 111.17. nprtook vales in the range 0.6 to 0.95. The constant parameters
for both variations of turbine and compressor polytropic efficiencies were
TIT=1500 K and 17mm =0.8. For variation of turbine polytropic efficiency, npc
was kept constant at 0.46, while np7=0.9 for variation of compressor polytropic
efficiency. These values were the optimum values generated by Miiller and
Fréchette in their study on micro gas turbines (Miiller and Fréchette 2002).

The same conclusions as for variation of compressor polytropic efficiency can be
drawn in the case of variable turbine polytropic efficiency. As I)” increases,
thermal efficiency (rm), specific work (w) and baseline compressor pressure ratio
(R) increase, while SFC decreases.

Variation of Polytropic Turbine Efficiency

   
   
 
 
 

 

 

 

 

 

4 [ 200 7 “mm .015
11m=0~
TIT=1500K
3 - g 150 5‘
7; _ 3 < 0.1 5
_, . _
x f o
2’ 2 » g 100 1 "E,
if .é’ E
w i -o.05 3
1 - m 50 - .q,,=o.95 is
f , — «1,5095
”we” 2
o - 0 T I I i o

Compressor Pressure Ratio

Figure 111.17: Optimum points for all performance evaluation parameters
function of polytropic turbine efficiency.

83

Probably the most important parameter in construction the wave rotor for UpGT
design space is the Turbine Inlet Temperature. Several graphs present optimum
points for SFC, specific work and thermal efficiency, based on variable TIT.
Figure 111.18 shows a comparison of all the performance measuring parameters

and their response to the increase of TIT from 1300K to 2000K.

Variation of Turbine Inlet Temperature

 

w
Thermal Efficiency

SFC (kg/kJ s)
N
Specific Work (kJIkg)

d
1

 

 

 

 

 

Compressor Pressure Ratio

Figure 111.18: Optimum points for all performance evaluation parameters
function of turbine inlet temperature (TIT).

The expected response is observed, for both untopped (17m=1) and topped
(Hy/pl) engines, as TIT increases, also 770» w, and R increases, while SFC
decreases.

The following three graphs (Figures 111.19, 111.20, 111.21) present the same
results as Figure 111.18, but taking each performance evaluation parameter (17m,
wor SFC) separately. Using the approach stated above, TIT and 17m were fixed

84

while R was varied to locate one optimum point, then increment TIT and 17m to
the next fixed value to find the next optimum point. Some extra lines aré shown
on the graphs. Compressor exit temperature lines (T5) are displayed as vertical
dashed lines, turbine inlet pressure ratio (p4/po) in dashed brown lines and
overall pressure ration lines (170) in dark dotted lines. The same constants 17mm

=0.8, nm= 0.46 and npr=0.9 were used in this case.

Variation of Turbine Inlet Temperature
300 -__.___-____.-_- ”3.. ..-i-..-----...e.. ..-fi.__ .____.___w_____2

 

nM=Oes
“"317
II “:30.“

 

 

250

Specific Work (kJIkg)

 

 

 

Compressor Pressure Ratio

Figure 111.19: Optimum points for specific work for variation of turbine inlet
temperature ( l I l').

85

Variation of Turbine Inlet Temperature

4 -. ..fl 2.__,,-__.. _, ,1, ,--i #

src (kg/kJ.s)
N

 

 

 

 

\
1 . 2.5 P4/Po=3

Compressor Pressure Ratio

Figure 111.20: Optimum points for specific fuel consumption for variation of
turbine inlet temperature (T1l').

It can be seen that from the thermal efficiency point of view, for a fixed wave
rotor compression pressure ratio of 2 (like the one used for all the numerical
simulations so far), and a fixed turbine inlet temperature of 1500K, the optimum

point would be for a baseline compressor pressure ratio of 1.6 (Figure. 111.21).

86

Variation of Turbine Inlet Temperature

 

0.1

 

 

   

Tc=375K x1."

 

  

Thermal Efficiency

 

 

 

 

 

0.05 =25 4‘”
p4/p°=2.75
I \
rpdpo = 131/130 1
o I I U
1 1 5 2 2 5 3

Compressor Pressure Ratio

Figure 111.21: Optimum points for thermal efficiency for variation of turbine inlet
temperature ( lIl ).

Also, on the thermal efficiency graphs 3 new line was highlighted (solid orange
line) denominated p4/po =p1/p0 which represents the optimum points where the
pressure at the turbine inlet is the same as the pressure at the compressor exit.
Or, in wave rotor terms, the LPA pressure is equal to the LPG pressure. The red
lines at the right of the equal pressures line represent points in the design space
where the pressure at the turbine inlet is lower than the pressure at the
compressor exit. During the previous analysis of the wave rotor input data, in
section v.3, the point of LPA=1.95 bar and LPG=1.62 was used. Although this
configuration with the turbine inlet pressure lower than the combustor exit one
has not been documented before, the design space analysis performed here
shows that such a phenomenon occurs even for thermodynamically optimized

design point. The explanation of this fact lays in the high of the combustor
87

pressure loss ratio at microscale. With the same baseline engine (compressor,
combustor and turbine) but without wave rotor, this thermodynamic cycle would
not be self-sustained. Although the cycle does not show a pressure gain from
compressor to turbine, the wave rotor introduces a gain by reducing the effective
pressure drop from compressor to turbine through the combustion chamber and

only its use enables a positive work output of the thermodynamic cycle.

88

Chapter IV

STRESS INVESTIGATIONS

1V.1 Materials Used and Properties

The proposed materials for fabrication are silicon (Si), polycrystalline silicon
(Poly-Si), silicon carbide (SiC), and silicon nitride (Si3N4). Polycrystalline diamond
(Poly-C) can be used for microfabrication of a test rig. This test rig can be used
only for compressibility measurements, using compressed air as working fluid,
since the maximum sustainable temperature of Poly-C is 500K.

Silicon is the most common material used in MEMS fabrication. It offers a sum of
advantages: great structural characteristics, commercial availability, and
extensive knowledge of fabrication technology. Table A.1 in Appendix 1 presents
the main characteristics of Si.

Silicon carbide and Silicon Nitride can be used to create a hybrid, reinforced
structure, by etching channels in silicon and depositing SiC. Properties of these

two materials are listed in Appendix 1, Tables A2 and A3.

89

1V.2 Radial and Tangential Stresses with and without

Thermal Effects

The compressor/turbine unit was analyzed as a solid disk with constant thickness

( t). The schematic of this assembly is presented in Figure 1V.1.

 

Figure 1V.1: Model of a single compressor/turbine disc.

IV .2.1 No thermal effects

Two cases were analyzed. One is the stress state without the thermal effects,
radial and tangential stresses being generated only by centrifugal force, due to

high speed of rotation (Ugural and Fenster 1995).

 

 

V23+v r2
0',(r)=L-g— 8 [ls-37] (V.1)
23 3 3 2
O't(f)=-)%— ;U[1-—3+T;U-%?] (V.2)

90

where:

a = 0m (inner radius of the disk)

b = 8 “10'3m (outer radius of the disk)

V = 388 m/s (tangential velocity)

g = 9.81 m/s2 (gravitational acceleration)
p = 2320 kg/m3 (density)

7 = p ' g(specific weight)

a = 4.2 '10‘6 1/°C (thermal expansion coefficient)

E = 160 GPa (elastic modulus)

v = 0.28 (Poisson’s ratio)

 

200 l l T f 1 l l

100

0 [MP3]

50

 

 

 

i—
i.-

-50 1 1 1 1 l

 

r [mm]

Figure 1V.2: Radial and tangential stresses without thermal effects along the
radius of the disk (compressor/turbine rotor).

The results show that radial and tangential stresses have almost identical
patterns and values. Although the maximum stress is noticed at the center of the

disc, its value is influenced by the radius of the disc and its velocity.

91

IV.2.2 Thermalgeffects
The equations for the radial and tangential stresses with thermal effect are the

following (Timoshenko 1956).

Radial stress:

_a_5_

0,,(r)=1U(-—r3-3T(r)rdr+—2(EZ———)j7'(r)rdr) (v.3)

Tangential stress:
0“”):11-5071—1 jT(r)rdr+r—2r(;T+_a—;2—)I7'(r)rdr— 7(0) (v.4)

For temperature distribution, three cases were analyzed:

- linear

- quadratic
- logarithmic
A linear distribution of the temperature on the radial direction was assumed for
the calculations. Maximum temperature, which is the turbine inlet temperature
(TIT) occurs on the outer radius. At the center of the disk, atmospheric

conditions were assumed.

T.(r)= (T... —T,..),’)'+T,-.. (v.5)

Tmin = 300 K

Tmax = 1465 K

92

If a quadratic distribution of the temperature along the radial direction is

considered

1881 -3T.... [{er _ 967.5) T (V-6)

T = . .
2(r) sz 2b b [nit
The disk can be considered as a short cylinder with inner radius zero. In this

case, conduction is the process through which the heat is transferred through

the thickness of the cylinder (Incropera and DeWitt 1990).

The temperature distribution in this case has a logarithmic profile:

73(r)=-T—’”’—‘—;;—”E’—ln[%]+rm (v.7)
ln(3)

IV.2.3 Summag and conclusions

One case without thermal effects, three temperature distributions for the case

with thermal effects:

 

 

T [K]

 

 

 

 

 

r [m]

Figure IV.3: Temperature distribution in the three sub-cases: linear, quadratic
and logarithmic.

93

The resultant stresses were compared with the adiabatic case and results plotted

in Figure NA. The values of maximum stresses are displayed in Table 1V.1.

 

 

3.19 111°
3t? 011sz
it“) 35.9
jug“) ott3(0

 

 

 

 

 

 

 

r [mm]

Figure 1V.4: Radial and tangential stresses with thermal effects along the radius
of the disk (compressor/turbine rotor).

Table 1V.1: Radial and tangential stresses in a rotating disc.

 

 

 

with temp.

Stresses“ w/o temp. linear quadratic logarithmic
6(0) 137.1 299.6 352. 1 455.2
e,(r) 0 0 0 0
01(0) 137.1 295.9 345.6 351.3
010’) -12.2 -303.4 -193.1 -103.9

 

g ' all results are displayed in MPa

The failure stress for silicon is 07 z 7000 MPa.

As noted for the adiabatic case, in the temperature influenced case the
maximum stress is located at the center of the spinning disc. Maximum values
are calculated for a logarithmic temperature distribution.

Thermal effect has an important impact over the stress state; but still for the
considered loading conditions, the highest stress is less than 10% of the
admissible stress for silicon.

The differences between the three temperature distributions are seen mostly for

tangential stress at outer radius.

95

Chapter V

DESIGN OF ULTRA-MICRO WAVE ROTORS (UpWR)

When trying to do MEMS experimental investigation, the first problem that arises
is cost. Fabrication costs are high, and this is one of the reasons the research is
progressing with a slow pace. Another reason is that diagnostics and
measurement at microscale are difficult and often destructive. An alternate and
viable solution to experiment is numerical investigation. Either using specialized
in-house codes or the newly developed CFD commercial codes, the research
process time is tremendously decreased. Numerical analyses are faster and more
affordable than experimental ones, the later ones being necessary only after the
numerical model has been thoroughly verified. In the field of shock waves
simulated by available commercial codes, the literature is not too vast. Although
the wave rotor is based on a relatively simple engineering idea, its simulation is
rather difficult to achieve. Shock waves behave differently at microscale than at
macro scale. For a given Mach number the resulting particle velocity is lower, but
the pressure is higher (Brouillette 2003). The diffusive transport phenomena can
no longer be neglected at micro scale, and viscous stresses at the boundaries
tend to deform the shock wave front. Also, the heat conduction to the wall
Prevents the flow from remaining adiabatic. At a small scale the pressure rise
across the shock increases with the decrease in the Re 'D/4L factor for a constant

Mach number.
96

v.1 Gasdynamics of Compressible Flow

As a first step in analyzing a wave rotor and its components, it is necessary to
present some basic notions about a one-dimensional fluid flow; the gasdynamics
and thermodynamics of it together with some knowledge on modeling a
compressible fluid flow traveling through a channel. The next subchapter will
describe some details of the simulation process, while the following subchapter

will present the mathematical modeling of compressible flow.

v.2 Modeling of Unsteady Compressible Flow

In subchapter 1.2.2, some basic thermodynamic relations used in modeling
unsteady compressible flows were presented. First, the numerical method used
was the visual method of characteristics in the 19605. Advances in computer
technology brought a fresh start to numerical methods, so the Euler equations
(Eqs. 1.1 to 1.3) were solved by different explicit and implicit codes, some written
specifically for these applications (in-house codes), other created as software
packages for solving any kind of fluid dynamics problem (Computational Fluid

Dynamics commercial packages).

V.2.1 Expligit vs. Implicit

Always, a first issue that comes in solving a fluid dynamics problem is what
Solver to use. The debate centered on explicit vs. implicit solutions has dated

from the beginnings of numerical simulations, and it is still going on. There is no

97

clear criterion to decide which solution should be used for each problem; in fact
some problems may provide similar results regardless of the solver used.

In general, explicit methods compute the next time step solution directly based
on the known current time information. It is therefore necessary to keep the
time step within the limit of physics in order to obtain accurate sequential
solution in time. The implicit methods evaluate the solutions at two or more time
space. In this way, one can improve the accuracy of the solution, in principle.
There are many examples in the integration of an ordinary differential equation
by using multi-steps.

The main problems that arise from using one or the other solution are numerical
stability and numerical accuracy. For stability, the implicit solution method, which
is more complex, allows for a larger time step than the explicit solution. But,
since it is more complex, it requires more computational effort so even if the
time step is larger, the computational time is also higher. For the explicit
solution, it can be proved that the condition of accuracy is strong related to the
stability condition. For the implicit solution, a factor of relaxation (damping) is
introduced, which will make the solution more stable, thus making possible the
increase in time step, but in the same time the results will be less accurate.

As an example, for a wave propagating through a tube, the implicit solution with
high damping will capture only the steady-state results, while an explicit one
permits the investigation of transient processes. To be able to use the implicit

method in this case, a very small time step has to be used.

98

For non-viscous flows, where solution is conditionally stable, the explicit method
works best.

As stated previously, the debate between an implicit and explicit solution has not
been solved; and for the case of unsteady waves traveling through a
channel/tube both methods have been used. Horrocks (Horrocks, Reizes et al.
1998), Pekkan (Pekkan and Nalim 2002) and Lee (Lee, Arslan et al. 2004),
DeCourtye (DeCourtye, Sen et al. 1998) have used implicit methods; Welch
(Welch and Chima 1993; Welch 1996; Welch 1997), Piechna (Piechna 1998;
Piechna and Lisewski 1998; Piechna 1999), Larosiliere (Larosiliere and Mawid
1995), Eidelmann (Eidelman, Grossmann et al. 1991) and Paxson (Paxson 1992;
Paxson 1995) have used explicit, while Greendyke (Greendyke, Paxson et al.

2000) has used a combination of explicit and implicit model.

99

V.3 Design Methodology

The first step in the calculation of the port timing is to decide on a corresponding
wave pattern which, in turn, will generate a wave diagram. In the literature so
far, there are several types of wave patterns for a four port wave rotor. Among
these, two of them are presented next. The first one (Figure v.1), developed
initially for a five port wave rotor by Cornell University was adapted to a four port

wave rotor (Resler, Mocsari et al. 1993).

—> Shockwave
m— Expansion wave

——> Direction of the
ow

-11.---11---

I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I

Fuel 4 @533

V

 

T‘ LP part
HP part

r"-'“—*~ _‘ M17 !HF;&)

$893!} 47 ----__ -.-_.

 

 

 

 

------J
-- -------|

Figure v.1: Wave pattern for a four port wave rotor (adapted after Resler et al.).

NASA presented in 1997 (Welch, Jones et al. 1997) the wave patterns for a

through—flow and a reverse-flow wave rotors (see Figure v.2)

100

I
I
—> Shockwave :
w Expansion wave :
—> Direction of the
flow

l-.---------

i /=: 1:661
1.91 <1 *V _

[315571)] 4*

  

l----.---.| ‘ r-------------.

 

 

 

 

 

 

 

 

 

 

LP part
5 HP part
r.__-._w -‘ _ V (HPA—(2)7. . V lip-11(2);
01391914 * _ 111891.31; —‘—‘—’
TE

Figure v.2: NASA wave patterns for the four port wave rotor. Left — through-flow
configuration, right — reverse-flow configuration.

V.3.1 Through — Flow Solution

The solution chosen for the ultra-micro wave rotor, based on the thermodynamic
conditions in the four ports is the following. The HPG port opens, generating a
shock wave (51) that travels to the end of the channel and reflects as shock
wave S2 (Figure v.3). Immediately after 51 reaches the end of the channel, the
HPA port opens. When S2 has traveled the channel lengths and reaches the HPG
port, the port closes, generating an expansion wave (E1). When the head of E1
arrives to the HPA port, the port closes, and on the arrival of the tail of E1 to the

right side, the LPG port opens. The opening of the LPG generates an expansion

101

wave (E2) that moves to the left side. When E2 has traveled the length of the
channel, the LPA port is opening. The closing of the LPG port will generate a

shock wave (S3) parallel with E2 and traveling in the same direction regulating

the closure of the LPA port.

—-> Shockmvc

---—> Expansion wave

 

i LPA "(1) ! —> Direction 0! flow
L. — ' ' ----- Gas/A'I Imoflaco

: LPG (4il ._ _ Low Pressure Air

L ' ’ ‘ ’ fi—W 7 217 High Prossu'o A'I
LP part Low Pressure Gas

-____ ___L_ ______ HighProamGas
HP part
PM (2» "i

BEEP!

 

Figure v.3: Wave pattern for a four port through-flow wave rotor.

The horizontal axis represents the axis of the channel, while the vertical axis is
the time (although this t-x diagram is more representative for an axial wave
rotor, it can be applied for a preliminary design of a radial one — ignoring
centrifugal forces effects, which will be discussed later). The presented wave
pattern deals with an ideal situation, in which exhaust gases are fully scavenged

to the turbine, while compressed air flows entirely to the combustion chamber.
102

The air/gas interface is just a temperature interface, since no pressure waves are

crossing this interface; pressure is assumed to be constant all over a zone. Also,

in generating the initial timing of the wave rotor, all fluids are assumed to be air

and are treated as ideal gas. For convenience, initial high pressure, high

temperature fluid will be referred to as gas, while initial low pressure, low

temperature fluid as air.

The pressure exchange process in Figure v.3 is described as follows:

zone I: the channel is filled with air coming from the compressor (fresh air)
shock wave 51 travels to the right, realizing the first stage of the
compression of the fresh air while expanding the high pressure, high
temperature gases coming from the combustion chamber

zone II: first stage compressed air and first stage expanded gas; zone is
divided by the air/gas interface

a second shock wave (52) is reflected by the right end plate, just before the
HPA port is opening, compressing the air further up the desired pressure in
the combustion chamber

zone III: end of air compression, the zone is connected to the HPA port;
zone is divided by the air/gas interface

expansion wave E1 further lowers the gases pressure and reducing the flow
velocity in the channels to zero

zone IV: the channels are fully expanded combustion gases

103

- expansion wave E; which will fully reduce the gases pressure to the inlet
pressure of the turbine

- zone V: a mixture of low pressure gases and low pressure air entering the
channels; the air/gas interface is present throughout the zone

- a weak shock wave S3 generated by the closure of LPG port, which will

return the channels to initial conditions and zone I

The gasdynamic cycle that allows for a prediction on the port timing uses the

following background relations (Weber 1992; Anderson 2003):

 

 

 

- shock wave relations:
17, = 52. (v1.1)
[’1
r LL: + ”5
1 1+ ———-175
7 —1
w = a, F1075 -—1)+ 1 (v1.3)
2r
_2_z_
a 1
up =4(Hs —1) 7+ _1 (v1.4)
7 V 175 + r
7 +1

 

where: 1 — conditions in front of the shock, 2 - conditions behind the shock, w—
induced velocity of the flow in front of the shock, up - induced velocity of the
flow behind the wave.

104

- expansion wave relations:

 

a2 7 ‘1 ”2 T ”1
— = 1 i V1.5
a1 2 a1 ( )
r a 2
—2— = [A] (V1.6)
7: al
2_7
£2. = [173.) H (v1.7)
.01 at
um, = a1 :t u1 (VI 8)
Ulail = 32 i ”2

where: 1 - conditions in front of the wave, 2 - conditions behind the wave, ahead
— velocity of the head of the wave, Uta/7" velocity of the tail of the wave and the

:L- sign represents the direction of the flow with respect to the direction of the

wave.
- general equations:
a = y R T (V1.9)
- total to static equations:
%=1+l—;—1M2 (v1.10)
— 1 711‘
%=(1+Z—2—M2) (v1.11)

The procedure assumed the stagnation properties in all ports are known. Since

air is considered the only working gas in the model, in zones II, III and V, the

105

air/gas interface is differentiating only in temperature the two gases. The
pressures of air and exhaust gas are the same as no pressure wave comes
between the two fluids.

I - II

Assumptions: u, =0, p, =p1 =p01, 7', = 7'1 2 T0,, u,, =u3 =0, p,, =p3 =po3,
T11 = T3. = 7-03

From relation V1.1, setting p2 = p3 and p1 = p, it results

17,, = 39— (v1.12)

F1
The velocity of the shock is defined as the velocity of the flow in front of the

shock, if the flow was initially at rest.

 

w,1 = a, $12171 (1751 — 1)+ 1 (v1.13)

where a, is the speed of sound in region 1 (LPA port) and defined by Eq. V1.9.

The time it takes the wave to travel the length of the channel is equal to

L
W51

 

(v1.14)

t’51 :

The time t51 will define the opening of the HPA port and will call thAqm. t is the
length of the channel.

The induced velocity of the flow behind the shock is the velocity of the flow in

zone II.

106

 

 

 

 

 

l 27
a + 1
u,, = 11,,1 — —‘(1751 -1) 7 _ 1 (V1.15)
7 17 +
$1
7 + 1
The air temperature in zone 11 can be calculated using Eq. V1.2.
7 + 1 + H5,
TIIair = T! 1751 7 + 1 (“'16)
1 + Z— 1751
y - 1

While the gas total temperature in zone II is equal to the gas total temperature
in HPG port.

To T03 (VI-17)

119.35 =
The Mach number of zone IIgas is defined as

Milgas = U” = U” __ (V1.18)

aIIgas 7 R Tllgas

Applying Eqs. V1.18 and V1.10 for zone 119.5 the value of the static temperature

can be obtained

— 1 u2
TIIgas : 7;)st _ YTfi (VI-19)

Using the definition of Mach number and speed of sound at zone II... the rest of

the properties of the air can be calculated.

— 1
T..... = T [1 + 17114.2...) (W20)
:1
- 1 1;le v1 21
pile/r - p0 [Ia/r 1“ 2 Hair ( - )

107

II - III

Assumption: p0,” 2 p02.

Reflection of the primary shock wave will increase the pressure of the fresh air
further, since it is known that one shock cannot raise the pressure of the driven
gas higher than the pressure of the driving gas. As seen in previous paragraph
these two shock waves are regulating the opening and closing of the HPA and
HPG ports.

From relation V1.1, setting p1 = p3 it results the pressure ratio across the second

shock wave.

17,2 = & (v1.22)
P3

To find the static pressure of HPA port (p2), the following system of equation

needs to be solved:

+ 7 ‘ 1 M22 (v1.23)

 

 

 

Simplifying the previous system of equations using also Eqs. V1.4, V1.9, V1.22 the

following result is obtained:

108

r-l

 

_ 7
\[7 R 7'02 _2_114_l 2 ”pl _J 2R T3 p3 p02 A _1 (V1.24)
7,-

 

 

r-l

—— p
p..(y+11A ' +(7-1)P3 3

7—1

where the unknown is A = 1 + M}.

 

Equation V1.24 is best solved numerically. Calculation of M2 yields to solutions for
the other unknowns (p2, T2, U2, U...)

The velocity of the second shock wave as defined by Eq. V1.3 is

 

1
W52 = a3\/%(1752 -1)+1 (V1.25)

The time necessary for the second shock to travel to the left side of the wave
rotor is called tsz and is defined by the definition of velocity.

L
W52

 

(V1.26)

tsz =

Time tsz is the delay between the opening of HPA port and closing of HPG port.

The opening of HPG is set to be 05 (tflm = 0) and the closing is
tflmcm, = (‘51 + t52 (V1.27)
The time while the a port is open is defined as follows.
t... = am... - am)... (ms)
Both air and gas temperatures in zone III are defined by Eq. V1.2.

7+1

 

1 + 1752
Tm ' = TIIalr 17$2 7

all

 

(v1.29)

109

 

T 1752 7’1

111935

J

”gas

(V1.30)

 

 

Pressure in the zone III is the same for air and gas.
The velocity of the flow induced by the shock wave 52 is up; and is computed

with Eq. V1.4 and is oriented in the direction of the shock travel.

 

 

(V1.31)

 

The velocity at the exit of the channel to the HPA port U; is given by the sum of
velocity in zone 11 (from Eq. V1.15) and induced velocity from second shock
wave, upz.

- u

u2 = u (V1.32)

p1 p2

III - I V

Assumptions: u“, = 0, u,,, =u2.

Velocity of the expansion wave E1 is defined by the velocities of the head and tail
of the expansion wave (Eq. V1.8). Since high pressure is needed in the HPA port
and the pressure is lower towards moving to the tail of the shock wave, the head
of the shock reaching the right side of the wave rotor will regulate the closing of

the HPA port. To avoid the reflection of the expansion wave and lowering the

110

pressure in the channels even further, the tail of the expansion wave will

determine the opening of the LPG port.

From Eq. V1.8,

{Una-aw :aIH +0111
Uta/I1 =31V +U1v

amcan be found out using Eq. V1.5.

31v =1+7-1U1V-U111

 

3111 2 3111

(V1.33)

(v1.34)

The times required by the expansion wave's head and tail to reach the other end

of the channel are

 

L
t... —
uhaadl
it 1
taill " —
L Uta/71

 

The closing of HPA port is defined as

tum... = tHPGdos‘e + 5....
While the opening of LPG port is

tmen = tHFGc/ose + (35,,1

The pressure in zone N is according to Eq. V1.7.

ll.
,0” _ [31V )7—1
P111 an!

IV-I/

(V1.35)

(V1.36)

(v1.37)

(V1.38)

The traveling of the second expansion (E2) wave will influence the opening of

LPA port. Since the lowest pressure in the channel is needed for maximum inflow

111

of fresh air, the arrival of the tail of the second expansion wave will determine
the opening of the LPA port.

Applying Eq. V1.5 for amend av will result in finding the value of av.

avgas ___ 1 + 7 ’1 ”IV —U,,ga5 (V1.39)
an, 2 a,.,

To find avg... the value of Ty... is needed. It is assumed that 7L... = 7'4 and

To... = T... Applying Eq. v1.10

 

73v. 7 - 1 2 7 — 1 ”5
__as = 1 __ M = 1 98‘ V1.40
7,9,, + 2 V9“ + 2 7 R Tm. ( )

From Eqs. V1.39 and V1.40,

7- _7R712Vgas(7-1)+2alzv_4ajzv(7"1)

 

 

 

 

 

V9“ _ 7R0 + 1) 7R0 + 1)2 (VI 41)
2J27R(r - 1121312272.... + 212/3%.... - 4r R at.)
+
rZRZH + 1)2
thus
2 R
UVgas = fi(70l/gas _ 71/935) (V142)
From Eq. V1.8, aheadzand (Aware
{uneadz = 311/ ‘ ”1v (V1 43)
”mi/2 = anas — quas

both of them traveling in the opposite direction of the flow.

The corresponding durations the waves travel are

112

 

 

,
L
theadz = U
< [“2 (V1.44)
t , =
L tal2 “(an

 

Opening time of LPA port is the sum of opening time of LPG port and tam.

tLPAopen = ttPGopen + t 131/2 (VI-45)

V—I
Shock wave 53 is generated by the closing of the LPG port and its arrival at the
low pressure air side will determine the closing of LPA port. From Eq. V1.1,

setting p2 = p1 and p1 = p4 it results

17.. =fl (V1.46)
p4

The velocity of the shock is defined by Eq. V1.3

 

7+1

W53 = aw, J77— (H53 " 1)+ 1 (V1.47)

where a... is the speed of sound in region 1 (LPA port) and defined by Eq.
(V1.9).

The time it takes the wave to travel the length of the channel is equal to

I.
t = — (V1.48)
$3 “/53
It results that
tLPAdose = tLPGdose + :53 (VI-49)

113

The missing information, closing time of LPG port (tum...) can be revealed by an
overall mass balance over the entire port system.
Taking the velocities in the absolute values, thus considering flows in HPG and
LPA ports as inflows, while HPA and LPG ports providing outflows, the following
relation can be written.
n'7,,,,G + mm = m,“ + m,,,,, (V1.50)
Knowing
m=puA (wsn
where A is the cross-sectional area, defined as
A=HW=Htv (V1.52)
H is the height of the port, Wis the width of the port, which can be computed as
the time while the port is open, 1; multiplied by the tangential velocity of the
rotor, v.

Also, from the equation of state of an ideal gas (Moran and Shapiro 2004)

 

p
= ___ V1.53
p RT ( )
From Eqs. V1.50-VI.53
pHPG UHPGtHPG + Pflumtm = ‘LWAUHPAtHPA + p—LPG'ULPGtLPG (V154)
THFG TLPA THPA TM?

The velocities in the LPA and LPG ports are assumed to be the same. Applying
Eq. V1.28 for LPA and LPG ports and Eqs. V1.45 and V1.49, the time while LPA is
open, 121..., can be deduced as function as tune.

t,” = ta; + t53 - rm (V1.55)

114

Introducing Eq. V1.55 into Eq. V1.54, only one value remains unknown, tuna. Once
this equation is solved, all the times of port opening and closing are known, so a
preliminary porting solution is generated.

The results generated by the previous analysis were compared with the
numerical ones obtained using the 1D code. Results are presented in a graphic

format in Figure V.4.

11.49/11.36/11.40

    
     
   

i ””4111? ’1 _10.22/1o.09/7.9s
“'Wi LPG(4)
6.02/6.19/8.06 ‘77-‘77“flm-J

 

‘ 4.64/6.00/5.68

3.37/3.28/3.29 » 5 , ms, 1-.
. , HPA( ) I

 

Figure v.4: Comparison between analytical results and numerical results for an
initial port prediction of a through-flow wave rotor (first number is analytically
obtained, the second one - numerically).

115

For an optimum port timing calculation, a feedback loop was created between
the two models, thus reducing the error in continuity equation from 6.4% to 2%.
The mass flow rate graph function of time is presented in Figure V.5. Flow rate
through all the ports is positive, meaning that the fluid always travels to the right
(positive x-axis). Thus, for the left boundary the positive flow rate means inflow

to the channel, while negative means outflow from the channel. The reverse is

valid for the right boundary.

Mass Flow Rate

700.00T ., ,. -3 m ___--- L. 1--

600.00 »~ - - ~~

500.00 -~

g

  

—Right 8nd
_ ES“, BN1.--

    

 

mags flow rate. [9/s]
8

200.00 ,_

100.00

 

0.00

1 10 19 28 37 46 55 64 73 82 91 100109118127136145154163172181190
timestep

Figure v.5: Mass flow rate through the boundaries of a wave rotor channel in
through-flow configuration, [kg/s].

116

V.3.2 Reverse — Flow Solution

Next, the reverse-flow configuration is presented. The wave pattern is identical
with the through-flow configuration for the high pressure part, while the low

pressure part pattern is mirrored (Figure v.6).

—> Shockwavo
—-—-’ Expansion wave

—> Direction oHIow

5 LPA, (1)i ..... Gas/Air Interface
i (PG (4; ' Low Proust" Ai
l . . . .I ['j‘fi High Prawn A‘I
LP part Low Pressuo Gas
‘_ _ ,_,. _ HighProsuan
HP part
‘HPA 121;
115191.?

 

Figure v.6: Wave pattern for a four port reverse-flow wave rotor.
The analyh'cal solution follows the same steps as for through-flow model. Again,
the results from the theoretical analysis and the numerical ones were compared,

being displayed in Figure V.7. The mass flow rate graph is shown in Figure V.8,

Where the reverse-flow effect can be seen. On the high pressure part, on both

b0undaries, the flow rate is positive, which means for the left boundary flow

QOes into the channel. On the low pressure side, both flow rates are negative;

meaning that for the left boundary, fluid leaves the channel.

117

1......

LP part

7 923/937

 
 

7T ///////////2

V

\

§

\
§®
\.

s ,

   
  

105/7.14 \ ”

1111 ._ _

\
.N
.\
¥
§
§
§
\
§

  

’1 HPA(2) ;

Lbfiim i Kip—8157’
106 s] -_- v—~~———--J

Figure v.7: Comparison between analytical results and numerical results for an
initial port prediction of a reverse-flow wave rotor (first number is analytically
obtained, the second one — numerically).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

00000 , .-.,_. __
/i— HPG
/—L HPA
50000 ~ --~
7‘ LPG
71:" r— LPA
5240000
3
E —PlgmBnd
g 200 00 A —Lel'l Bnd
c \ /
(I)
In
to i i i
E 000 -
10 19 23 37 46 55 54 73W12713515154103172181190
.200 00 i
.40000

time step

Figure v.8: Mass flow rate through the boundaries of a wave rotor channel in
reverse-flow configuration, [kg/s].

118

Chapter VI

NUMERICAL SIMULATIONS OF UuWR

V1.1 Setting up GAMBIT

GAMBIT 2.1 was used as a pre-processor for creating the geometry, mesh, and
domains necessary for the CFD software. The 3D objects were converted into 20
models to reduce the computational load. The axial wave rotor channels were
designed as a sequence of faces, using the unfolded view method, which allows
3D objects to be projected onto 2D surfaces, described in the previous chapter.
Figure V1.1 illustrates the geometry used for creating the mesh of the axial wave
rotor in through-flow and reverse-flow configurations. The edge boundaries
comprise two pressure inlets and two pressure outiets for the ports (ducts), as
well as two sliding interfaces between stationary walls and moving channels.

The mesh was created using standard, quad elements placed in map and pave
type distributions. For simple geometries like the one of a wave rotor, the quad
elements are suitable to use and they decrease the computational time. The
pave distribution was used to accommodate the transition from finer mesh along
the interface to a coarser mesh towards the end of the ports (Figure V1.2). In the
case of the axial wave rotor model, the solid walls were modeled as adiabatic

ones.

119

 

4020

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

B
l
4
S

 

5

 

 

 

 

 

     

a) b)

Figure V1.1: Axial wave rotor in 2D developed view: a) through-flow
configuration; b) reverse-flow configuration (values in pm).

The dynamic aspect was modeled as follows: the channels are sliding between
stationary ports with interface pairs created between end of channels and ports
(Figure V1.2). The pair of interfaces works only if at least one of the interfaces is
made out of a single edge. If multiple edges are used for both interfaces in the
pair, then the property transfer is not realized between the surfaces in contact.
The situation of Figure VI.2-a is acceptable, but for the one in Figure VI.2b a
small area was added to the end of the channels, which will transform all the
edges from the end of the channel into one. This is actually a more accurate

simulation, because this will account for the leakage between the rotor and the

120

casing (which contains the ports). Another way of creating the interface is to join
the two ports together by a small slit (Figure VI.2—c). To be noticed that the slits
added to the interfaces are 100 times narrower than the length of the channel.
They might be created even smaller with the purpose of realistic modeling; but

in this case, the mesh has to be finer, which in turn will generate slower results.

I I.
E'gégge‘

I:

‘-
I.

1!..-

Fixed interfaces

I
‘ III
‘ Ii;!:fi§’
....~.

I
I
5, :

_ , Fixed interfaces
Movrn nterfaces

A

  
   

i r I I. ‘3 a)

; I Movmg channel

 
   

Fixed interfaces

 

Moving channels
C)
Figure V1.2: Mesh and interfaces setup for 2D axial wave rotor investigations: a)

Single port — multiple channel interface, b) single port - multiple channel interface
with additional gap, c) multiple port — multiple channel interface with gap.

Moving channel

The axial wave rotor mesh adopted here is comprised of 9,406 nodes and 7,836
elements. In the case of the radial wave rotor, the transformation of the 3D

object into a 2D model was simpler. A horizontal cross-section of the rotor and

121

ports was used to create the model. An example of a rotor is illustrated in Figure
V1.3. In order to decrease the computational time, a reduced model with a single

cycle per revolution was utilized for pin-pointing the final design. The reduced
model is basically a quarter of the full model presented in Figure V1.3 with one

set of ports and approximately 30 rotating channels. The design schematic can

be seen in Figure V1.4.

30

@ \\\\\ .

    
    
    
   

 

 

 

 

s25 if

\
\

/¢/

%
447/

//

‘\</////lilil\\\\\\\\\

\/

‘\

figure V1.3: Radial wave rotor cross-sectional view [dimensions in mm].

122

 

Figure V1.4: Radial wave rotor cross-sectional view - reduced model.

Following a grid sensitivity study with refinements from 10,000 to approximately
170,000 elements, the final design was set to 38,101 elements and 52,519 nodes
for the full model and 10,210 elements and 12,884 nodes for the reduced model.
The contact zones between fluid region and solid region (channels’ interior and

walls) have been defined as coup/ed walls Section VII.3 will present more details

about heat transfer modeling.

An example of mesh for a through-flow radial wave rotor, reduced model, is

presented in Figure V1.5.

123

 

Figure V1.5: Radial waver rotor in a through flow (T F) configuration: reduced
model and zoom in of the mesh.

124

V1.2 Setting up FLUENT

For simulating the behavior of the flow through an ultra-micro wave rotor, the
commercial CFD package, FLUENT 6.1 was used. An extensive study of using
modern CFD commercial packages to simulate fluid flows in various conditions,
either laminar or turbulent, steady or unsteady was done by Kochevsky in 2004.
His conclusions were that CFD packages, including Fluent, are capable of
simulating accurately unsteady flow behavior (Kochevky 2004). The following
paragraph will describe the solver settings as well as some boundary conditions
and convergence criteria used.

The fluid was considered as compressible ideal gas, having constant specific heat
and constant thermal conductivity, while the viscosity varied with temperature.
Since the difference in gas constant for air and exhaust gases is minor, for
modeling simplification only one gas was considered as working fluid - air.

The solid regions were considered to be silicon made, having constant specific
heat and temperature dependent thermal conductivity. The properties for the
material considered are presented in Annex 1.

The ports were modeled as pressure inlets and outlets, with a fixed value set in
the boundary condition. Once the model was started, the Patch option was used
to increase dramatically the pressure and temperature in the HPG port, allowing
the simulation of the unsteady flow phenomena. The inlet and outlet pressure
boundary conditions used for modeling inlet and outlet flow to limit the mesh

space is a well know technique even for the free flow around objects. Hunt and

125

his group at the University at Canterbury have used it for modeling the flow
around a plane wing (Hunt, Rudge et al. 2002).

A double-precision solver was chosen due to the nature of the problem. Since
the problem is unsteady, the residuals of the Euler equations will tend not to be
in the same order of magnitude. The double-precision solver allows for a twelve
order of magnitude drop of the residuals. The coup/ed solver allows for both
implicit and explicit methods to be used, solving the governing equations of
continuity, momentum, and energy simultaneously as a set of equations. If the
coupled solver is used together with the energy equation, the viscous terms
(artificial viscosity) are added to the later automatically. The stability of the
solution is given by the CFL criterion. Let g be a flow variable. Its value after at a
time t+At, function of previous time step, t, can be described in a basic Taylor

series.

g(t+At)=g(t)+[%€—) At+--- (VII.1)

am
But Atcannot be arbitrary. It has to be less or equal than some maximum value,
estimated by a stability analysis performed on a set of linear equations in order
for the solution to converge. The CFL criterion says that At must be less than
equal to the time required for a sound wave to travel between two adjacent grid
points (Courant, Friedrichs et al. 1928; Courant, Friedridis et al. 1967).

But At /Ax (distance between adjacent grid points) is proportional to the Courant

number (or CFL number). Because of this coupling, reducing the grid size will

126

increase the solving time, unless the Courant number is increased, up to the
stability limit. For an explicit solution it is set to 1 and can go up to 2, while for
an implicit solution, it is set to 5 and can go up to 100 (Fluent 2003). For the
coupled solver, this is the main stability control parameter.

When using laminar flow conditions, the viscosity is modeled as a function of
temperature, based on the Sudredand model (Brillouin 1938; Kim and Chair

2002)

 

1.5
7' T +5
z” __ ’9’ W12

where my = 1.789105 kg/ms is the reference viscosity, Tm: = 273.11 K is the
reference temperature and 5 = 110.56 K is the effective temperature in the three
coefficients Sutherland law (Sutherland 1893).

The solution controls are Courant number (which is automatically adjusted for
convergence of solution) and type of accuracy determined by the solution
scheme. The first order upwind scheme has been used, which is a first order
accuracy solution, meaning that the quantities at faces are determined by
assuming constant values through out the cell, calculated in the center and
averaged over the cell. This scheme is useful and accurate when the flow is
aligned with the grid. Otherwise, first order convective discretization increases

the numerical error (due to diffusion). The same upwind scheme was used by Liu

127

and his team when modeling a 4mm diameter shock tube used for delivering a
powder vaccine (Liu, Truong et al. 2004).

Convergence is attained once each residual of the continuity equation, energy
equation, and flow velocities dropped at least three orders of magnitude. The
residuals were monitored, allowing the computation to advance to the next time
step once the convergence criterion was met.

Results show that the flow is well into the continuous and laminar region, thus
determining an accurate simulation. The Reynolds numbers vary between 10 and
1000, while the Knudsen number stays lower than 10“.

As discussed in Chapter VI, the debate over the explicit and implicit solver has
arguments for boat sides. For solving the numerical model of a wave rotor, a
coupled implicit solver was used, flow being modeled as laminar viscous, but not
before doing some investigations on proper type of solver to be used. Thus, it
was concluded that between laminar viscous and inviscid flow as well as between
implicit and explicit solver, the difference is not significant.

In the Lax scheme that FLUENT uses when the coupled option is used, a term
called “artificial viscosity" appears when solving an inviscid flow model. This
artificial viscosity behaves just like the viscous term in the Navier-Stokes
equation. Assuming two properties f and 9 functions of time and space (1; x),
related through a simple partial differential equation (Eq. VII.3)

a_9 z .61 (VII.3)
at 6x

128

According to Lax, the time derivative is based on an average value of 9 between

points (i -1) and (i + 1)

 

[2%)]: = 9;” -0'5(gf+1 + gik-l) (VII.4)
at i At

Alter some mathematical operations with the two equations,

2
Q3 = 2: + Mal (VII.5)
at 6X 2A! 5X2

Equations V113 and VII.5 are different. By applying Lax’s finite-difference
procedure (Lax 1954) to Eq. VII.3, a difference equation was obtained; and by
applying the definition of the derivative to this equation, the partial differential
equation (VILS) was obtained. This equation contains the extra, second order
term (S'E'g/aa2 multiplied by (Axf/ZAt. This coefficient is called artificial viscosity
and is a consequence of the mathematical procedure, not a physical term. This
term is specifically added to the equation to account for a more realistic
simulation (Anderson 2003).

When examining the results obtained with the CFD code, it can be seen that the
difference between artificial viscosity and laminar viscosity in the wave rotor case
is negligible. The artificial (numerical) viscosity is triggered by the pressure
gradients, while the real (physical) viscosity is activated by the velocity gradients.
Since the velocity is induced by the force of the shock, which is the pressure
ratio, it can be clearly seen why the two viscosities generate the same effect.
Figure V1.6 presents the pressure and temperature distribution in the cases of

inviscid and laminar viscous flows.

129

 

laminar viscous flow

  

b) inviscid flow ' laminar viscous flow

Figure 11.1: ZD simulation of axial wave rotor: a) pressure distribution,
b) temperature distribution.

When comparing the explicit and implicit solvers, the numerical model proved to

be robust enough, thus indifferent to the type of solver. Since the time step was

130

small enough for both explicit and implicit solution to converge, the two solutions
provided almost identical results. The time steps varied from 1e-9 to 2.5e-8
seconds. Figure II. presents the distribution of pressure and temperature for a

model with laminar viscous flow solved with an explicit and an implicit solver.

4UBe+US
3936+05
3 7Ee+05
363e+05
34Be+05
‘ 3332+05
BlBe+DS
3039+05
2879+US
27Qe+05
257e+05
2428*05
227e+05
2128+05
L97e+05
182e+05
1669+05
LSle+US
l36€+05
1219+05

a) explicit solver
1588+03 .

1 52e+03
146e+03
. 1 39e+03
" 1.33e+03
1 1 27e+03
1 1 219+03
, ,1 l158+03
1 09e+03

103e+UB
s 648+02
9 name
a 4le+E12
7 seem
7 13e+02
6.57e+o2
595e+02
5 34e+02
4 73e+02
Alle+02

b) explicit solver meifiiolicit solver
Figure 11]: 2D simulation of axial wave rotor: a) pressure distribution,
b) temperature distribution.

     
       

131

V1.3 Heat Transfer Simulations

When FLUENT is used to solve the heat conjugate problem, the energy equation
(1.3) becomes

%[p[e + (’72)) + V[pu[e + (172)] + V(pu) — )0fo — 5,, —

(VII.6)
—V[ke,, -VT—Zhjjj +6“ 17] =0
1

where

5),: heat of chemical reaction and other volumetric heat sources
- ken! effective conductivity
- h): enthalpy of species j
- 1,: diffusion of species j
- (39,, ~17: viscous dissipation
Since the simulation accounts for only one species and no chemical reactions,

Eq. VII.6 can be simplified as follows:

a u2 u2
5F[p[e + 7]] + V£pu[e + 7]] + V(pu) — pfxu — (VII.7)

—V(ke,, -VT-h]+&e,, -u)=o
The microscale flow is described using a set of non - dimensional parameters.
These parameters define the continuity of the flow and conduction properties
(Knudsen number), temperature gradient at the surface (Nusselt number), heat
transfer resistance of the interior and surface of a body (Biot number), diffusivity

(Prandd number), advection (Pec/et number) and convection (Eckert number).

132

The Knudsen number is defined as mean free path of the molecules divided by

the characteristic length.

 

2.
Kn = —— VII.8
A ( )
For a one-dimensional microchannel
Kn = J;— —l—— ” (W13)
2 VRT pDH

Based on previous investigations, the Knudsen number of the flow inside the
channels of the ultra-micro wave rotor was calculated as Kn = 2.75 - 3.39 '10“.
These values indicate that the flow is inside the continuous flow domain.

The Nusselt number is defined as a dimensionless indicator of the temperature
gradient at the surface and compares the real heat transfer from a surface with
the heat transfer obtained taking into consideration only conduction.

Nu = or; (VII.10)

For silicon microchannels, convective heat transfer coefficients have been
reported in the range of 24 kW/mZ'K (Kang, Chen et al. 2002) up to 10 MW/mZ'K
(T uckerman and Pease 1981).

The thermal conductivity of silicon varies with temperature. For the numerical
simulations, a linear variation was considered based on the following values:

k = 98.9 W/m'K at 400 K and k = 31.2 W/m'K at 1000 K (www.efunda.com).
The convective heat flux is calculated in FLUENT using Eq. VII.11

dzhA(Tw —T,) (VII.11)

133

where A is the contact area, T.., is the wall temperature, and 7} is the fluid
temperature.

Next, a study was performed to investigate the influences of heat transfer upon
the pressure exchange process inside the ultra-micro wave rotor channels. Three
models were created and analyzed.

First model assumed adiabatic walls. The channels were modeled as a single
fluid zone. The energy transfer between the channels is done only through the

interface regions at the ends (see Figure V1.8).

/ ‘fi ’-

 

 

 

 

 

 

Grid (Time=51 CDOe-OG) Jm 20, 2(1):;
FLUENT 61 (2d, up, coupled imp, ram. unsteady)

 

 

 

Figure V1.8: Mesh of radial wave rotor with adiabatic walls — zoom-in view.

gond model had a limited heat transfer. A mixed (convection- radiation) model
was used; but the emissivity coefficient was set to 1, so only the convective part

was active (see BC in the Figure VI.9). The continuum fluid zone was identical

134

with the first model. The value for the heat transfer coefficient was chosen based

on previous approximate calculations and literature figures.

.— -- 'I I“ ‘ Isa-m.

Zone Home

[Tan

Adjacent Cell Zone
[channels

 

 

Thermal IDPM ] Momentumi Species] Radiation! 008 I

 

 

 

 

 

 

 

 

 

Thermal Conditions
p Heat Flux Heat Transfer Coefficient MmZ—k] [15” acoustant j
r‘ Temperature i Fr e StreamT to tote
r Comedian e 12 were lid [on [constant :1
r Radiation External Emissivity [1 [constant :1
6 Mixed l
‘ External Radiation Tern erature ‘ v
Mater!" Mm P N [one ,constant __I
[aluminum 1.} “Edit... Wall Thickness [ml l'
Heat Generation Rate W311. Econstant I]
i

 

 

 

 

---9:<._1 2135:1311

 

Figure V1.9: Wall boundary conditions — set up window.

Third mmel had an unrestricted heat transfer, governed only by the material
properties. Material properties of silicon are presented in Table. A1

The model uses a two continuum zones: a fluid for over the interior of the
channels and a solid for the walls. The interface between the continua is defined
as a coupled wall, which is a two-sided wall. This kind of boundary condition is
defined when the wall zone has a fluid and a solid region on each side. In this
case no additional thermal boundary conditions are required because the solver
will calculate heat transfer direcfly from the solution in the adjacent cells. All that
needs to be specified are the material properties. The Figure V1.10 shows the

meshes of the channels’ interior and walls.

135

 

 

 

 

..-,_ _._ -4-—4;— . —

 

 

1 4. .
l _- 1 ‘
— - c T" t t ‘ 1 ‘ 1* T ‘T f
l i ' l— A " 1» -1- 1 _
1‘ x ‘1 1 ’1 r ‘ f F _.. 1 - -04..— +
l ; I 1 f 1 |
Grid (Time=51000e-06) .111 20, 2005
FIUENT 61 (2d, dp. coupled imp. lam, unsteady)

 

 

 

Figure VI.10: Mesh of radial wave rotor with solid walls — zoom-in view.

The three examples were based on a through-flow radial wave rotor, but the
simulation was reduced to a single cycle, single set of ports.

All the models used the coupled implicit solver with laminar viscosity. The gas
was defined as compressible ideal gas with a laminar viscosity dependent on
temperature - Sutherland law (Sutherland 1893). The implicit solver used the
unsteady flow option with the first order, upwind scheme. No-slip boundary
conditions were defined for all three examples.

If the coupled solver option is used in setting up the numerical model of a
compressible flow, the pressure work and kinetic energy as well as diffusion at

inlets is automatically accounted for.

136

Table V1.1: Comparison of numerical results between the three models.

 

 

Model 1 Model 2 Model 3
pm... [bar] 4.56 4.61 4.56
T..... [K] . 1680 1630 1620
q,,,,-d[W/m2] 0 -1-106 -1.66°106
q”... [W/mz] N/A N/A 1.66106
hm... [W/mz'K] 0 -1540 -11000
umax-nu1d [m/s] 291 283 288

 

137

Table V1.2: Comparison of contour plots between the three models: pressure,
temperature, velocity, heat flux and heat transfer coefficient.

 

Pressure [Pa] Temperature [K]

 

Model 1 Model 1

    

 

msmmmmlm-sm-osv mums mutuaexTo-aawamuu-cmw Imam
WIHND1WW_MI manufacturer-mummy
1

Model 2 Model 2

   

 

 

MD,“
FLLB'ISI (MO.WW _.\l~fl

“unwound-um
L nwflsum.omu-lq.-wu~n

[cameraman-maximum lino.“

 

Model 3

 

 

 

muuhnmmrimm mmm‘

, Mann‘s
FLLCN'I‘ m.O.MW.-cll—llfli

 

 

 

 

Positive Radial Velocity [m/s] Surface Heat Flux [W/mz]

 

Model 1 Model 1

 

 

mum cmrmwumtuwi 1mmw manna
maritime: rum-exam) rmsvmw.m¢fl~hm1

 

Model 2 Model 2

norm
mm
1M
Iran-a?
ash-or
7M
5M
3w
1.01
out-m

WMMVMW) (V-dflmm mm m Wiquwuflni‘fl) (HEM) ~D,“
mansion O‘M” nurse-m Mrsv(h.q.cnwao.- um;

   

 

Model 3 Model 3

      

moth-mmmflh-um not ms 1 mm.”
Wstmo.mumba.-,m l Marianna: who—.11")

 

 

 

139

 

Surface Heat Transfer Coefficient [W/K-mz]

 

Model 1

(mums-luminvstacw (we) [nu-aliens) my.“
Funds"): 0 maul-a mm)

 

 

Model 2

    

vernal:
Wala,a.w~h.haw—am

 

Model 3

mama-nummwzyn-umm mum
Wllmt,w—.-m

 

 

 

140

The results seem conform with the conclusions from extant literature on heat
transfer impact on shock tubes and Pulse Detonation engines (PDE). Studying
the behavior of PDE and Pulse Detonation Tubes (PDT), the research group at
Stanford University led by Dr. Hanson, proved that heat transfer plays an
important role during the blowdown of a PDT (Barbour, Hanson et al. 2005;
Radulescu and Hanson 2005). But, in their studies, the friction effect was not
considered having a separate influence on the behavior of the flow, instead they
incorporated the effect of friction into the heat transfer, based on the Reynolds

analogy.

The heat transfer coefficient Ch has the form

= C, p cp|u — uw|
2

 

Ch (VII.12)

where C, is the friction coefficient, 0 is the flow velocity and u.., is the wall
velocity (u.., = Q.
The heat transfer mechanism that influences the flow field in a PDE is mainly

convective. The heat loss rate per unit mass is modeled following the equation:

2
q=§115 (T.. ‘T°)=}€h5 [T.. _[1_—7;—1‘C’—2]T] (VII.13)

Their result is similar with one obtained 30 years earlier when studying the
influence of the wall heat transfer on detonation waves by Edwards, Brown and
others in the United Kingdom. When analyzing the expansion waves, it was
assumed that the Reynolds analogy holds between friction force and convective
heat transfer, so that both effects can be accounted for by means of a single

141

friction coefficient, C} (Edwards, Brown et al. 1970). The conclusion is that the

rate of heat transfer falls linear with pressure, which requires 4(1‘) to vary

linearly with flow velocity and thus initial density. It was concluded that

a = 75.54.45 .10-2 (VII.14)
where 5! is the Stanton number.
. h 06/5 -2
Thus, q = Ema-4.46 ' 10 (VILIS)

Again, it was proven that the convective term is the one that influences the heat
transfer from the fluid to the walls of a shock tube.

This was the conclusion of the research group at NASA investigating the wave
rotors and the gasdynamic process inside the rotor cells (Paxson and Wilson
1993). Moreover, Dr. Wilson stated that the heat losses are very low and could
be incorporated in the friction losses, since both depend on the same parameter,

the friction coefficient (Wilson 1998).

Conclusions

Pressure, temperature, and velocity are the parameters mat characterize an
unsteady compression process. When comparing their distributions between the
three models, small variations can be noticed. The maximum pressure difference
between models is 1%, temperature - 3.5%, velocity — 2.7%. As expected, the
maximum temperature and maximum velocity of the flow was reduced when

heat transfer was included in the model.

142

The heat flux values are similar between model 2 and 3, but the surface heat
coefficient is much higher when calculated automatically by FLUENT. The
maximum heat transfer coefficient is 11 kW/m2 'K, which is below the values
documented previously.

The heat transfer process was implemented successfully to the numerical model
by two methods. The pressure and temperature distributions were compared
with the original (no heat transfer) model and differences in results were
computed from 1% to 3.5%. The distribution of parameters was unchanged
when heat transfer was included.

Section VII.5 contains CFD simulations of more detailed models of radial wave
rotors. It will be shown that convective heat transfer plays a more important role
in influencing the flow field inside the rotor cells than conductive heat transfer by

analyzing the Nusselt number.

143

v1.4 Axial UpWR

There are two possible configurations of the axial wave rotor: through-flow and
reverse—flow. Based on data available from the MIT Micro Gas Turbine Project
(Kang 2001; Epstein 2004; Frechette, Jacobson et al. 2005) initial
thermodynamic calculations were performed to find the optimum design point. A
detailed description of these calculations was presented in section III.5.

Two sets of data were extracted from the design space of ultra-micro wave
rotors. The first set was determined by enforcing the continuity equation. Port
dimensioning was based on time calculations and a set tangential speed of
183m/s. The second set of thermodynamic parameters was based on
maintaining the essence of wave rotor engine, thus supplying exhaust gas to the

turbine with higher pressure than fresh air coming from the compressor.

Table V1.3: Thermodynamic parameters of the ultra-micro wave rotor - set one.

 

Pressure [bar] Temperature [K]

 

Low Pressure Air (LPA) 1.96 435
High Pressure Air (HPA) 3.93 542
Low Pressure Gas (LPG) 1.62 1500
High Pressure Gas (HPG) 3.53 1589

 

144

Table V1.4: Thermodynamic parameters of me ultra-micro wave rotor - set two.

 

Pressure [bar] Temperature [K]

 

Low Pressure Air (LPA) 1.965 435
High Pressure Air (HPA) 3.93 542
Low Pressure Gas (LPG) 2.72 1500
High Pressure Gas (HPG) 3.53 1589

 

Table V1.5: General thermodynamic parameters of the ultra-micro wave rotor.

 

Wave Rotor Pressure Ratio 17m 2
Ambient Temperature 7'0 293K
Specific Heat for Air Cpai, 1.005 kJ/Kg'K
Polytropic Coefficient for Air 73,-, 1.4
Efficiency of Combustion mm 80%

 

Using the 1D code for the one channel described above, and having the overall
geometric dimensions of the wave rotor from the design in Figure II.1, a porting
solution was found for the axial wave rotor. The next table presents this set of

data.

Table VI.6: Details of the full model.

 

Length of channels 1mm
Radius of the rotor 5mm
Number of cells (channels) 240

Cell width 130um
Rotational speed 350,000RPM
Tangential velocity 183m/s

 

145

 

Port openings Degree Circ. Length [mm] Time [s]

 

HPG open 0.00 0.000 0.00E-06
HPG close 6.87 0.600 3.28E-06
HPA open 3.83 0.335 1.83E-06
HPA close 9.08 0.792 4.33E-06
LPA open 12.98 1.133 6.19E-06
LPA close 23.33 2.037 1.11E-05
LPG open 9.93 0.867 4.74E-06
LPG close 18.74 1.636 8.94E-06

 

The full model had a 12 cycles per revolution (Figure VI.11-a) configuration; but
due to enormous computational volume, a reduced model was later created. The
reduced model had a one cycle per revolution configuration and kept the same
dimensions of the channel, the same tangential speed and same boundary
conditions (Figure VI.11-b). The data for the reduced model are presented in the

following table.

Table V1.7: Details of the reduced model.

 

Length of channels 1mm
Radius of the rotor 0.42mm
Number of cells (channels) 20

Cell width 130pm
Rotational speed 4,200,000RPM
Tangential velocity 183m/s

 

146

 

Port openings Degree Circ. Length [mm] Time [s]

 

HPG open 0 0.000 0.00E-06
HPG close 81.88 0.600 3.28E-06
HPA open 45.68 0.335 1.83E-06
HPA close 108.09 0.792 4.33E-06
LPA open 154.53 1.133 6.19E-06
LPA close 277.85 2.037 1.11E-05
LPG open 118.33 0.867 4.74E-06
LPG close 223.18 1.636 8.94E-06

 

 

a) b)

Figure II.11: 3D model of axial wave rotor: a) full model with 12 cycles per
revolution, b) reduced model with 1 cycle per revolution.

The gap between the rotating drum and the end plates that house the ports is
essential. A study on the influence of this gap prove that for both 211m and 200m

the pressure rise has comparable values (Figure II.1) and the wave pattern is

147

almost the same. For future investigations a 200m clearance will be used. The
gap has both a physical and a computational effect. The 2pm gap would be
extremely difficult to obtain with today’s microfabrication possibilities. Also, from
the computational one point of view such a gap would be difficult to obtain, since
the mesh in the gap has to have a certain length/width ratio, which affects the

rest of the meshes in the model. A too coarse mesh in the gap will result in

inaccurate results; a too fine mesh will result in huge computational time.

 

Figure VI.12: Pressure distribution for a single channel mode: a) 211m gap, b)
20pm gap.

Through F/owAQe verse How
Both CFD models (TF & RF) predict the wave pattern desired, the pattern decided
for the porting sd'teme by the 1D in-house code. It appears though, that the HPA
port is opening too soon, meaning that the speed of the rotor is too high. In Frgure
V1.13 it can be seen the expected pressure wave pattern with two shock and an
expansion wave for the high pressure part and one shock and one expansion for the

low pressure part, very close to the theoretical prediction displayed on the right

148

side. The contour plots are very similar with the ones in Figures V4 and V6, Whid’l
were results of the 10 code. The temperature distribution (Figure V1.14) shows that
the shock heats up the fresh air but a lot less than the temperature of the hot
gases, which are around 1500K. The advantage of the RF wave rotor is that hot
gases exit on the same side as they enter, thus scavenging all the hot temperature

fluid and keeping the rotor cooled.

LPA

HPG

   

149

 

Figure V1.13: Pressure distribution for ZD simulation of axial wave rotor:
a) TF model, b) RF model, [Pa].

 

a) b)

Figure V1.14: Temperature distribution for 20 simulation of axial wave rotor:
a) TF model, b) RF model, [K].

150

air temperature
increase by shock

 

Figure V1.15: Low temperature distribution.

Figure V1.15 is a zoom-in from Figure V1.14, having the maximum temperature
value limited to 1000K (red color). The flow temperature is increased by the
shock wave; this phenomenon being clearly observed in the figure. Thus,
disregarding the high temperature of the exhaust gas, the shock trajectory can
be traced on the temperature contour plot.

The velocity distribution in Figure V1.16-a demonstrates that this is a truly TF
wave rotor, having all the inflows and outflows in the same direction. The
Figures V1.16 b and c, presenting a RF wave rotor displays a correct direction of
the flow through the ports, with a positive direction on the high pressure part
and negative on the low pressure part. Some oscillations in the flow direction are
noticed when channels are closed, but their magnitude indicate that they do not

influence the flow on the ends of the channels.

151

 

b) C)

Figure V1.16: Velocity distribution in an axial wave rotor: a) TF - positive
direction flow, a) RF — negative direction flow, c) RF — positive direction flow,
[m/s].

The Reynolds number is below 400 in all the channels and at all times, as shown
in the snap-shot presented in Figure V1.17. Based on previous research, stating
that laminar flow in microchannels is characterized by Re below 1500 — 2000
(Choi, Barron et al. 1991; Hao, He et al. 2005), the flow in the wave rotor

channels is well into the laminar region. This result enforces the accuracy of the
152

CFD model, by reducing the number of inaccuracies in the fluid dynamics

equations.

 

Through-flow Reverse-flow

 

Figure VI.17: Reynolds number distribution for axial wave rotor.

Figure V1.18 presents the flow Mach number. It can be seen that the maximum
value for the axial wave rotor, inside the channel, for both through-flow and
reverse-flow configurations is 0.8. That means the shock Mach number reaches

1.59, thus the shock travels at supersonic speed.

153

in”.
ii .
9

      

230e-O1 Through-flow Reverse-flow

Figure V1.18: Flow Mach number distribution for axial wave rotor.

Results of 3D investigation of die reduced model show that a higher rotational
speed is needed, the shock wave reaching the end of the channel short of the

high pressure exhaust port (Figure V1.19).

154

3.16:005
3.0%.!)5

   

- Y
1.0511005 &
z

holiles oi Stiit: Inseam [pascal] [I’ime=7.56001:-06] Oct 07. ”04
EU!” 6.1(36. fl. coqled by. Ian. linearly]

 

 

Figure V1.19: Pressure distribution in the channels of the 3D reduced axial wave
rotor model.

155

V1.5 Radial UpWR

As described in section 11.2 a new geometry has been envisioned for the wave
rotor — the radial wave rotor (wave disc). For wave discs, centrifugal acceleration
acting on the fluid in the channels and increasing with radius needs to be
considered in governing equations additionally. In a proper port configuration the
presence of centrifugal forces can improve the scavenging process, which is a
typical challenge in wave rotor design and Operation. In the radial configuration,
depending on the application, the wave rotor can be designed with several cycles
per revolution. The overall dimensions and the mass flow rate, as well as the
wave pattern will determine the width of the ports. Increase of wave disc
rotational speed increases centrifugal forces and reduces the number of ports,
which can be located in a disc of the same diameter. Hence, for higher speed,
instead of several port sets and two cycles per revolution only one port set and
one cycle per revolution could be used.

There exist four configurations in each the wave disc ports can be positioned: (1)
a through-flow wave rotor with fluids traveling from inside to outside radius, (2)
a through-flow with flow coming from outside to inside, (3) a reverse-flow with
gas ports located on the inner radius, and (4) a reverse-flow with air ports
located on the outer radius.

In this study only three models were created and analyzed (models 1, 3, and 4)

since model 2 presents no apparent advantage.

156

VI.5.1 Through-Flow Rglial Wave Rotor

A single cycle was studied in the beginning to build confidence in the model. At
the same time, the single cycle model was used to establish the final
configuration of the porting scheme. Starting with the port configuration given by
the 1D gasdynamic model, the Gambit model was created and analyzed into
Fluent — first iteration. Only some of the channels are used to reduce calculation
time, thus allowing for simple tests of compression and expansion processes with
a much finer grid. This method is used to find a rotational speed at which the
compression and expansion process is better tuned with the port opening and
closing fixed in this study.

Figure V1.20 shows the porting solution as well as the flows (air and gas)

trajectories.

LPG

* HPA

 

Figure V1.20: Through-flow wave disc — porting schematic.

157

Figure V1.21 presents the static pressure distribution for the first iteration. As it
can be seen from the tentative pressure wave trajectories, the port timing needs
some modifications, since neither the first expansion wave on the high pressure
part, nor the pressure waves in the low pressure part do not meet the ports at
their proper times. This effect can be also observed in the radial velocity contour
plots shown in Figure V1.22, where there is some outflow in the LPA port, instead

of inflow.

pressure wave

 

High Prssure Part Low Mame Part

Figure V1.21: Pressure distribution for the through-flow configuration (first
iteration), [Pa].

158

 

Figure V1.22: Radial velocity distribution for the through-flow configuration (first
iteration), [m/s].

The second iteration incorporates all the above mentioned changes to the

following model (Figure V1.23).

   

First model Second model
Figure V1.23: Comparison between initial and updated models.
Figure V1.24 presents the pressure distribution for the high and low pressure

parts of the wave rotor. Both pictures show the same results, but the scale of

159

pressure values is different in each plot to visualize pressure trajectories in each
part more accurately. The picture on the left shows the full pressure spectrum,
while the one on the right shows the pressure values characteristic of the high
pressure part. It can be seen that the behavior of the flow is as expected.
Primary shock generated by the opening of the HPG port arrives at the outer
radius at the moment when the HPA port opens. It reflects off the end wall as a
secondary shock wave. An expansion wave generated by closing of the HPG port
travels to the point of closing the HPA port. In the low pressure part, the results
reveal small design offsets. An expansion wave is generated by closing of the
LPG port, while a shock wave is produced by the closing of the LPA port. The
second wave appears to be advanced by one channel width and reached the LPG

port earlier than expected.

 

Figure V1.24: Through-flow wave disc— static pressure distribution, [Pa], left: full
pressure spectrum, right: pressure values form 2510 5 to 3.9310 5 Pa.

Figure V1.25 shows the temperature distribution revealing the penetration of hot
gases towards the end of the channel. Centrifugal forces assist driving the gases
from the inner ports towards the outer side. The gas penetration length is

160

increased by boosting the pressure of the high-pressure part (or lowering the
pressure of the low-pressure part) and increasing the number of port sets

(cycles) as shown in the next figure.

 

Figure 11.25: Through-flow wave disc — static temperature distribution, [K].

To simulate the wave rotor internal gasdynamic process through several cycles, a
four cycle per revolution model was created. As seen in Figure 11.1-a, the
temperature distribution shows that after several cycles, the hot gases travel the
channel length and exit at the outer ports. In addition, the average temperature
of the fluid in the hot zone of the channels reduces from about 1300K to 1000K.
The hot gas penetration is even deeper if the port pressures are changed and
the shock strength is increased. Figure II.1-b simulates such a situation where

corresponding port pressures are listed in Table 11.1.

161

   

a) b)

Figure V1.26: Through-flow wave disc — static temperature distribution, [K]
a) lower port pressures, b) boosted port pressures.

Table V1.8: Wave rotor operating conditions adjusted for higher pressures in
the high-pressure region and lower pressures for the low-pressure region.

Pressure [bar] Temperature [K]

 

Low Pressure Air (LPA) 1.50 435

High Pressure Air (HPA) 4.50 542

Low Pressure Gas (LPG) 1.62 1500
High Pressure Gas (HPG) 4.00 1589

 

The radial velocity vectors presented in Figure V1.27 represent well the
characteristics of radial-flow wave rotors. As expected for the through-flow
configuration, the flows are directed from the inner ports toward outer ports.
They are also indicators of some offset port timing, for instance the part of the
outflow at the HPA port (lower right corner) tends to return to the channels. This

shows that the width of the HPA is designed greater than the optimized value.

162

 

1 .67e+02
1 .30e+02
921 e+01

 

 

 

Figure 11.27: Through-flow wave disc - velocity vectors distribution, [m/s].

Although the second model delivers improved results in terms of pressure waves
and port timing, as well as inflows and outflows, the problem of resultant velocities
of the outflow and inflow has remained. The flow has both a radial component due
to flow traveling along the channel, but also a tangential component due to the
rotation of the disc (Figure 11.27). The third iteration works on improving the
shape of the ports. Figure 11.3 highlights the port shape changes as well as an

improvement in the flow through the ports.

163

 

Figure V1.28: Radial velocity distribution for the through-flow configuration (third
iteration), [m/s].

Overall, the influence of the centrifugal force is best seen when comparing the
axial wave rotor with the radial one after one cycle, the models having identical
initial and boundary conditions. Figure V1.29 shows the difference in hot gas
penetration along the channel. It can be seen that flow with temperature of
1300K goes almost all the way to the right side wall in the case of the wave disc,

while for the axial wave rotor it travels only three quarters of the way.

164

       

Radial mnfiguration Axial configuraion

Figure V1.29: Comparison of radial and axial flow wave rotors — static
temperature distribution, [K].

As proven in section VII.3, the heat transfer between adjacent cells is not
influencing significantly the energy exchange process inside the wave rotor.
Next, the influence of other components of the ultra-micro gas turbine was
investigated. Heat transfer coming from the combustion chamber located below
the wave disc, or the turbine located in the lower interior of the wave disc is
studied. For this, constant temperature boundary conditions have been set: in
the first case, the walls between the cells were considered having a constant
2000K temperature; in the second case, the interior wall between the ports was
assigned the same boundary condition (Figure V1.30). Results have shown that
in the first case, the overall temperature of the fluid inside the channels has
increased (Figure V1.31), but that did not affect the overall pressure distribution

(Figure V1.32).

165

11...] /

 

HT—case1 HT-case2

Figure V1.30: Temperature boundary conditions for the external heat transfer
investigations, [K].

no external heat transfer HT — case 1 HT - case 2

   

Figure V1.31: Comparison of temperature distributions without and with external
heat transfer, [K].

166

 

no external heat transfer HT — case 1 HT — case 2

Figure V1.32: Comparison of pressure distributions without and with external
heat transfer, [Pa].

When examining the Nusselt number distribution along the cells’ walls, Figure
V1.33, it can be noticed that the values are going up to several thousands.
Considering the definition of Nusselt number (Eq. VII.10), the conclusion is that
the convective heat transfer is much higher than the conductive one. So heat will
be transferred from the walls (the heat source in case 2) to the fluid, but not
from one cell to the other through the walls. Flow in one channel does not

influence the flow in the adjacent channels through the walls.

167

      
 

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Figure V1.33: Comparison of Nusselt number distributions along the rotor walls
without and with external heat transfer.

Entry Lengths and Boundary Layers

Important factors in the fluid flow behavior and heat transfer to and from the
walls are the flow and thermal entry lengths, as well as velocity and thermal
boundary layers thicknesses. Figure V1.34, below, describes schematically the
flow at the entrance to the channels, showing the entry lengths and boundary

layers.

168

 

 

 

 

 

 

 

 

: ‘—e—-
um:
Z: Free Stream
}“ E: """"""""""""""""""" i ‘ ' ‘ ‘ 1.; “““ U; “““
no _, .~ ——-—>
_. O10‘)
l—p
:: 000
:: 51 a TM : . ury) ';
LT T=TW u=0
LE
Y
I 3 Velocity Boundary Layer
I a Thermal Boundary Layer x

Figure V1.34: Schematic of flow entry into a channel.

It is known from preliminary investigations that the flow has a highly laminar
aspect (Re<1000), thus the calculation of the flow (velocity) entry length can be
performed using Eq. VII.16 (Sabersky, Acosta et al. 1998)

£35 z 0.06 Re (VII.16)

Assuming that Re varies from 100 to 1000 along the channel length, and
knowing that the average diameter is 300nm, it results in an average entry
length L; = 9mm. The minimum and maximum entry lengths are 1.8mm and
18mm respectively. The conclusion is that the flow has not reached the fully

developed state while passing through the wave rotor channels.

169

A similar formula can be found for calculating the thermal entry length

(Incropera and DeWitt 1990)

 

507— z 0.05 Re Pr (VII.17)
Knowing that
Nu
r = VII.18
Re St ( )

it shows that the Prandtl number varies from 0 to 101.84 across the thermal
boundary layer. Thus, the thermal entry length varies from 0 to 750mm.

As expected for such small channel diameters and high temperatures, the entire
flow is placed in the combined entry lengths region. A pressure drop in
developing regions exceeds its value in the fully developed region because it
must overcome the wall shear and increase in flow momentum. Similarly, the
heat transfer has increased values, but not high enough to influence the flow
behavior.

When investigating the boundary layers thicknesses, the Euler equations lead to

specific solutions for the case studied. The thermal boundary layer thickness is

aX

 

6,(x) = 3.6 (V1119)

Q

where x is the coordinate along the channel (see Figure V1.34) and Um is the
velocity of the free stream.
The Reynolds analogy between the flow field and the thermal field along the

wave rotor channel lengdi is used. Introducing the assumption of large Prandtl

170

number (Pr>5), it results the following relation between the velocity and thermal

boundary layer thickness:
é; = 0.975 tip—r (V1120)

Using Eqs. VII.19 and VII.20 the two boundary layers thickness can be
computed: are 53pm and 6:: 15pm. Although these values are not identical with
the one provided by the CFD code (are 75pm and 6e 48pm) it has been shown
that the range of values are similar. The discrepancies in results come from the .
many approximations and averaging of the non-dimensional parameters used in

the theoretical formulas.

V1.5.2 Reverse-Flofladial Wave Rotor

In this section, two different reverse-flow models are studied to highlight the
differences between such configurations. Results of such a comparison can be
used to evaluate the advantageous and disadvantageous of each design for a
specific application. Figure V1.35 shows the flow trajectories for the air and
exhaust gases of each case. The same procedure was applied for the reverse-
flow configuration as for the through-flow. Initially a single cycle was studied
until the best porting solution was found, then alter the CFD iterations, the full

model with four-cycle per revolution was investigated.

171

 

Reverse Flow Gas Inside Reverse Flow Air Inside

Figure V1.35: Reverse-flow wave disc — possible port arrangements.

The pressure distribution of the two models, displayed in Figure V1.36, are
similar in the high-pressure part (bottom part of the figures), considering the
direction of the flow. Some discrepancies exist due to the influence of the
centrifugal forces for different flow directions. On the low-pressure part (top
part), a better stratification of the flow can be seen for the air inside model. The
wave patterns are in agreement with the wave rotor gasdynamic theory and they

clearly show the effects of compression and expansion waves.

172

   

I "900‘

Reverse Flow Gas Inside Reverse Flow Air Inside

 

Figure V1.36: Reverse-flow wave disc — static pressure distribution, [Pa].

The temperature distributions shown in Figure V1.37 show that the air inside
model has a better hot flow scavenging feature due to the positive influence of
the centrifugal forces. For bod) models, most of the hot gases are exhausted

through the LPG ports.

HPG

   

Reverse Flow Gas Inside Reverse Flow Air Inside
Figure V1.37: Reverse-flow wave disc - static temperature distribution, [K].

The ideal gas flow assumption allows for considering density as directly

proportional with pressure at constant temperatures regions. Thus, by studying
173

the density plots for the two models shown in Figure V1.38, it can be seen that a
larger amount of high pressurized air is extracted by the HPA port on the gas
inside model, rather than air inside model. The results clearly indicate that the

configuration with inner air ports has a better scavenging feature.

 

Reverse Flow Gas Inside Reverse Flow Air Inside

Figure V1.38: Reverse-flow wave disc — density distribution, [kg/m3].

Figure V1.39 shows the radial velocity distributions (inward and outward). The
flow patterns are consistent with the predictions for reverse-flow configurations.
By studying the velocity contour plots, one can see that further improvements
can be done in the geometry of the ports for better flow guidance and avoiding
backflows or undesired flow direction. For example, in the configuration with gas
inside (figures on the left), the HPA port has a zone where the air flows into the
channels which is not desired. The ports should be adjusted to account for
tangential component of flow velocity, by inclining the walls with respect to the
channels. Some small backflows can be seen in the LPG port of the rotor with

inside air configuration.

174

. 1g i g

E

poslflv

Persimmm—
" 1v 111-11' .

 

Reverse Flow Gas Inside Reverse Flow Air Inside

Figure V1.39 Reverse-flow wave disc — radial velocity distribution, [m/s].

Figures V1.40, indicating the temperature distributions in the reverse-flow wave
disc with inner air ports, compares the model with one set of ports with a full
model with four cycles per revolution. Alternatively, Figure V1.41 makes a similar
comparison for the reverse-flow wave disc with inner gas ports. The port timing,
rotor geometry, and the operating conditions are the same in both full models.
In Figure V1.40, the gas penetration reduces alter several revolutions while it

increases for the reverse-flow configuration with the gas ports on the inner

175

radius shown in Figure V1.41. Therefore, the channel wall mean temperature is
less for the reverse-flow wave disc with the inner air ports. It is seen that the
burned gas almost leaves the channel at the end of each cycle. Residual gases of
the reverse-flow wave disc with inner gas ports keep the wall temperature at a
high temperature during the wave rotor operation, causing a high rate of heat

transfer and non-uniform temperature distribution along the rotor channels.

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Figure V1.40: Reverse-flow wave disc with air ports on inner diameter —
temperature distribution, [K]: a) results after first cycle, b) results after several
cycles.

176

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Figure V1.41: Reverse-flow wave disc with gas ports on inner diameter -
temperature distribution, [K]: a) results after first cycle, b) results after several
cycles.

Figure V1.42 presents the static pressure distribution, and it can be clearly seen
that the updated geometry provides an accurate wave pattern for both reverse-
flow configurations. Also the velocity distribution (Figure V1.43) shows the
appropriate directions of the flow through each port, red arrows indicate the

active ports.

177

 

Figure V1.42: Reverse-flow wave disc - static pressure distribution: left — air ports
located on inner diameter, right — gas ports located on inner diameter, [Pa].

 

Figure V1.43: Reverse-flow wave disc — static pressure distribution: left - air ports
located on inner diameter, right — gas ports located on inner diameter, [Pa].

178

The port inclined solution delivers more accurate results and better conclusions
can be formulated. The Mach number is higher for the configuration with air
ports located on the inner diameter, showing that pressure waves travel faster
and thus improving the flow and energy exchange in the low pressure part. For
the high pressure part, the values are comparable for both configurations (Figure
V1.44).

The Reynolds number distribution (Figure V1.45) shows similar values for both
cases, with a maximum around 1300 inside the channels. This will place the flow

in the wave rotor cells well inside the laminar region.

 

Figure V1.44: Reverse-flow wave disc — Mach number distribution: left — air
ports located on inner diameter, right — gas ports located on inner diameter.

179

 

Figure V1.45: Reverse-flow wave disc — Reynolds number distribution: left - air
ports located on inner diameter, right — gas ports located on inner diameter.

As for the through—flow configuration, the reverse-flow was investigated with a
new set of given parameters, in which the pressure of the LPG port is higher
than the one of the LPA port. This is a true wave rotor configuration in which the
pressure exchanger actually tops the baseline cycle. Based on a new design
cycle, a new geometry was created for a model of reverse-flow wave rotor with
air ports on the inside of the rotor. The values of pressure and temperature in

the ports are presented next:

Table V1.9: Wave rotor operating conditions adjusted for higher pressures in
the high-pressure region and lower pressures for the low-pressure region.

Pressure [bar] Temperature [K]

 

 

Low Pressure Air (LPA) 1.94 443
High Pressure Air (HPA) 3.88 582
Low Pressure Gas (LPG) 2.11 1500
High Pressure Gas (HPG) 3.10 1616

 

180

The results are presented side by side with the one from the original RFAI
model. In Figure V1.46 the pressure dishibution is presented for the two models.
First observation is that the new model is not optimized in terms of port timing.
If for the original design (on the left) the pressure waves’ trajectories are clearly

defined, the same thing cannot be said about the new design.

   

original design Reverse Flow Air Inside new design
Figure V1.46: Static pressure distribution for the RFAI models, [Pa].

The low pressure part shows a slightly higher pressure in the LPG port compared
to the LPA port, the opposite being valid for the original model.

Figure V1.47 shows the temperature distribution over more than four cycles of
operation. In terms of absolute values, the two models are comparable, both
having the top temperature of about 1700K. When studying the distribution, it
can be noticed that the new model has more hot gas penetration into the
channels and also, it utilizes the whole length of the LPG port to scavenge the
hot gas. This difference it attributed to the lack of geometry optimization in the

case of the new design.

181

 

original design Reverse Flow Air Inside new design

Frgure V1.47: Static temperature distribution for the RFAI models, [K].

But when studying the Mach number distribution (Figure V1.48), a 20% decrease
in the Mach number of the flow is observed for the new design model. That
means the flow velocities are smaller through the channels (considering almost
matching temperatures distribution), which in turn deliver slower flow to the
ports and other components. One can conclude that the process will be less
efficient, but complete efficiency evaluations could not be performed without

investigations of the full thermodynamic system.

182

 

original design Reverse Flow Air Inside new design

Figure V1.48: Mach number distribution for the RFAI models.

V1.5.3 Comparison of Radial Configurations

To better study the performance of the wave rotor and to compare the three
radial configurations (through-flow, reverse-flow with air ports at the inner part,
and reverse-flow with gas ports at the inner part), a series of graphs
representing pressure, temperature, and Mach number along the inner and outer
circumference of the disc have been extracted.

The values at the middle of each channel opening have been plotted against the
angle of the channel.

Figure V1.49 presents the pressure distributions along the inner and outer
circumference for the three configurations. It can be easily noticed that the
distribution is periodic over the four cycles. Thus, for clarity purpose, the
following results will present only one cycle (0 to 90 degrees), like in Figure

VI.50.

183

 

 

multiple
cycles

 

 

Figure V1.49: Pressure diagram for inner and outer circumference for the three
configurations, [Pa].

In Figure V1.50, it is noticed mat the pressure distribution is divided into a high
and a low pressure part. To compare more effectively the three configurations,
the pressure, temperature, and Mach number distributions were compared based
on the location of the ports. Although the ports do not have the same length and
location for all configurations, each graph was translated and scaled to the same
length that is why there is no variable associated with the abscissa. The ordinate

values of pressure, temperature, and Mach number are the exact values.

184

 

4.50E+06-» 4“ » —. — ._- .4

4.00E+05 -

 

 

 

3.50905

 

 

 

 

    
 

 

 

 

w-ijFGLout

 

 

 

 

 

 

 

2.00E+05 A
l
l

””5 w v \N = -
l
l

1 .00E+05 r l

0 10 20 30 4O 50 60 70 80 90

Figure 1.10: Pressure diagram for inner and outer circumference displayed for
one cycle only, [Pa].

Figure 1.2 presents both gas ports for each configuration. The first conclusion
that can be stated, is that the pressure in the HPG port for the RFAI
configuration is the highest (Figure 1.2-a) due to the centrifugal force that
compresses the gas as it enters the channel. Studying this effect, it is expected
that the Mach number should be the lowest for this configuration at the HPG
port.

On the low pressure side, it can be seen that the pressure drop is stopped by the
opening of the LPA port, soon after the opening of the LPG (Figure 1.2—b). The
RFGI configuration shows almost constant pressure distribution, the pressure

drop being attenuated by the centrifugal forces effect.

185

RFGI configuration shows almost constant pressure distribution, the pressure

drop being attenuated by the centrifugal forces effect.

4.50805 ‘ Reverse-Flow Revenge-Flo;
Inside

    

4.00905 '_

3.50E+05

 

3.00E*05 Mach!

 

0.500

pnaauro

2.501905 ' 0,400 J .

0.300

 

2.00E+05
0.200 4

1.50E+05

 

0.1001

 

 

 

 

 

 

0.000

 

1.00E +05

Figure V1.51: Pressure diagram for high and low pressure gas for the three
configurations, [Pa].

On the air side (Figure V1.52) the HPA distribution is almost identical for all the
configurations. That is an indication that pressure at these ports is not affected
by the centrifugal effects, but the flow rate is. Studying the Mach number for the
same port, it is noticed that RFGI shows the highest Mach number. Taking into
consideration the fact the RFGI configuration has the lowest temperature (Figure

V1.55-a), it results that it generates the highest flow rate for HPA.

186

 

4.00905

 

 

 

 

 

 

 

 

TF
RFGI out Run"
3.00605
2 -
=
O
I
2 250905
a.

 

Machfl
RFAlln
2005105 7 -1 0500 RFGIout [

‘
1.50905 0300 RPM in

0.200
Figure V1.52: Pressure diagram for high and low pressure air for the three
configurations, [Pa].

 

 

1<

 

 

 

 

!

 

 

 

 

 

 

 

1.00E't05

 

 

 

The pressure in the through-flow configuration for the LPA port has a lowest
value (Figure V1.52-b) where the LPG port closes. An increase in pressure and a
decrease in Mach number accompanies the LPG closing (Figure V1.56).

The temperature distribution of air ports shows, as expected, the highest values
in the through-flow configuration (Figure V1.55), associated with the worst
scavenging of hot flow.

Figure V1.53 shows the distribution of the temperature in all cases for a complete

cycle. As for the pressure distribution in Figure V1.50, the temperature graphs

187

are divided into a high temperature part and a low temperature one. These parts

are consistent with the high and low pressure zones.

1800 1.11-.-.” ._. —-— ,-,,_..,_,... __. _..,_,-, -11..-. ‘ Reverse-How Ram" Zita”
g‘Alr Inside

 

 

 

 

 

 

 

 

 

Figure V1.53: Temperature diagram for inner and outer circumference displayed
for one cycle only, [K].

The HPG temperature has almost identical distributions for all cases, with a
slower temperature rise in the case of RFGI (Figure V1.54-a). The RFGI
scavenges the LPG at highest temperature (Figure V1.54-b), an effect that is

beneficial for the air, which is scavenged at lowest temperature (Figure V1.55).

188

1800 1800

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1700 1700
1600 --—-~ 1,- - 1600
1500 1 ~——————--——— 1500
i400 ‘ — T_TF_ln 1400
1300 é———~—~——— _ T-TF-m 1300
_‘ T .1...— 1_R1=A1_out
1200 » ~-——-—~ __ T_RFG|_h 1200
g 1100 F— 5 1100
E 1000 E 1000
.. 900 .. 900
800 1— HPG — 300
700 700
600 600
500 500
400 400
300 . 300
a) b)

Figure V1.54: Temperature diagram for high and low pressure gas for the three
configurations, [K].

189

Mach I

. ll . rse-El' .. ._ _.
Through-Flow Gas R
\

     
      

 

temperature

900

800

700

600

500

h.
400

 
  
   

300 V ' ' ' ' ’
Figure V1.55: Temperature diagram for high and low pressure air, [K].

 

_M_RFAl_ln
----MgRFA1_om
—M~RFGl_ln
"MM-RFGl_om

 

 

 

 

o 10 20 30 40 50 60 70 80 90
dogma

Figure V1.56: Mach number diagram for inner and outer circumference.

190

Chapter VII

FINAL DESIGN OF THE UuWAVE ROTOR

Although the UuWR was designed for integration with a microfabricated gas
turbine, it is not the purpose of this study to investigate the gas turbine. In the
final design of the wave rotor, the gas turbine is just introduced as a guideline
for wave rotor positioning and overall dimensioning. The dimensions of the ports
and ducts are exact dimensions obtained from the designing procedure of the
wave rotor, but their connection with the baseline turbomachinery is schematic.
Only some tentative calculations of flow rates have been performed to establish
the geometry of the ducts from compressor to wave rotor, and further away, to
the turbine.

Starting from the MIT H2 Demo engine, the ultra-micro wave rotor has been
designed, having the overall geometry adaptable to the baseline turbomachinery.
This section will present some 3D renderings of the most important components
of a wave rotor topped ultra-micro gas turbine. Although most of the
components are going to be etched away in silicon wafers, these drawings
present the negative part (mold) for clarity purposes.

First, the overall engine is presented in two isometric views and with the main
components labeled (Figure VII.1). The design presented has a through-flow
configuration, but similar designs can be constructed for reverse-flow

configurations.

191

Radial compressor
Radial wave rotor
LPA port
HPG port
Combustor
LPG port
HPA port
Radial turbine

   

Figure VII.1: Full assembly of the wave rotor topped ultra-micro gas turbine.

Figure VII.2 shows several cross-sectional views of the final design. In these
figures, the combustor, ports and ducts are shown as in the final product as
cavities, compared to the previous set of figures where they are shown as

negative.

192

 

Figure VII.2: Cross-sectional views of the UpGT unit.

Some details of each component are displayed in three pictures (grouped in the
Figure VII.3). The wave rotor is placed at the same level as the radial
compressor, surrounding it. From the compressor, ducts lead to the LPA ports of
the wave rotor and on the internal part HPG ports where combustion gases come
from the burner to the rotor. The combustion chamber has an annular shape and
is placed directly beneath the wave rotor. The channels for fuel intake as well as
the ignition system have not been included in this design. On the outer part of
the rotor, the HPA and LPG ports take the air to the combustor and pre-

expanded gases to the turbine, respectively. The turbine is placed at the interior

193

part, and its rotor is connected by a shaft to the rotor of the compressor (not

shown).

Radial compressor
Radial wave rotor

LPA port

LPG port

HPA port -- - g .
Radial turbine

Combustor

       

 

Figure V11.3: Partial assembly views of the UuGT, showing different components.

The last figure in this section (Figure VII.4) explains graphically the directions of
the two flows involved in the energy exchange process: the air and exhaust gas
flows. The directions of the flows have been schematically superimposed on the

top and bottom views of the UuGT.

194

 

Figure VII.4: Top and bottom view of the UpGT, showing also flow paths.

195

Chapter VIII

EXPERIMENTAL INVESTIGATIONS

VIII.1 Axial Ultra-Micro Wave Rotor

The rotor in the axial wave rotor configuration is a series of channels placed at
the periphery of a spinning cylinder or disc. The fabrication process of these
channels is vertical etching into a silicon wafer. Figure VIII.1 presents a

computer rendering of the wave rotor model.

 

Figure VIII.1: Axial ultra-micro wave rotor.

196

The top and side cross-sectional views are displayed in Figure VIII.2.

 

 

Figure VIII.2: Axial ultra-micro wave rotor: left - top view; right -— cross-section.

The microfabrication process uses standard techniques for developing micro-
electro-mechanical systems. It is a ten-step procedure using two
photolithographic masks, one SiOz etch step, and one deep reactive ion etching
step. A schematic illustration of the process flow is shown in Figure VIII.3,
below. The vertical scaling was highly exaggerated for clarity since the layers in

the figures vary from 111111 to 5000m.

197

 

 

  
    

Step 1. Chemical cleaned Si wafer.

 

 

 

  
 

.myig .._ _ -

smog. EtchtheSlOzlnRIEorBl-F

 

 

E

 

 

111111111 111101111111111—111111—1

 

 

. 21 s :5 it ’
512114 Exposemumgntposiuvenaskmuvrigm :5; 13 '5 §..
I I I I I . g 1:»; l“ '81 .
~ .~.-.v 1 0.; 5 Pg #9.: F;
[ J K in in
1141-. . .1 . 51:910. Fusionbondmvafersmgether.
I I I I

 

I I
Step5.DevdopPRaMbalretohardenlt.

_Sllloon - Oxide E Photoresist

Figure VIII.3: Schematic process flow for microfabrication of axial wave rotor.

The process starts with a clean silicon wafer, 500pm thick. On the wafer a 111m
silicon oxide is deposited in a furnace at 900-1200 C, that will help tailor the
DRIE step. Through a photolithography process the oxide layer is patterned,

following a ZSOum deep etching of silicon substrate (Ayon, Bayt et al. 2001). The

photolithography process uses a 100m photoresist (PR) layer that is patterned by

exposure to UV light though a positive mask. The mask (Figure VIII.4) is made
of glass, and the pattern is formed by impregnating a thin metal film on the glass

(Chromium or Gold). The photoresist is a polymer, whose chemical properties

198

change when exposed to radiation. The PR is commonly in a liquid phase that
can be spun onto the silicon oxide layer at speeds of thousands of RPM’s. The
spinning process creates a uniform film thickness. After the application, the PR is
baked at 90-100C to remove the solvents. Steps 1 to 9 target both faces of the
wafer. Once the etching is completed and the channels are etched all the way
dwrough, the layers of SiOz are stripped in a BHF solution. For wafer-through
etching, a quarlz wafer (called handling wafer) might need to be attached to the
working wafer to prevent the wafer-back cooling Helium from leaking into the
plasma chamber (Lin, Ghodssi et al. 1999). Two such wafers are prepared.
Before aligned fusion bonding (Ayon, Zhang et al. 2003; Miki, Zhang et al. 2003),

the two wafers are cleaned by ashing.

 

Figure VIII.4: Positive mask used in step 5 of axial wave rotor fabrication.

199

VIII.2 Radial Ultra-Micro Wave Rotor

In a similar fashion, the radial ultra-micro wave rotor will be fabricated. The main
difference lays in the fact that width/depth etch ratio is much higher for the
radial rotor, and DRIE process is no longer required. The channels are going to
be created by isotropic etching each half the width of the channels into a wafer
and bond the two wafers in the end. Figures VIII.5 and VIII.6: show computers

rendering of the rotor and two cross-sectional views (top and side).

 

Figure VIII.5: Radial ultra-micro wave rotor: a) 3D view; b) side view; c) top

view.

200

 

Cross-sectional View - side

 

Cross-sectional vlew — top

Figure VIII.6: Radial wave rotor: left - A-A cross-section (from Fig.5); right - B-B

cross-section.

The microfabrication process starts Wlfl‘l cutting the wafer out of the interior of
the rotor, using the Laser MicroJet® cutting technique developed by The Gem
City Engineering and Synova (Dushkina, Wagner et al.). For the radial wave rotor
250pm thick wafers are going to be used, and as the axial one, the rotor will be
made out of two wafers fusion bonded together. Steps 3 to 7 are similar with the
ones for the fabrication of axial wave rotor. The process is shown schematically

in Figure VIII.7.

 

 

 

i 1.2!:

1 .,*' , -; :-.,._.;- ‘11.: ‘ . . . . . - _ E 71 E
Step 1. Chemical cleaned Si wafer ' . 1

Step 7. Etch the SO, in RIE or BHF etchant

 

Step 2. Laser MlcroJetK'v cut

 

 

   

Step 3. Deposit of SiO2 by thermal oxidation

 

 

 

1 :1 1.: 1 :1

Step 4. Spin and bake Photoresist (PR)

11111111111111W11lllllllllt’.
[

1 1 j E7‘l’s"77§i3?'75'5f ”'71 [ 1 q

._. I Step 11. Fusuon bond two wafers together

 

Step 10. Etch the SiO2 in RIE or BHF etchant

 

 

Step 5. Expose PR thought positive mask to UV light

 

 

I‘ 1; -

. . 5 3.? ..1-1'5‘1Yx'r'fvg‘etr
Step 6. Develop PR and bake to harden it Step 12. Laser MicroJetG wt

Silicon - Oxide fr : Photoresist

Figure VIII.7: Process flow for radial ultra-micro wave rotor fabrication.

74—5111.
1
1
M

 

The etching of the channels is going to be an isotropic etch, thus creating
circular channels but with a larger cross-section on the outer diameter (Figure

VIII.8).

 

Figure VIII.8: Radial wave rotor with rounded cross-sectional channels.

202

The last step involves cutting the outer edge of the wafer, which has not been
etched, to reveal the outer opening of the channels. The mask used in step 5 is

presented in Figure VIII.9.

 

Figure V111.9: Positive mask used in step 5 of radial wave rotor fabrication.

VIII.2.1 Fabrication of the Radial Wave Rotor Test Rig

The process flow for microfabrication of the radial wave rotor test rig uses four
wafers and nine masks. The process follows the same procedure as described in
section IX.1 and IX.2, but here it applies to both the rotor and the plenums and
ports. The flow plenums are some cavities into which the fluid comes from
external sources, is collected and its pressure raised to specifications and then

directed to the wave rotor channels by means of porls.

203

Figure VIII.10 presents the exploded view of the rotor with the four etched
layers of the two wafers, while Figure VIII.11 presents a similar view of the static

part comprising plenums and ports.

Layer 2
Rotor Wafer 1

Layer1
Rotor Wafer 1

Layer 1
Rotor Wafer 2

15
i-——i

Layer 2
Rotor Wafer 2

 

Figure VIII.10: Wafers used for rotor fabrication.

204

 

.—

Layer 2
Plenum Wafer 1

Layer1
Plenum Wafer 1

Layer1
Plenum Wafer 2

Layer 2
Plenum Wafer 2

Layer 3
Plenum Wafer 2

Figure VIII.11: Wafers used for port; and plenums fabrication.

205

Figures VIII.12 and VIII.13 present cross-sectional views of these parts. It can
be seen that the rotor part is made out of 4 layers (each involving a different
etch step and utilizing a different mask), 2 for each 500mm wafer, while the
stationary part comprises 5 layers, 2 for the top wafer and 3 for the bottom
wafer. The masks have alignment marks on them, under the form of etched
rectangles, positive for one mask and negative for the other mask. The

alignment marks are displayed in Figure VIII.15.

Motor shalt
location

[um]

Snap-tabs

 

Wave rotor
channels

Figure VIII.12: Cut-view of the rotor wafers' assembly.

Plenums

and ports

   

luml

Pipes location

Figure VIII.13: Cut-view of the ports’ and plenums’ wafer assembly.

206

. m ‘ v
\\\\\\\\\\‘\\\\\\\\\\\\\\\\\\\\\\\‘
m

 

assembly

Figure VIII.14: Full wave rotor assembly.

 

0.5 mm

 

 

 

on DC] DE]
DE! an EU

Figure VIII.15: Alignment marks — example.

Annex 2 presents the dimensions of the design as well as the masks used for

each DRIE step.

207

VIII.3 Single Channel Experiment

A single channel experiment has been developed to investigate the wave
phenomenon inside a single wave rotor cell. The channel has a square cross-section
with a 360pm side length and 3mm length. To be able to obtain more information,
the channel was replicated at different scales on the same design matrix. Although
the depth of the channel was maintained at 360mm, the length and width was
varied to 90X75011m2, 180x1500pm2, 360x3000pm2, 7ZOXGOOOpm2.

The process flow used in microfabricatjng the single dwannel test rig is described in
Figure VIII.16. The process uses both a silicon and a glass wafer. Two glass masks
are created for the two etch steps. One step creates the channels, while the other
step creates the access holes for the tubing. The masks are shown in Figure VIII.17.

The glass wafer is bonded to the silicon wafer to close and insulate the dwannels.

 

E; ‘1‘ ' ’-" ““fi VA Steps7 11RepeatstepsZ-stocreatememellinsaccess
:141.’ 1 .. “ "*1 -~ holesontheback side

 

. - .11: 1",k,,)ll
Step 1. Chemical cleaned Si wafa

Step 2. Spin and bake Photoresist (PR)

1111111111 11111111111111111111111 1 --~~ £1

 

 

 

 

Step 12. Fusion bond the glass wafer on top of the silicon one
4 .

Step 3. Expose PR thought positive mask to UV light

 

 

 

 

 

 

 

Step 13. Attach the sminless steel tubing

 

kiszf-T‘TT‘TS’ZFL' if 1.: i V V. _ 1*" 7:? z: 3

Step 6. Stripthe PR

Figure VIII.16: Process flow for microfabrication of single channel test rig.

208

 

 

MASK 1
.. /_,/ channels

lenums
4/ p

’ / /aignment mar
/

 

 

 

 

3mm

 

 

 

MASK 2
“x? piping access holes

/”°‘:““7 alignment marks

 

 

 

O O

 

 

Figure VIII.17: Masks used for etching single channels.

209

Figure VIII.18 presents photos of the silicon/glass microfabricated dies. In the
Figure VIII.18-a) an array of dies is displayed. Figures VIII.18—b) and VIII.18—c)
present a single die - front side and back side. On the front side, the channels
and the flow plenums can be observed. The quality of the geometry resulted
from the microfabrication technique is impressive, allowing for clear view of the

smallest channel (90pm in width). On the back side, the access holes for the flow

pipes are precisely etched, and the alignment marks are also visible.

 

Figure VIII.18: Silicon microchannels: a) array of silicon dies; b) single die —
front view; c) single die- back view.

When examining the die under an optical microscope, it can be seen that the

geometry is accurate enough, errors varying from 1.3% to 95% (Figure VIII.19).

210

Part of this error is generated by the optical measurement of channels’ width.
Since the silicon is not transparent, reflection had to be used for visualizing the
die instead of transmittance, and the walls generated some light interference,
thus the walls looking blurry. Due to this an exact positioning of the side walls

was not possible.

 

Figure VIII.19: Different size channels visualized with optical microscope.

This effect becomes more evident when trying to visualize the smallest channel,
with a width of 90pm. On a 5x magnification it looks like the ends of the channel
are obstructed, but when magnifying to 20x, it can be seen that the light
reflected from the chamfered edges between plenum and channel creates the
distorted image (Figure VIII.20). The microscope used was an Olympus BH2
optical microscope equipped with a SPOT Camera (by Diagnostic Instruments

Inc.).

0.75 mm

 

5x magnification 20x magnification

Figure VIII.20: Light reflection interference when visualizing silicon channels with
optical microscope.

The next step was the Scanning Electron Microscope (SEM) imagining of the
microfabricated channels. In Figure VIII.21 the four channels are photographed.
With a small magnification factor the four channels appear to have very clean
and well-defined geometry. In Figure VIII.21—a) the smaller channels are

presented, while the larger ones are shown in Figure VIII.21—b).

   

b)

Figure VIII.21: Different size channels visualized with SEM: 3) 90pm and 180 pm
wide channels; b) 360 pm and 720 pm wide channels.

212

Going to a higher magnification, the details of manufacturing can be observed.
In Figure VIII.22-a) and c) it can be observed that the walls are not smooth, but
wrinkles in the axis of the channel. This characteristic might affect the boundary
layer of the flow through the channels, although the wrinkles are a few microns
in height. In Figure VIII.22—b) a different aspect is noticed, that the walls are
underetched. The lateral walls are deviated from the vertical with approximately
20pm on the bottom (ie. an angle of 3 degrees), thus transforming the cross-
sectional shape of the channels from rectangular to trapezoidal. Although this
will not affect the microchannel measurements or the wave rotor performance,

this aspects plays an important role for some of the turbomachinery components.

 

Figure VIII.22: Details of microfabrication of me silicon channel.

213

The great achievement of this fabrication process is the quality of the bonded
structure. In Figure VIII.23, the bond between silicon and glass wafers is

highlighted and it can be noticed that the bond is almost indistinguishable.

  

1'“: “.7” ,31?‘:§I%‘Irl$"
magsmem‘imw" #131 ~ 1

Figure VIII.23: Bond between silicon and glass wafers.

Last step of the manufacturing part was to create a bracket for handling the
silicon die (chip). The bracket was created on the same system as the chip itself,
based on a layer structure (Figure VIII.24-a). A 1mm thick aluminum plate was
the middle layer (Figure VIII.24-b) that holds the waver from moving sideways.
Two Plexiglas plates (5mm thick) restrain the chip from the top and bottom. The
Plexiglas was used for its transparent property which allows for flow visualization
equipment to be used. Further more, the bottom Plexiglas plate had a set of
2mm wide holes to allow the 1mm (outer diameter) flow pipes to be connected
to the chip. The whole assembly is fastened with four screws, one in each

corner.

214

 

b) C)

Figure VIII.24: Mounting bracket for the silicon chip: a) assembly; b) middle
aluminum plate; c) bottom plate with access holes.

215

VIII.4 End Plates and Ducting

The rest of the wave rotor components, end plates and ducting will be designed
as a function of the micro-turbomachinery to which the wave rotor will be
integrated. The same processes will be applied to create these components. In
addition, for high precision lithography, Extreme Ultraviolet Lithography (EUVL)
can be used (Stulen), or for high depth/width ratio, Time Multiplexed Deep
Etching (TMDE) (Ayon, Zhang et al. 2001). Other modern processes that can be
used are directional etching (Ayon, Nagle et al. 2000) and gray-scale lithography
(Waits, Morgan et al. 2005) that can create inclined surfaces or oblique channels.

Drilling micron-size holes can be accomplished by Electrical Discharge Machining

(EDM).

216

Chapter IX

SUMMARY AND CONCLUSIONS

Ix.1 Summary

Given any ultra-micro gas turbine, using the information presented in this work,
it is possible to find an optimum design point, where, by introducing the ultra-
micro wave rotor and modifying the work load on the baseline engine, the
topped gas turbine will operate at improved performance conditions. Calculations
of wave rotor superior efficiency at microscale, as well as design schemes for
wave diagrams, porting, wave rotor geometry, are presented. Also, detailed
description of 2D wave rotor setup and investigations using CFD commercial
code FLUENT are introduced. In the end, one configuration for final design and
manufacturing process flow, fabrication steps are given. Incipient experimental
investigations, as well as blueprints for a more complex test rig are also

presented.

217

IX.2 Conclusions

Utilizing a wave rotor to improve the performance of an UpGT appears to be a
promising solution. Even if the pressure ratio of the baseline engine is already
optimized, the wave rotor can still enhance both the overall thermal efficiency
and cycle specific work output if the wave rotor compression efficiency is higher
than that of the baseline engine compressor. Adding a wave rotor also reduces
the baseline compressor pressure ratio and the exit temperature of the
compressor. Furthermore, this may reduce the compressor diameter and
rotational speed, which results in reduced mechanical and thermal stresses and
relaxed design constraints. From the manufacturing point of view, adding a wave
rotor is much easier at microscale than at macro scale because the wave rotor
can easily be etched in silicon due to its common extruded 2D shape.
Additionally, in a regenerative way the wave rotor is able to harvest some of the
significant amount of heat conducted away from the combustor through the
structure, which is a severe problem for microfabricated gas turbines and also
reduces the efficiency of the spool compressor severely.

Four possible designs for integrating a wave rotor in microfabricated gas turbines
are introduced: three axial and one radial wave rotor. Based on documented
wave rotor efficiencies at larger scale and subsidized by a gasdynamic model that
includes wall friction, the wave rotor compression efficiency at microfabrication
scale could be estimated with about 70%, which is much higher than the

obtained efficiency of compressors in a microfabricated gas turbine. It is shown

218

that at such ultra-micro scale, the wave rotor can have the highest efficiency for
shock wave pressure ratios in the range of 1.7-2, assuming that the
microfabrication can generate a smooth enough surface with a low friction
coefficient. The results show that the efficiency depends not only on pressure
gain across the shock wave traveling through the wave rotor channel but also
depends highly on the loss coefficient for the channel geometry. According to the
here employed model that is applicable for all wave rotor sizes, shorter wave
rotor channels with larger diameter let expect a higher compression efficiency of
the wave rotor.

Several innovative ideas and concepts have been introduced and investigated in
the present dissertation. The most important one is the delivery of a vible
solution for improving the performance of a ultra-micro gas turbine, by adding a
miniaturized wave rotor. Second, for the first time, the variable efficiency
compression process has been incorporated into wave rotor design space
investigations. This sheds a new light on where, when and under what conditions
the topping of gas turbines with wave rotors is efficient and desirable. Third, the
concept of radial wave rotor (wave disc) is an important step forward for wave
rotor technology. Its unique features can improve the compression process
and/or flow scavenging, and also phase separation. The manufacturing process
sounds is ideal for microfabrication. Being able to embed the compressor inside
the wave discs, the overall dimensions can be reduced. Last, simulation of

unsteady gas dynamic process inside the ultra-micro wave rotor channels using a

219

commercial CFD package is a first. FLUENT offers tools that allow for relatively
easy preparation of geometries, some range of typical boundary conditions,
relatively fast and robust solvers and a wide range of post-processing which are
valuable tools for engineers beside scientists. Using FLUENT it has been shown
extensively that such tools can be effectively used for simulation of rather

complex time dependent flow phenomena that occur typically in wave rotors.

220

IX.3 Suggestions for Future Work

IX.3.1 Wave Disc with Curved Channels

Reduction of the wave disc diameter can be obtained by the use of curved or
spiral channels. Curving the channel allows for modulating the acceleration in
flow direction because the component of the centrifugal force that is tangential
to the path of the fluid motion affects the fluid acceleration. Thus, the channel
shape, which may be easier to modify in a wave disc configuration, is another
parameter that should be taken into account for a proper wave disc design. To
fully realize the unsteady flow phenomena occurring inside rotor channels, the
channel length to width ratio should be a large value (e.g., 6-10). This
requirement influences the dimensions of the wave disc. Figure IX.1 presents a
possible configuration of a radial wave rotor in a reverse-flow configuration with

curved channels, and Figure IX.2 presents a 3D rendering of such a rotor.

/ LPG

\ \\\
@1111 111.7
fi’W%

   

LPA K

Figure IX.1: Wave disc with curved channels - ports schematic.

221

 

Figure IX.2: Wave disc with curved channels — 3D rendering.

IX.3.2 Optimization of the Thermodynamic Parameters

Using the newly available design space for ultra-micro gas turbines, baseline and
topped with wave rotors, points in this domain can be found for optimum design
performance. These optimum points, from the thermodynamic point of view, can
be incorporated as input for the wave rotor design scheme. Then, through
geometry and port timing iterations (as described in Chapters V and VI), the best

solution, from mechanical point of view, can be found.

IX.3.3 Experimental Testing
A new, simplified, design for a ultra-micro wave rotor test rig is presented in the

end of this work. This design uses only two silicon wafers for the whole setup

222

(both rotational and stationary part) and only two masks for etching. The masks

as well as the cross-sectional assembly are displayed next.

Rotor

Pipes location

    
    
 

  

.
’pl l‘mal

‘E 'II- ‘
I Plenums and port

     

I
I
I
I
I
10 mm 3

   

assembly

Figure IX.3: Simplified ultra-micro wave rotor test rig.

IX.3.4 3D CFD Investigations

Since the regular 3D CFD models are difficult to investigate, not to mention
extremely time and resource consuming, the author proposes building “quasi-3D”
mesh models, as presented next. The models account for a two-dimensional
mesh and elements arranged into a three-dimensional geometry. The following
figure displays the concept of the single channel test setup, having one of the

reservoirs (plenums) out of plane with the channel.

223

 

1A.

Quasi 3D mesh model for 3D CFD investigations.

Figure IX.4

224

Appendices

Appendix 1 — Material Properties

Table A.1: Properties of Silicon <1 0 0>

 

 

 

Si <1 0 0> properties Value
elasticity modulus, E 130 GPa
Poisson's ration, v 0.28
density, p 2320 Kg/m3

thermal expansion coefficient, a

thermal conductivity, k

specific heat, cp
thermal conductivity, k
heat transfer coefficient, h

failure stress, or

 

2.33-1045 1/K @ 300K
410'6 UK @ 1000K
98.9 W/m'K @ 400 K

31.2 W/m'K @ 1000 K

700 J/kg'K
157 W/m K
24 kW/mz'K - 1o MW/m2°K

1.1 - 3.4 GPa

 

(Tuckerman and Pease 1981; Kovacs 1998; Mehra, Waitz et al. 1999; Kang,

Chen et al. 2002; www.efunda.com 2005)

 

Table AZ: Properties of Silicon Carbide

 

 

 

SiC (hot-pressed) properties Value
elasticity modulus, E 450 GPa
Poisson’s ration, v 0.14
density, p 2550 Kg/m3
mermal expansion coefficient, a 4.5'106 1/ K
thermal conductivity, k 55 W/m K

heat transfer coefficient, h

failure stress, 07

 

24 kW/mZ'K - 1o MW/mZ'K

1.1 — 3.4 GPa

 

(Stark 1999)

Table A3: Properties of Silicon Nitride

 

 

 

Si3N4 (hot-pressed) properties Value
elasticity modulus, E 310 GPa
Poisson’s ration, v 0.27
density, p 3290 l<g/m3
thermal expansion coefficient, a 3.3 '10'6 UK
thermal conductivity, k 30 W/m K

 

 

(www.accuratus.com 2005)

226

 

 

Appendix 2 - UpWR Fabrication Drawings

Figure A.5: Technical drawing of the ultra-micro wave rotor in a through-flow
configuration.

Figure A.6: Technical drawing of the ultra-micro wave rotor in a reverse-flow
configuration with air ports placed on the inside region.

227

 

 

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Figure A.7: Mask used for first etch step of rotor wafer 1.

 

Figure A.8: Mask used for second etch step of rotor wafer 1.

230

 

Figure A.9: Mask used for first etch step of rotor wafer 2.

 

Figure A.10: Mask used for second etch step of rotor wafer 2.

231

 

Figure A.11: Mask used for first etch step of plenum wafer 1.

Figure A.12: Mask used for second etch step of plenum wafer 1.

232

 

 

Figure A.13: Mask used for first etch step of plenum wafer 2.

Figure A.14: Mask used for second etch step of plenum wafer 2.

233

 

Figure A.15: Mask used for third etch step of plenum wafer 2.

234

Appendix 3 — Microfabrication Detailsa

Mask Alignment
Equipment used. MA6/BA6 Mask Aligner

Purpose. Photolithography involves transferring a pattern from a mask to a wafer
coated with photo resist. MAG has the capability of processing both top
and backside alignment. This tool is primarily used for high-resolution
lithography (<2pm) and/or critical alignment tolerances (<1um).

Procedure

Soft contact exposure - the substrate is brought into contact with the mask by a
preset force during exposure, for features 2 2pm.

Flood Exposure: for first level exposure. Once the mask and wafer are loaded the
aligner proceeds to expose skipping the alignment step.

Alignment Features

Top side: TSA, the top microscope is used to align mask features to the topside
of the wafer.

Back side: BSA, the bottom objectives are used to align mask features to the
back of the wafer. This is achieved by aligning a captured image of the
mask and the real image of the wafer.

Mask Clean - Dip in Acetone/ IPA #1/ IPA #2 and N 2 dry.

 

3 Material extracted from the University of Michigan, WIMS Laboratory — Lab notebooks.

235

Photo Resist - Positive resist (Any resist exposed to ultra-violet light is developed
away) and Negative resist (Resist remains on the surface where exposed).

Lamp Power Supply: 405nm (20 mW/cmz) and 365nm (11mW/ cmz)

Configuration:MA6 for lithography/8A6 is for bonding alignment.

The alignment marks are used to ensure each mask step fits on top of the
previous step. If anything is misaligned you have the chance for devices

to fail.

 

Figure A.16: MA6/BA6 Mask Aligner — mask trey.

Deep Reactive Ion Etching
Equipment usedl ST S Etch System

Purpose. It is a deep reactive etch (DRIE) system that uses SF6 for etching and

C4F3 for passivation.

236

Procedure

Carrier Wafer Bonding: For any substrate etched more than 250nm deep, shall
be bonded to a carrier wafer.

Chiller temperature between 40°C and 45°C to start the process.

Turbo rotational velocity - 3600rpm.

The process consists of two steps: one is an isotropic etch using SF5 high density
plasma, the other is a passivation step in which the wafer is covered is
covered with a C4F3 film. Ion bombardment removes preferentially the
passivation film from the horizontal surfaces, allowing these surfaces to be

isotropic etched, thus creating anisotropic geometries.

 

Figure A.17: Wafer holder for etching.

am
Equment used 536 Bonder
Purpose: The $36 is used for anodic, diffusion and thermal/compression bonding

of 4-inch substrates.

237

Procedure

Following materials are allowed in the system, besides silicon wafers: tin, indium
or solder, glass, BoroFloat, Pyrex, borosilicate glass with thermal
characteristics to silicon wafers.

Compressed air: 6-10 bar

Vacuum: 90-95 mbar

Inert Gas: N2 at 1.1 -10 bar

Room temperature: 20-22C

Temperature inside the chamber: 100C to 550C

Humidity: 40-45°/o

Silicon Direct Bonding, Fusion Bond is used to join two silicon wafers by creating
a hydrophobic or hydrophilic surface. (Hydrophobic: an HF dip is advisable
for a better bond; Hydrophilic: a standard RCA clean is required)

Bond Chamber is designed for processing pressures from 510'5 mbar to 3 bar
(absolute). Voltage: -2000V to + 2000V possible, change the polarity as

required for bonding.

m1

Equipment used Micro Automation Dicing Saw

Purpose The dicing saw is used to separate dies from the wafer. A specified
blade (dependant on substrate type) cuts the scribes lines in the x and y

direction.

238

Procedure

The wafer is temporary placed on an adhesive film to hold it on a vacuum chuck.

The wafer is marked for cutting. It is important to know the width of streets
(scribe lines), thickness of cut and location of alignment marks.

Cleavage Plane: {100} wafers, natural cleavage planes exist perpendicular to the
surface of the wafer in the directions parallel and perpendicular to the
wafer fiat. {111} wafers, a vertical cleavage plane runs parallel to the
‘wafer flat.

Types of Blades: The grit size of a blade is dependant on material to be cut.
Blade 777 is used to cut glass or silicon, the cut width is 230um
(9.05mils). Blade 42525 is used only to cut silicon, the cut width is 110um
(4.33mil).

Thickness of the wafers: Silicon wafer: 24mils for 4 inch (500-550um). Glass
wafer: 33.5 mils. Adhesive film: 3.5 to 4 mils.

Cutting Speed: Silicon — 100, Glass - 50

 

Figure A.18: Wafer dicing saw.

239

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