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PRELIMINARY INVESTIGATION OF THE FIRST
GENERATION INTERNAL COMBUSTION WAVE DISC
ENGINE

presented by
KANISHKA SHARMA

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DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5’08 K./Prqlec&Pres/CIRCIDaIeDue.indd

PRELIMINARY DESIGN APPROACH TO THE FIRST GENERATION
INTERNAL COMBUSTION WAVE DISC ENGINE

By

Kanishka Sharma

A THESIS

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

MASTER OF SCIENCE
Department of Mechanical Engineering

2008

ABSTRACT

PRELIMINARY DESIGN APPROACH FOR THE FIRST GENERATION
INTERNAL COMBUSTION WAVE DISC ENGINE

by
Kanishka Sharma

For the past decade the miniaturization of power generation devices has been a
fascinating research topic. With the available micro fabrication methods and high
specific energy of the hydrocarbon fuels, it gives us a compelling reason to
explore and develop the possibilities of using such fuels for ‘power generation on
a chip. The Internal Combustion Wave Disc Engine (IC WDE) is one such
concept. It is an unsteady flow device using energy exchanges via waves. The
waves travel in channels which are arranged inside the disc, to extract work, to
propel the disc, and to produce torque. The first part of the work discusses the
working principle of the WDE and the gas dynamic relations that are used later to
establish the gas dynamic model of the wave disc engine. Challenges of micro
combustion are also presented. The second part of the work involves numerical
simulations of an axial wave rotor that has been successfully commercialized as
COMPREX® and can be seen as a predecessor among the unsteady flow
devices. FLUENT® is used for these simulations and results are compared with a
1 D algebraic code developed and being used to design wave rotor porting and
how to employ the same approach for the modeling of a WDE. In the third part of
this work, supporting experimental work is presented that covers flow studies
inside 4 different microchannels machined in a Si wafer. Friction factor are

determined and compared with the available data from the literature.

To my family and friends

ACKNOWLEDGEMENTS

I would like to express my sincere and deepest gratitude to Prof. Norbert Mtiller
for giving me this opportunity to work on this research project and make it an
enriching learning experience. I would like to thank him for the independence he
allowed me to explore different directions in this project, his guidance, motivation
and his very positive outlook which really helped me enjoy this work. I am really
honored and consider myself very lucky to have him as my advisor, mentor and a
fnend.

I would also like to express my sincere thanks to committee members Prof.
l.S.Wichman and Prof. Guy Raguin for their very valuable suggestions and
patience without which this work would not have been complete. I am particularly
thankful to Dr Wichman for giving me an opportunity to perform my graduate
studies at Michigan State University where I arrived in fall of 2005.

I am also sincerely thankful to Dr Januz Piechna and Dr Witold Selerowicz from
Warsaw University of Technology, Poland. Dr Piechna’s guidance in the area of
CFD modeling was invaluable. My experimental work would not have been
complete without the kind support of Dr Selerowicz.

I would also like to thank Dr D. Aslam and his students for their kind help and
support in providing us with Si wafers for performing microfluidic experiments.
This work would not have been complete without the keen insight and
conversation from my good friend and mentor Ludek Pohorelsky. I would
sincerely like to thank him for the knowledge he shared with me, his patience and
his never ending enthusiasm and motivation.

iv

I would also like thank my friends and colleagues, especially Marco Vagani,
Pranav Sane, Suyash Sidhaye, Gaurav Dabholkar, Amol Patki, Hela Jaziri and
Pradeep Kumar and few more for their patience & understanding and also for
being there when things did not go as planned.

Last but not the least I would like to thank my parents and my dear sister, for
their brilliant support and affection without which I would never be able to make it

so far.

TABLE OF CONTENTS

List of Tables ....................................................................................... viii
List of Figures ...................................................................................... ix
Key to Symbols ................................................................................... xii
Chapter 1: Background and Introduction ............................................................... 1
1.1 Background ................................................................................................ 1

1.2 Unsteady flow devices ................................................................................................. 3

1.3 Microscale power devices .......................................................................................... 8

1.4 Wave Disc Engine ...................................................................................................... 10

1.5 Work presented ........................................................................................................... 10

Chapter 2: Wave Disc Engine Theory ................................................................. 12

2. 1 Wave Theory ............................................................................................................... 12

2.1.1 Shock wave generation .................................................................................. 13

2.1.2 Expansion wave generation .......................................................................... 14

2. 2 Principle of Operation ............................................................................................... 16
Chapter 3 Gas Dynamics of Wave Disc Engine .................................................. 21
3.1 Method of Characteristics ......................................................................................... 21
3.1.1 Derivation of the characteristic line ............................................................. 21

3.1.2 Generalization of the characteristic lines .................................................. 26

3.2 State Diagram of the wave disc engine ................................................................ 28

3.2.1 Governing Equations ...................................................................................... 30

3.2.2 Calculation of the Gas Air Interface ............................................................ 32

3.2.3 Boundary conditions ........................................................................................ 32

3.3 External combustion wave disc engine; an overview ...................................... 33

Chapter 4 Combustion at micro scale ................................................................. 40

4.1 Thermo-physical Aspects of Micro combustion ................................................. 42

4.2 Fluid flow in micro devices ....................................................................................... 45

4.3 Thermal and heat transfer issues in micro-combustion .................................. 47

4.4 Combustion at micro-scale ...................................................................................... 48

Chapter 5: 2-D Numerical simulations and design verification of a wave rotor ...52

5.1 Wave Rotors ................................................................................................................. 52
5.2 Formulation of the Analytical code ........................................................................ 55

vi

5.4 Numerical Results ....................................................................................................... 66

5.5 Approach for modeling the Wave Disc Engine .................................................. 73
Chapter 6 : Preliminary analytical results for wave disc engine .......................... 75
6.1 Results and Discussion ............................................................................................. 75
Chapter 7: Friction factor studies in microchannels ............................................ 83
7.1 Theory ............................................................................................................................ 84
7.2 Experimental setup ..................................................................................................... 86
7.3 Results ........................................................................................................................... 88
Chapter 8 Conclusions ........................................................................................ 93
References: .......................................................................................................................... 96

vii

LIST OF TABLES

Table 1 Experimental data for the (750um x 90pm x 360um) microchannel ....... 88

Table 2 Experimental data for (1500um x 180pm x 360um) microchannel ........ 89

Table 3 Experimental data for (3000pm x 360um x 360um) microchannel ......... 89

viii

LIST OF FIGURES

(Images in this thesis are presented in color)

Fig 1 From the MIT micro gas turbine project .............................................. 2
Fig 2 Scheme of a commercial version of wave supercharger — known as

Comprex® ........................................................................................... 4
Fig 3 Mazda engine cut-view and the Comprex® rotor ................................. 5

Fig 4 Temperature Entropy diagram for ultra-micro gas turbines, with and without
waverotor.......................... ............................................. 6

Fig 5 Schematic showing a gas turbine topped by a wave rotor (left), and low

trajectories in a through-flow axial wave rotor (right) ....................................... 7
Fig 6 Conceptual design of UuGT — “Classic” design ..................................... 9
Fig 7 Conceptual design of UpGT - “Radial” design ...................................... 9

Fig 8 Flow behavior inside a tube when the diaphragm is suddenly ruptured ....13
Fig 9 Shock wave generated as the channel is suddenly closed on the right ....14

Fig 10 Expansion wave generated as the channel is suddenly closed on the
left ....................................................................................................................... 15

Fig 11 Schematic showing the wave disc engine cycle ................................. 16

Fig 12 Wave diagram showing the wave propagation on a relative frame of
reference .............................................................................................. 18

Fig 13 Wave diagram showing the wave propagation on an absolute frame of
reference .............................................................................................. 20

Fig 14 Propagation of the expansion wave and its reflection at the open end.. . .22

Fig 15 Change of state properties as the wave propagates............................ 22
Fig 16 State Diagram depicting the expansion wave ..................................... 25
Fig 17 State Diagram depicting compression and expansion waves in all four

quadrants ............................................................................................................ 26
Fig 18 State diagram representing the wave disc engine cycle ...................... 28

Fig 19 Possible construction of the single-stage compression wave engine in

reverse-flow configuration ....................................................................... 32
Fig 20 Single-stage compression wave engine scheme in reverse flow
configuration ....................................................................................... 33
Fig 21 Exploded view of the wave-engine construction ................................. 34
Fig 22 Details of the two-step compression wave-engine construction ............. 35
Fig 23 Specific energy for different energy producing devices ........................ 39
Fig 24 (a) Integrated catalytic combustor—thermoelectric micro power generator,
(b) MEMS fabricated array of “Digital-Propulsion” micro-thrusters ................... 50
Fig 25 Schematic showing the rotor and ports ............................................ 52
Fig 26 A 3 D model developed in Catia to model the wave rotor test rig. Showing
the arrangement of face plates and rotor over a shaft .................................. 53
Fig 27 Wave Patter in a through flow wave rotor configuration ....................... 55
Fig 28 Inlet Side plate, Blue showing air inlet (Al) and Red showing exhaust inlet
(El) ................................................................................................... 59
Fig 29 Outlet side, orange showing the exhaust gas outlet (E0) and blue showing
the compressed air outlet (A0) angle ....................................................... 59
Fig 30 A 2D grid showing the channels and the porting .......................... . ...... 62
Fig 31 (a) & (b) showing the mesh entry and the leakage area ....................... 63
Fig 32 Static pressure contours showing the wave pattern in a through flow
configuration ........................................................................................ 65
Fig 33 Total pressure contours showing the wave pattern in the channels ........ 66

Fig 34 Static temperature profile showing the flow pattern and the exhaust gas
recirculation in the exhaust outlet, E0 ...................................................... 66

Fig 35 Total temperature profile showing the flow pattern and the exhaust gas
recirculation in the exhaust outlet, EO ...................................................... 67

Fig 36 1 D Analytical model results showing the wave behavior , the red dots
showing the gas air interface and the green traces showing the net flow
velocities .............................................................................................................. 68

Fig 37 X velocity comparison of the Exhaust Inlet Port ................................. 69

Fig 37 X velocity comparison of the Air Inlet Port ........................................ 69
Fig 38 X velocity comparison of the Exhaust Outlet Port ............................... 70
Fig 39 X velocity comparison of the Air Outlet Port ...................................... 70

Fig 40 Velocity magnitude vectors showing the backflow in exhaust inlet port...71

Fig 41 (a) Examples of some wave discs, (b) Curved channel variation ......... .73
Fig 42 Wave pattern on a Time v/s Distance plot ......................................... 75
Fig 43 Temperature and Up5 velocity distribution for various pressures ........... 75
Fig 44 Temperature and Up6 velocity distribution for various pressures ........... 76
Fig 45 Temperature and Up7 velocity distribution for various pressures ........... 76
Fig 46 Temperature and Up8 velocity distribution for various pressures ........... 77
Fig 47 Temperature and Up9 velocity distribution for various pressures ........... 77
Fig 48 Temperature and Up10 velocity distribution for various pressures..........78
Fig 49 Gas air interface distribution for a 4 bar post combustion pressure. . . . . ...80
Fig 50 Gas air interface for a 8 bar post combustion temperature ................... 81
Fig 51 Silicon microchannels: (a) front view, (D) back view ............................ 82
Fig 52 Channels visualized with SEM: a) 90um and 180 um wide channels; b)
360 um and 720 um wide channels .......................................................... 83
Fig 53 Experimental setup ...................................................................... 86

Fig 54 Plot showing Reynolds number versus the Normalized friction coefficient
for three different micro channel dimensions .............................................. 89

Fig 55 Plot showing the percentage of density change for different channel
lengths and for different R990

xi

Q

I.

[\N

831:3»

PRW

ZUQ-

Re

KEY TO SYMBOLS

speed of sound (m/s)
cross-sectional area (m2)
specific heat (J/kg'K)
diameter (m)

hydraulic diameter (m)
internal energy (J)

friction factor

specific heat ratio

pressure drop (Pa)

polytropic efficiency (%)
isentropic efficiency (%)
channel length (m)

distance to sonic conditions (m)
entrance loss coefficient
Mach number

kinematic viscosity (St)
pressure ratio

pressure (Pa)

wave rotor compression ratio
heat flux (W/mz)

specific gas constant (J/kg'K)
density (kg/m3)

Reynolds number

time (5)

temperature (K)

flow velocity (m/s)

induced flow velocity behind shock wave (m/s)

xii

w shock wave velocity (m/s)

x coordinate along the channel

xiii

CHAPTER 1: BACKGROUND AND INTRODUCTION

Every research work has its roots in historical work and past research. This
chapter provides a historical perspective and also brief introductions of the state
of research in the related works. The idea and motivation behind this effort has

been described.

1. 1 Background

The past century has seen a considerable research interest and focus to
develop different ways of using heat energy from fuel to generate torque and
produce power. Minds across the century have come up with novel ways of
converting fuel energy for the purpose of generating torque or propulsion,
examples of which are everywhere around us. It began during the Industrial
revolution during which in everyday language an ‘engine’ was any sort of
mechanical device that converted some form of energy into mechanical or motion
force. The term "gin" as in cotton gin is recognized as originating from the Old
French word ’engin' as a short form of its usage. Beginning from Sadi Carnot’s
fundamental theory of two stroke reciprocating engine, automotive production
has used a variety of energy conversion systems which include electric, steam,
solar, turbine, rotary, and piston-type internal combustion engines.

For just over a decade now, the energy community is geared towards designing
and now fabricating devices at the meso, micro and even the nano scale. Gas
Turbine laboratory at M.I.T, [1, 2] has been a leader in miniaturization of

rotational turbomachinery.

 

 

(a) Microturbine, (b) Compressor, (c) Combustor & Turbine

Fig 56 From the MIT micro gas turbine project, [3]
Smaller and more functional, power generating devices have been designed and
tested but none has been commercialized yet. With the MEMS reactive ion
etching technique already developed, batch production and commercialization of
such small scale devices with precise geometry is very viable and also a
motivating factor to design and study micro scale propulsion, combustors,
turbines and other pressure wave exchange devices. This class of research has
be named as Power MEMS characterized by thermal, electrical, and mechanical
power densities equivalent to those in the best large-sized machines produced
today, thus producing powers of 10 to 100 watts in sub-centimeter-slzed
packages. Based on classical thermodynamic cycles (Brayton, Rankine, am),
such devices would have significantly different behavior than, but equivalent
performance to, their more familiar full-sized embodiments. They could see
widespread application as mobile power sources, propulsion engines, and
coolers. However, the realization of power MEMS presents new challenges both
to micromachining and to the traditional mechanical and electrical engineering
disciplines of fluid dynamics, structural mechanics, bearings and rotor dynamics,

combustion, and electric machinery design, [4] .

The use of unsteady flow devices gives us an interesting alternative to such

issues with Power MEMS devices and may provide a way around it.

1.2 Unsteady flow devices

Unsteady flow devices like shock tubes, wave rotors, pulse detonation engines
have been around for some time. By exploiting the unsteady flow and pressure
exchanges, we can expect a significant increase in engine performance. Also, a
less complex, more durable and robust design becomes possible as the use of
lot of conventional mechanical components like impellers, and compression
pistons is eliminated.

The Wave Rotors also known as Pressure Wave Machines or Pressure
Exchangers are unsteady-flow devices that can transfer energy directly between
two fluids, by means of pressure waves (shock waves). In a wave rotor, two
fluids with different pressures are brought into direct contact. Then pressure
exchange occurs faster than mixing. The wave rotor can have a higher isentropic
efficiency than steady-flow devices, like compressors or diffusers, but may be
more challenging to control. In the past, because of the unsteady nature of the
flow inside the wave rotor, process simulation was very inaccurate, time
consuming and labor intensive. Recently, because of the increase in calculation
power of the computers and more accurate commercially available software
packages, significant progress was made in understanding the complex wave
phenomena.

Among the most know applications of the unsteady flow characteristics, the

Comprex® Pressure Wave Supercharger developed in Switzerland for boosting

3

the pressure in internal combustion engines has found its way into production.
The main shortcoming of steady flow devices, like turbochargers, is the lack of
boost capability at low engine speed. Devices based on the unsteady flow
principle like Comprex, however typically produces higher boost over the entire
speed range. The difference is most conspicuous at low engine speed and

becomes quite apparent during transient operation.

 

 
    
 
 

   

Intake
port

   
 

Exhaust
port

\

R

 

Port C

 

z?

 

 

 

Fig 57 Scheme of a commercial version of wave supercharger - known as Comprex

Early experiments with the PE were made at the beginning of the 20th century by
Knauff (1906), Burghard (1913) and Lebre (1928), but the first real application of
a PWM was made by Claude Seippel (1940) of Brown Boveri Company (later
Asea Brown Boveri), who used it as a high pressure stage for a gas turbine

locomotive engine. The best known industrial application of the wave rotor is the

Pressure Wave Supercharger (PWS), which is an alternative pressure-boosting

device to the more famous Turbocharger (TC), [5].

 

Fig 58 Mazda engine cut-view and the Comprex® rotor

Although extensive tests were made by the BBC from the late 40’s until the 80’s
in order to develop the PWS, the real breakthrough came in 1986 when the
Mazda Company introduced its Mazda 626 Cappela model, which had a 2 liter
Diesel engine equipped with a Comprex® wave rotor. Mazda produced 150 000
Comprex® Diesel cars, this being the major industrial application for a wave
rotor. Other car manufacturer like Opel, Mercedes, Peugeot and even Ferrari
used the Comprex® with promising results. To date, the Comprex® is the only
commercially available wave rotor, and Swissauto Wenko AG of Switzerland is
the only company who produces a modern version of the Comprex®, called the
Hyprex®. This type of wave rotor is designed for small gasoline engines
applications, [6].

Extensive studies have been done in the past to compare the shock wave
compression efficiency and its comparison with diffuser and compressor

efficiencies.

0 — 1b — 4b — 5b baseline engine
0 — 1A— 2A— 3A— 4A— 5A topped engine

Tenperature

Tturbine

 

 

 

Entropy
Fig 59 Temperature Entropy diagram for ultra-micro gas turbines, with and without wave rotor, [6]

Figure 59 shows the shows variations of these parameters as functions of the
pressure gain p2 /p1 obtained by a shock wave in a frictionless channel and
shows it obvious advantage. Besides this, there are several important
advantages of wave rotor machines. Their rotational speed is low compared with
turbomachines, which results in low material stresses. But they can respond on
the timescale of pressure waves, with no rotor inertial lag. From a mechanical
point of view, their geometries can be simpler than those of turbomachines.
Therefore, they can be manufactured relatively inexpensively. Also, the rotor
channels are less prone to erosion damage than the blades of turbomachines.
This is mainly due to the lower velocity of the working fluid in the channels, which

is about one-third of what is typical within turbomachines [7]. Another important

advantage of wave rotors is their self-cooling capabilities. They are naturally
cooled by the fresh cold fluid ingested by the rotor. Therefore, applied to a heat
engine, the rotor channels pass through both cool air and hot gas flow in the
cycle at least once per rotor revolution. As a result, the rotor material temperature
is always maintained between the temperature of the cool air which is being

compressed, and the hot gas which is being expanded.

 

Combustion Chamber

    
    

Wave rotor

 

Turbine

/

   

Compressor

 

 

 

\

 

 

 

Fig 60 Schematic showing a gas turbine topped by a wave rotor , [6]

Despite very attractive features, several challenges have impeded the vast
appearance of commercial wave rotors in some applications though numerous
research efforts have been carried out during the past century. Besides unusual
flow complexity and anticipated off-design problems and uncertainties about the
selection of the best wave rotor configuration for a particular application, the

obstacles have been mainly of a mechanical nature, like sealing and thermal

expansion issues, as mentioned throughout this study. However, due to the
recent energy crises, technology improvement, and economic reasons, new

ideas for wave rotor technology have been simulated [6].

1. 3 Microscale power devices

As an improvement to the wave rotor technology, unconventional designs have
been proposed and presented. This includes the design and simulations of an
Ultra Micro Wave Rotor (UuWR) carried out at the Turbomachinery Laboratory,
Michigan State University, [8]. It is a part of the most investigated power sources
in the past decade. The class of gas turbines with structures of micrometer size
that have been referred to as Ultra-Micro Gas Turbine (UuGT) to distinguish
them from small industry gas turbines of 1250 kW that are often referred to as
microturbines, [9].

Due to their high power density, ultra-micro gas turbines (UuGT) are appropriate
solutions for powering small unmanned air-vehicles (UAV) and electronic
equipment associated with them, such as sensors, probes or cameras. A typical
size of a microfabricated (on-the-chip) UuGT is 10mmx10mmx3mm with a power
output between 1 and 100 W. Also these microfabricated gas turbines are
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 theoretic power density of turbomachinery increases while their size
decreases, the reason is the so called cube square law: The output power is
proportional to the mass flow rate of the working fluid that scales with the

through-flow area, which is proportional to the square of the characteristic length.

8

The mass or volume of the engine is proportional to the cube of the characteristic
length. Hence PowerNolume is proportional to the inverse of the characteristic
length, [10]. One such idea is presented below , Fig 6 which shows a conceptual

design of a Ultra Micro Gas Turbine topped with an Ultra Micro Wave Rotor.

Wave Rotor

 

 

 

 

 

 

 

 

 

 

 

 

 

4 cycle! revolution
(16 port wove rotor)

 

Fig 61 Conceptual design of UuGT — “Classic” design, [8]
For most thermodynamic applications, so far most widely axial-flow wave rotors
have been used and investigated. Pure scavenging is a challenging task in the
axial-flow configurations. 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 7 shows schematically a
simple radial-flow wave rotor with straight channels and a rectangular cross-

sectional area.

 
    

RotatingDisI

     

A! Indie COW

    

Tillie
Fig 62 Conceptual design of UpGT - “Radial” design. [8]

1.4 Wave Disc Engine

The concept provided in this work uses a hybrid approach by combining the
pressure wave exchange principle for transfer of energy and utilizing the internal
combustion (constant volume) principle, at a micro scale to generate the energy.
By using appropriate geometry of the channels, channels port timings can be
used to generate the change of angular momentum. Not much literature is
available at this moment which talks about an independent power generating
wave disc concept. Piechna, et. al have proposed a similar design with a

separate combustion chamber, [11] .
1.5 Work presented

This work has covered more than one facets of a preliminary design for wave
disc engine. Numerical and experimental work leading to understanding of

10

important concepts in design of this micro scale device has been presented. The
work includes:

(A) Numerical model of the micro scale internal combustion wave disc engine
using the method of characteristics and normal shock wave relations. Gas
Dynamic wave diagram is presented and explained.

(B) A Computational fluid dynamics (CFD) model of the wave rotor is presented.
This model is prepared using the commercially available software,
FLUENT®6.2.Port geometries have been optimized by researchers at the
Turbomachinery Laboratory at Michigan State University. This is a part of the
wave rotor test rig being built and tested here at the Turbomachinery Laboratory,
MSU.

(C) Micro fluidic experiments to compute friction factor in four different lengths
micro channels inside a Silicon wafer, were performed at University of
Technology, Warsaw. Friction factors, as one of the fluid flow characteristic, was

studied, calculated and compared with the theoretical values.

11

CHAPTER 2: WAVE DISC ENGINE THEORY

This chapter explains the gas dynamic theory behind the wave disc engine and
the working principle. Basic wave theory is also explained, along with the wave

and state diagram of the wave disc engine.
2. 1 Wave Theory

The understanding of wave theory gas dynamics is crucial to developing the
wave disc engine. It is very convenient and easy to explain this concept using a
single stationary channel, very similar to a shock tube. The wave diagram, as
shown in figure 8, is a way to represent gas motion on a time versus space plot.

When the wall or a diaphragm is broken between the two regions at different
pressures is broken, typically two types of ‘waves’ are generated at the point on
rupture. A shock wave travels towards right into the low pressure region or the
driven section. The wave which travels towards the left is the expansion wave
and it’s also referred to as the driver section. The shock wave increases the
pressure and temperature of the driven section rapidly and induces a mass
motion behind itself. The interface between the driver and driven gases, called
the contact surface, moves with an induced velocity in the same direction as the
incident shock. The expansion wave decreases the pressure and temperature of
the driver section smoothly. Therefore, across the contact surface the pressure
and velocity are preserved while the temperature and entropy change

discontinuously.

12

 

Before I
diapm'agm High —pressure flow at rest ' Low pressure NOW at “351
Opening

Afler
(Itaphragnl «a l »

opening

 

 

 

 

 

 

 

 

ll

 

 

Time
0°“ ,_"-""
4X” ' ’
/

 

 

0 Distance

 

 

Pressure

 

 

 

 

 

 

Fig 63 Flow behavior inside a tube when the diaphragm is suddenly ruptured, [12]

2.1.1 Shock wave generation

In unsteady flow devices shock waves are typically generated by either sudden
opening of the port or like in wave disc engine design, sudden closing of the port.
This is explained with the figure 9. When the fluid is suddenly brought to rest by
closing the channel, it generates a shock wave in the direction opposite to the
incoming fluid flow velocity. As this shock wave travels towards the left, it brings

the fluid at rest and thus raising the pressure of the fluid.

13

 

 

 

 

‘-
PA: UA UB=0
Gas in M otion
i Gas at Rest
4—

Normal Shock wave, W5

 

 

Pressure

 

 

4L

Distance

Fig 64 Shock wave generated as the channel is suddenly closed on the right

2.1.2 Expansion wave generation

When a gas at high pressure is suddenly exposed to lower pressure, it expands.
When the end of the tube is rapidly opened, it results in the formation of an
expansion fan which propagates inside the tube inducing a gas flow out of the
tube. Such a scavenging flow process imitates the expansion process of the
driver section in a shock tube after sudden removal of the diaphragm. Another
way of expansion wave generation is by sudden closing of the flow (left port of
the shock tube shown in figure 8). Because the velocity of the gas in contact
with the closed end must be zero, an expansion wave propagates into the
moving gas, bringing it to rest. Note the pressure drop is not as sudden as in a

shock wave, as show in figure 10.

14

Expansion Wave

///

——_

Time

 

Distance

 

Pressure

 

Distance

Fig 65 Expansion wave generated as the channel is suddenly closed on the left

The above shown schematics show that sudden closing of a channel generates
shock and expansion waves inside a channel or a tube depending on the port

position and fluid flow direction.

For this work, the flow is assumed to be adiabatic, frictionless, and reversible.
For such isentropic behavior method of characteristics is used to compute the
pressures and flow properties. This is isentropic compression and expansion.

The final compression is before the combustion is assumed to be taking place
with a non-isentropic, yet adiabatic pressure wave, Le. a shock wave. In
subsequent chapters, the logic behind this assumption is explained along with

the analytical model.

15

2. 2 Principle of Operation

The cycle of operation is explained with a schematic, Fig 11 and wave diagrams

in absolute, Fig 12 and relative frames, Fig 13, are explained.

 

 

 

 

Fig 66 Schematic showing the wave disc engine cycle

1. Constant volume combustion takes place of the compressed air fuel
mixture. Channel closed at both ends. Combustion (Deflagration) taking
place near the middle. High pressure exhaust gases starts to accumulate
at other end. Port timing has to be such as to not let a reverse shock wave

develop.

2. Expansion of these high pressure and temperature begins as outer end of
the channel opens to ambient conditions. Torque generation is expected

in this process. Channel geometry can be so designed as to generate

16

partial propulsion from the exhaust gases. The tangential component
(using the Turbomachinery principle or Jet propulsion) will be added to the

net torque. This sudden expansion begins partial scavenging.

3. The inlet port, at ambient conditions, opens up and ingestion of fresh fuel
air mixture begins. Expansion wave due to exhaust gas outlet sucks in this
mixture and complete scavenging takes place. Centrifugal component of

the disc also partially helps in the scavenging process.

4. The outlet port suddenly closes and a shock wave is generated
compressing the fresh air fuel mixture. The other end of the port is still

open and closes as soon as the shock reaches the other end.

The next figure indicates the wave pattern in a relative frame of reference. Wave
propagation is plotted over a distance versus time plot. It also indicates the flow
velocity. It must be understood that the flow velocities depicted in this diagram is
the net flow velocity and not the instantaneous flow velocity. The width of the
velocity vectors gives a good understanding about the flow velocity magnitude as
well. The red arrows represent the compression wave and the blue arrows

represent the expansion wave.

The red channel indicates the channel just after combustion. It is the region of
high pressure and temperature. As the channel moves, it first opens to the

exhaust port, which is assumed to be at ambient conditions. Due to this sudden

17

opening to a low pressure region, an expansion wave starts at the beginning of
the exhaust port and travels towards the inlet port, between Zone ll & Ill. The
flow velocity is in the direction opposite to the expansion wave. The burnt
exhaust gases rushes out of the channel with this velocity. As the first expansion
wave reaches the opposite end, it gets reflected back just before the inlet port
opens. The induced flow velocity by this strong expansion wave is very high. This
expansion provides the motion to the disc and is the source of toque. This is

also the beginning of the scavenging process.

1%

VII

VI

Interface

Time
Exhaust (3)
Inlet (All + Fuel)
2

IV ~~~~~~~

Flow velocity

Bu rned Ga 8

 

 

 

It

Distance

Fig 67 Wave diagram showing the wave propagation on a relative frame of reference

18

The second expansion wave which is a reflected expansion wave, between Zone
Ill and IV travels, is a weaker expansion wave. The induced flow velocity by this
wave is lesser in magnitude and opposite in direction of the previous flow
direction. But the net flow velocity is still in the direction towards the exhaust flow.
This net induced flow brings in the fresh air fuel mixture into the channel. At this
point of time we have an interface between the unburnt charge and the exhaust
gases inside the channel. This is depicted with the red dotted line beginning in
Zone IV.

The boundary conditions which we have assumed for this model is that at
exhaust, the static pressure is slightly above atmospheric conditions and at inlet,
the static pressure conditions is slightly below atmospheric. As the second
expansion wave reaches the exhaust port boundary, due to a pressure difference
between Zone lV & V, a pressure wave (red) originates. This pressure wave and
the net fluid velocity it induces is still in the direction of the exhaust port.

As this first pressure wave reaches the inlet port which is less than atmospheric,
the third expansion is generated, and it travels towards the exhaust port. During
these really fast wave exchanges, scavenging takes place as shown by the
charge-exhaust gas interface. The channel is now almost filled with the fresh air
fuel mixture.

As the fourth expansion wave reaches the exhaust port end, the net induced
velocity is at its minimum. The exhaust port rapidly closes and due to this rapid
closure of end of a channel, a shock wave is generated, as depicted in the third

red arrow. This shock wave acts as the compression wave Zone Vlll - I and

19

increases the pressure and temperature of the charge just before the constant
volume combustion takes place which again starts the cycle.
This process is explained using figure 12, which shows the wave propagation.

Figure 13 indicates the wave propagation in an absolute frame of reference.

 

 

Exhaust (3)

 

 

 

Fig 68 Wave diagram showing the wave propagation on an absolute frame of reference

The expansion of the exhaust gases generates the necessary reaction force to
rotate the disc and generate torque. This torque can be transmitted to a center
shaft and used as power. This design encapsulates constant volume combustion
inside the microchannel. Combustion has been modeled by constant volume

heat addition.

20

CHAPTER 3 GAs DYNAMICS OF WAVE DIsc ENGINE

This chapter discusses the analytical technique which has been used to develop

the numerical code for optimizing and calculating the wave disc behavior.
3.1 Method of Characteristics

Due to the assumed isentropic nature of compression and expansion waves, the
method of characteristics can be used to find the flow properties across the
wave. This method is a very general and powerful technique for analyzing
compressible flow. For the specific problem considered in this study, only one-

dimensional version of this method is used.
3.1.1 Derivation of the characteristic line

The isentropic relations are:

"If-I13]; IT
p0 p0 a0 TD [1]

and the local speed of sound, a is given by
a = xi KRT [2]

21

The pressure relations for an expansion and compression wave relations can be
formulated using a piston analogy as shown in figure 14. This diagram shows the

beginning of expansion wave as the piston head reaches top dead center (TDC).

 

 

 

 

 

 

 

 

 

 

'o
'2-

"l—4 Expansion

 

u-qp--
DJ

5.;

2?

Inflow l...“
- 0., oooooooooooooo
rh—

l

_I

Compression

’-

‘

'O

'O
o

I
--- --- -----

Fig 69 Propagation of the expansion wave and its reflection at the open end

The expansion wave propagates towards left with the local speed of sound given
by equation 2. As this expansion wave reaches the left end, there is a sudden
inflow. This produces a compression wave which travels in the opposite direction

with the local speed of sound.

22

dx

A

 

 

 

dp, dp,da D, p,a, u=0

b

Fig 70 Change of state properties as the wave propagates

 

This wave disturbance produces a change in properties as shown in figure 15
and induces a flow. We will now develop the relations for the change in
properties.

Consider a single element of uniform cross sectional area A. The direction of the
induced flow is opposite to the direction of the travelling wave, as this is an

expansion wave.

 

p ——>

‘<—>—>

 

-a.At
!——~

 

 

Using the mass balance relationship we get

Am=Am —Am,.,,

01”

— a.dp.Ar = du.(,0 + dp).Ar —- O

From the differential form of the isotropic relations we get

23

dp_ 2g
,0 K—la

 

Using these relations we get

 

du = — da

K-l

Integrating this we have the following equation

 

u + a = Const.

K—l
Now dividing this relation throughout by ac as this will make the representation

and the computation a lot easier.

It 2 a _ Const.

_+ __ _
a0 K—1 (10 a0 [3]

 

And using the following substitutions

a ._.I E
00 170

From Equation 3 and these substitutions we get

K—l

 

A = ——U + C [4]
2
C: Constfl
Where a“ 2

24

Equation 4 is an equation of a straight line which will represent the state
properties change as it moves from one point to other. Also from the

substitutions, equation 4 can also be represented as

Ir—I
P2” :_K—IU+C0nst K—1 [5]
2 a0 2

 

To find out the constant part we find out the conditions when U=O, also we will

 

 

make another substitution P, = 11*-
P0
80 equation 5 becomes
5: C t K—l "
P 2K : OHS : Pflzr
a0 2
P 3“ = ——2 U + Pf [5]

Equation 6 is also an equation of the line of the form y=mx+C, where m is the

slope of the line. And it can be represented as shown

25

 

 

 

 

/\
V

 

Fig 71 State Diagram depicting the expansion wave

Figure 16 shows the line of equation 6 with the slope. In the similar derivation,
the line for compression wave with the induced velocity in the same direction can

be depicted with a positive slope. The derivation is similar and can be written as:

K'-I x—l
P 2x : £;_lU + P712“. [7]

Note the sign change of the slope. Now we have the basic understanding to

develop the characteristic lines on a state diagram.
3.1.2 Generalization of the characteristic lines

We can now generalize the characteristic lines in all four quadrants of the state
plane. The following diagram depicts all four quadrants. The initial conditions in

the tube are taken to be po=pA=1 bar as shown by [0, 1] on the abscissa. This

26

diagram gives us clear information about the direction and properties of the wave

propagating in any particular direction.

 

 

 

 

 

 

 

 

 

 

A
“- Quadrant 5:11 l. Quadrant
P .x
tar/N me
‘— —>
u u
< [0.1] l >
.U :
: U
III. Quadrant __________ I B N. Quadrant
\ _u+
Q U
a
a

 

Fig 72 State Diagram depicting compression and expansion waves in all four quadrants

i

The direction of ‘u’ indicates the direction of induced flow and the direction of ‘a
show the direction in which the wave is propagating. The case talked about
earlier is shown in quadrant IV, which shows and expansion wave travelling left.
The point B will depict the flow velocity and pressure at that instance. The other
properties can be computed if we have the knowledge of these state properties.

Quadrant I shows a compression wave travelling right and the induced flow in the

same direction, right. Quadrant II shows the compression wave and induced flow

27

in the same direction but travelling towards left. Quadrant III shows an expansion

wave travelling towards right and induced flow in the opposite direction.
3.2 State Diagram of the wave disc engine

Now we will be representing the wave disc cycle on a state plane and then

formulate it in a mathematical form with the technique discussed earlier.

The state diagram of the wave disc engine, figure 18 depicts in a legible form the

r—I
dependency between normalized pressure (p/p0)7 and normalized induced flow

velocity (ll/£10) . Positive flow velocity means flow direction to right [13, 14]. The

lines, so called state characteristics, within the axes of normalized flow velocity
and normalized pressure show the changes in the state within the disc channels
between boundary conditions represented by lines of Air Inlet (Al), and Exhaust

Outlet (E0).

28

x-I

 

 

 

 

W“
Pb \ 1
E1
\8
\ \6/ \4/ 2 no
\ /\ /\
[0.1] -—c3—E4-c2-—Ea—c1 £2 : u
V \l
--------------- . a0
/7\ /.\ >3<
'A.I

 

Fig 73 State diagram representing the wave disc engine cycle

Using this diagram it was possible to analyze the interdependency of the
velocities and pressures of each of these zones by varying any one of them. The
slopes of the state characteristics have been set according to the K and
temperature of the fluid that the wave is propagating through. For our
calculations we have assumed ideal gas conditions and for channels with both

gas & air and with just gas, we have used a correction factor.

The process begins at State 1, which is just after combustion and the fluid is at

zero velocity. The expansion wave E 1 travels from left to right with a negative

29

slope and changes the properties from State 1 to State 2. At State 2, it reaches
exhaust outlet boundary conditions and the second expansion wave, E 2
originates and travels towards left side. As it reaches the Air Inlet port a
compression wave C 1 starts and travels to the E0 with a negative slope. Due to
the high strength of the first expansion wave the net induced velocity will
continue to cause scavenging and help suck in the fresh air fuel mixture charge
in. For the ease of simplification we will assume the ‘K air’ for the fuel air mixture.
A5 C1 reaches E0, the third expansion wave E 3 begins traveling left with a
positive slope. These wave exchanges takes place till state 7, where the air inlet
port suddenly closes and a strong compression wave travels towards exhaust
outlet. This is state 8. This closing is so timed so that the channel is now just
filled with fresh air fuel mixture, compressed by C 3 and ready for the constant

volume combustion.
3.2.1 Governing Equations

Change of state (see Fig. 18) by this and also by the subsequent waves has
been described using method of characteristics as described earlier, by applying
the relationship between state quantity (local speed of sound) and the flow

velocity in the well known form :

 

daziygldu [8]

For the change of state by expansion wave propagating between states 1 and 2
and travelling towards the right can be shown by using the normalized state
quanfifies:

30

_____..__=______.__ [9]

For a wave propagating between State 1 and 2 and travelling towards the left

follows:

an 2 00 a0 2

As pressure waves work on the same theory as expansion waves, we can use

equation [8] — [10] to describe the pressure wave propagation as well.

Owing to the low pressure ratio between the states, both pressure waves and
expansion waves are weak and hence the waves were computed using method
of characteristics. Equations [8] — [10] are written for waves propagating only in
air. Nonetheless, in the wave disc engine the pressure or expansion waves
propagate in mediums of different temperature and composition (hot exhaust gas

and cold fresh air).

According to [8] and [10] the state characteristics — (see equation [8]) - for wave

propagating in exhaust gas yields to:

yin—I
d £11)”, =iy“’_1-"Oa~ .78“‘d( u ]

pO 2 aOgas yar'r aOair

 

 

 

[11]

From Eq. [11] follows that the magnitude of the induced flow velocity differs for

gas and air. In the introduced algebraic code, if the waves propagate both in gas

31

and in air the average of the induced flow velocities has been used for estimation

of the flow velocity in particular state.

3.2.2 Calculation of the Gas Air Interface

The code calculates the position of the gas-air interface at all zones which helps
analyze the scavenging ability of the design geometry and the operating
conditions. For example, to calculate the position of the interface in the HP
region, we know that the flow velocity for both mediums (air and gas) are the
same but the local speed of sound varies with temperature and thus influences
the wave propagation speed in different media.

The analytical code is based on these equations and the results will be presented

in the results section.

3.2.3 Boundary conditions

For the inlet and outlet of channels a quasi steady consideration has been
applied, i.e. it was assumed that a fast running wave will create a steady state at
the inlet and outlet ports, [13] .In the state diagram, figure 18, it is represented as
an intersection point of state characteristics (non-steady flow or the expansion
and compression lines) and equation of boundary condition (steady state flow).

It was assumed that at Al, the flow comes in from a reservoir or zero velocity,
and using the energy balance between the zero velocity reservoir conditions and
flow speed conditions inside the channels, the following inlet boundary condition

was used.

32

a 2 a 2 7 1 2
_1 = _2 _‘_. ”_2
[do] [‘10) + 2 [“0] [111a

which is an equation of an ellipse and can be seen as the Al condition in the
state diagram, figure 18. For the outflow boundary condition from the channel, it
is assumed that the wave reflects from the constant pressure at the end opening,

i.e. the fluids assume the constant static pressure in the outflow ports.
3.3 External combustion wave disc engine; an overview

The engine has only one rotating part, a compression-decompression disk and a
combustion chamber. In figure 19 a double port set with two parallel operating
combustion chambers with one step compression is shown. Arrows in the figure
explain the used flow field scheme. According to Epstein [1] and Frechette [10]

the motor—generator can be integrated within the engine.

Fresh air inlet

  
 
  
 

Exhaust gas outlet
, from combustion

Compressed chamberA
air port -
5 Combustion
Low pressure ’ chamber 8
exhaust gases,

 

 

Combustion — Exhaust gases
chamber A
, — Compressed air
"~ Fresh air
”'9" ”"3“" ”d Wave disk

"’9" mm‘” 9°“ electric generator

Fig 74 Possible construction of the single-stage compression wave engine in reverse-flow
configuration, [1 1]

33

The working principle of the single stage compression wave engine is neatly

described using the wave diagram in Figure 20.

A akin-I.
(a/a”)

 

 

 

 

Fig 75 Single-stage compression wave engine scheme in reverse flow configuration, [11]
The flow scheme of an external combustion wave engine is based on the wave
diagram shown in figure 19. On the left-hand side of the drawing, a schematic
wave diagram with positions of all ports is presented with the corresponding state
plane on the right-hand side. Flow parameters in areas on the wave diagram,
separated by waves, compression and expansion, are constant and are
described by the corresponding points on the state plane.

Numbers in wave diagram areas have equivalents on the state plane. Expanded
exhaust gases are rejected to the atmosphere (area 1) generating an expansion
wave inducing inflow of the fresh air (area 2). Fresh air is compressed (area 3) by

the high pressure hot gas from the combustion chamber. Compressed air

34

(area 4) is delivered to the combustion chamber. After heating in the combustion
chamber the hot mixture of air and exhaust gases is used for fresh air
compression and after expansion is rejected to the atmosphere.

The single-step compression reverse-flow wave engine configuration shown in
figures 19 and 21 was the first one considered. In figure 21 the exploded view of
the main wave-engine components is shown. Rotor diameter is 30 mm, [11].

The engine case can be prepared as a three part set. The most complicated part
contains the basic plate with all port arrangements. The second part forms the
combustion chambers and outflow mufflers. The third part is only the cover with
air inlets and exhaust gas outlets. The wave disk can be formed from two parts
etched together. The engine has only one rotating part, a compression—
decompression disk. The electric motor-generator can be imprinted in the case
part containing ports and in one of parts forming a wave disk as is shown in

figure 21.

   

Fig 76 Exploded view of the wave-engine construction, [11]

35

Other wave-engine constructions have also been considered. A wave engine can
also be built in the through- flow configuration. Higher engine efficiency can be
realized in the two step compression configuration. Double-stage compression

devices were considered and a detailed design is presented in figure 22.

exhaust gases from comb ustion
P0” " ., chamber ‘.

  
  
   
 
  
  

 

Exhaust gas
outlet

Wave disk _
electric generator Middle pussum
P855390
Compressed ,2 "
air port
= Exhaust gases

  

Compressed air

 

I
High pressure and Fresh air inlet Low pressure
Fresh arr mg" temperature port gfiaust gases

Fig 77 Details of the two-step compression wave-engine construction, [11]

In the proposed solution on the outer side of the wave disk the high pressure gas
port (port B), two middle pressure gas ports (inlet (port A) and outlet (port C)
connected by a passage, and low pressure gas outflow port (port D) are located.
The high pressure air port (port E) and low pressure fresh air port (port F) are

located on the inner side of the wave disk. In such a configuration the fresh air

36

enters the cell with pressure and velocity described by the position of point 9 on
the state diagram, then air is compressed to state 1, on the state plane, by the
middle pressure gas entering the cell from the middle pressure passage with
parameters described by point 6, and air is finally compressed to state 4 by the
high pressure gas. Air compressed twice to the high pressure is delivered to the
combustion chamber.

After mixing with the fuel it forms the mixture which is burned inside the
combustion chamber. Hot, high pressure gases leave the combustion chamber
and enter the cell at state 3 realizing the second step of air compression. Then
exhaust gases leave the cell and through the medium pressure passage (state 6)
enter the wave disk cells again (state 1), realizing the first stage of air
compression. Exhaust gases finally, after decompression, leave the cell to the
exhaust port (state 8).

The port’s geometry and flow diagram are developed in such a way that hot
gases are concentrated near the outer part of the wave disk and cold air
concentrates near the inner disk part. On the one hand such a configuration
generates non uniform temperature distribution and thermal stresses in the disk,
but on the other hand it reduces the heat exchange between disk walls, cold air
and hot gas. Generally this flow arrangement can be classified as the reversed
flow configuration, [1 1, 14].

The flow scheme was matched to the radial wave rotor geometry used in the
proposed solution. It was assumed that centrifugal forces can improve the flow

during the scavenging and slightly disturb the compression process. There is

37

enough energy during the compression process to overcome the negative
influence of centrifugal forces. The energy available during the end of the
scavenging process is not sufficient to completely remove exhaust gases from
cells. In that phase of the flow, centrifugal forces act in a way that improves the
scavenging process in the proposed configuration.

For the combustion modeling compressed air leaving the wave disk through port
E (figure 19), located on the inner disk side, is delivered to the combustion
chamber, then heated and returned to the cells of the wave disk through port B
(figure 13), on the outer side of the disk. The pressure and temperature in the
combustion chamber can be calculated from the energy and continuity equation

and equation of state:

’7

 

 

 

 

 

{ KRT’air “ii-fr Vain \
pairuair Eur + +
dp _ K—l K—1 2 2
7i;— V KRTGS “2m [12]
com]? p gas“ gas Fgas K 31 + 3 ]+ Qromh
k 7 7
dm m
dt _ _l0airu air air — pgasu gas Fgas [13]
T_ p Vc_o_mb
Rm [14]
Vcomb

The flow scheme in this kind of micro-engine was designed to generate a net

power. In the proposed engine version, [11] only straight cells are used. All ports

38

in which the flow is in the disk direction are expected to be equipped with vanes
directing the port flow almost tangentially to the disk.

From the equations of continuity and spin conservation the torque can be
calculated. Only in a relatively narrow range of engine port geometry and

rotational speed may positive torque and power be generated.

39

CHAPTER 4 COMBUSTION AT MICRO SCALE

The internal combustion taking place inside the channel is occurring at a micro
scale. This chapter will deal with the issues and approaches surrounding this
complex phenomenon. The concept behind this new field of high-specific-energy
micro-electro-mechanical power systems is to utilize the high specific energy of

liquid hydrocarbon fuels in combustion driven micro-devices to generate power.

Specific Energy

160 KIIo:]oulosIgram(|tjlg_)

 

 

 

Fig 78 Specific energy for different energy producing devices, [15]
Liquid hydrocarbon fuels have extremely high specific energy, (typically 45

MJ/kg) as compared to 1.2 MJ/kg for a lithium or 0.6 MJ/kg for an alkaline

40

battery. These miniature combustion devices with just about 3% efficiency would
compete with top batteries simply from the fact that the fuel is easily replaceable.
Although higher efficiencies are needed for combustion systems to displace
batteries, the high efficiencies obtained in large-scale power systems encourage
the development of miniaturized power generation devices using combustion,
with the expectation that devices with competitive efficiencies can be developed.
Another interesting and attractive aspect of miniaturization is the batch
fabrication capabilities availability of MEMS using rapid prototyping techniques
with their mass production and low cost characteristics, [15].

The power-generation devices addressed in this chapter are those that aim to
generate power in the range of a few watts to milliwatts. This is in contrast with
the so-called micro-turbines [1], which generate power of the order of kilowatts
and are not “micro” in the present sense but rather in the sense of being smaller
than their larger counterparts. Power generation in the watts range has multiple
applications, such as electronic devices (laptops, phones, etc), and miniaturized
mechanical systems (small robots, rovers, airplanes, etc.). The corresponding
combustion devices are of the order of one centimeter in size (meso-scale), and
their micro-fabrication techniques are relatively conventional (EDM), in some
cases with some MEMS components. Power generation in the milliwatt range
(micro-scale) has its application primarily in micro-electronic components
(sensors, transmitters, etc), with the ultimate goal of incorporating the power-
generation device into the micro-electronic component. These power generation

devices are constructed using primarily MEMS. The ultimate goal is to have

41

“power generation in a chip”. The system would then incorporate in the same unit
the power device, the microprocessor to control the overall system, and some
sort of sensor/emitter or actuator, [15].

Small-scale combustion has other useful applications than power generation and
heat production for use in power cycles. Positioning of localized heat is an
important example of its potential applications. Another interesting example is the
use of arrays of meso-scale burners to produce distributed combustion in large
scale gas turbine combustors, which has the potential for inter-turbine reheat,
and for premix or highly vitiated combustion, to reduce NOx [16].

We will now discuss some thermo-chemical and technological issues for power

generation devices.

4.1 Thermo-physical Aspects of Micro combustion

The characteristic length gives a measure of the average distance that the
products of the burnt fuel must travel to escape. In the present available designs,
this length is sufficiently larger than the than the molecular mean-free path of the
air and other gases flowing through the systems that the physical-chemical
behavior of the fluids is fundamentally the same as their macro-scale
counterparts. For example, the Knudsen number for air flowing through a 0.1 mm
wide channel is of the order of 103, which is much smaller than that for free-
molecule flow (Kn >1), [15]. So we are led to believe that standard no-slip

condition and the continuum hypotheses will still apply.

42

However, the small size of these devices causes some scaling issues which
causes some interesting changes to particular characteristics of fluid mechanics
and heat transfer.

These can be understood by normalizing the conservation equations of
momentum, energy and species in terms of the characteristic length and

parameters of the device and analyzing them as the length scale is reduced, [15].

 

 

 

[C a; -du_ pc 1519+ 1 —82u glc
—-+“ “ 2+ 2 [15]
Au. 3: ax p.143 pax NRC a? u.

 

 

 

 

 

 

1, a? —a_7_’__1—827 Q :—
—-_—+u a _2+Da_ w [16]
tcuc at 8x Pe Bx p C
[C 9:)“ +—ay__i_ 1 _azyi I -—II
— D _2 +Da—W [17]
Ice“ at ax L€Pe ax yIC
T —a’F
‘a—_=F0as _: [18]
at ax

Equations [15-18] gives the normalized form of the governing equations for the
gas and solid phase. Large power systems have large characteristic lengths and
generally the Reynolds (Re) and Peclet (Pe) numbers are also large. Thus the
fluid flows are mostly turbulent, and as seen from Equations (15 -18) the viscous
and diffusive effects are small compared to the convective effects. It is also

deduced that the characteristic time in these convective dominated flows is

43

C [19]

which is normally referred to as the residence time, [15]. As the size of the
devices become smaller, the character of the governing equations and the
importance of the different terms in the equations change. As the characteristic
length of the device is reduced, the Reynolds and Peclet numbers decrease and
fluid flow tends to be less turbulent, so the viscous effects and the diffusive
transport of mass and heat become increasingly important. From the combustion
stand point , an important issue is the magnitude of the residence time, because
it as the scale decreases, the magnitude of the residence time also, and it always
has to be larger than the chemical time for complete combustion.

For MEMS devices the flow is primarily laminar. As seen from equations (15 —
18), the viscous and diffusive effects dominate while the convective effects

become negligible. So the characteristic time becomes:

[2
I“:7Pe:a [20]

C

 

also called the diffusion time. Species mixing would primarily be done by
diffusion as the flow is primarily laminar and turbulent mixing is very small. This
makes diffusion time important as it has be lesser than the residence time in
order to have complete combustion.

Fourier number characterizes thermal diffusivity in the solids and it is given by

asctc
F0 = ‘72— [21]

44

Fo increases as the length scale is reduced. The characteristic time of the heat

conduction in solids is given by

 

sc [22]

The thermal diffusivity of proposed MEMS materials (typically Si, SIC) is of the
same order as that of air and gas. Air at 300 K has a thermal diffusivity of
0.000024 mz’s'1 while thermal diffusivity of Silicon at the same temperature is
0.00008 mzs". This factor is important as it has implications in heat transfer
behavior between gas to, or from solid especially if there are periodic heat fluxes
at the boundaries with characteristic times different than the diffusion time.

It can also be deduced that as the length scale becomes smaller while having a
constant wall and flow variables, the velocity gradients, wall frictional effects, gas
temperature and species gradients at the wall increase. In micro devices it’s
tough to keep flow velocities, temperature and mss concentration differences or

the same magnitude as compared to larger devices.
4.2 Fluid flow in micro devices

Typically, Reynolds number characterizes fluid flow in most engineering
applications. In micro scale devices Re is relatively small. This is due to the
smaller channel cross sectional areas for fuel intake, exhaust and in micro
combustors the actual size of the combustor. As computed in [15], for a 100 W
meso-scale device using a stoichiometric mixture of octane/air and with a system

efficiency of 10%, the volumetric flow rate of gaseous mixture to be 0.4 US and

45

assuming a 5 mm diameter intake tube, the Reynolds number will be of the order
of 5000 or below, depending on the gas temperature. Similarly, for a 100 mW
micro-scale device with a 0.5 mm diameter intake, the Reynolds number will be
around 50. Since below 5000 is considered laminar, the mixing of species would
take place primarily by diffusion.

Frictional losses in the channels would be high due to viscous effects and the
large aspect ratio of the micro-channels. This is experimentally studied in detail in
Chapter 6. But on the other hand, the high viscous forces can help reduce the
leakage through moving interfaces. This factor becomes increasingly important in
internal combustion engines like the IC WDE, as their efficiency is dependent on
the compression ratio.

Like macro scale combustion, even at micro scale, ambient air is the source of
oxygen for hydrocarbon fuel combustion. The fuel must be vaporized and mixed
with the air prior to entering the combustion chamber or the microchannel in
premixed system or have direct injection in non premixed combustions systems.
Previous studies have observed that the phase change in a micro scale channel
takes place suddenly an in an unstable way, [17]. This could be due to the large
surface area to volume ratio in micro-channels that enhances the nucleation and
wetting effects at the wall, and to the behavior of bubbles that is strongly affected
by the small length scales and significantly differs from macroscopic behavior,
[15]. Atomizing the fuel before it is injected into the combustion chamber is a
solution to increase fuel evaporation. But this adds the pressure and energy

requirements on the system. MEMS scale atomizers have been developed, [18]

46

but more sophisticated devices would be needed to produce micron size droplets
that will evaporate and mix with the air in the available micro-scale residence
time, [19].

Mixing is an issue in the micro scale combustion, with diffusion causing the major
part of the mixing. But since the residence time of the mixture is really small,
diffusion alone may not be sufficient to cause proper mixing. Different dynamic
approaches like flow instabilities and ultrasound, [20, 21] may have to be

implemented but this leads to fabrication and design complexities.

4.3 Thermal and heat transfer issues in micro-combustion

As the characteristic lengths are decreased the temperature gradients become
higher. This makes heat transfer by conduction through the gas to the
surrounding surfaces and by forced convection in the intake and exhaust
channels and in the combustion chamber a significant issue. In micro-scale
devices the surface to volume ratio is high, which combined with enhanced heat
flux, results in heat transfer effects becoming very important at the surface or
boundaries. This is a disadvantage for combustion chambers or channels as it

deters their performance due to surface heat losses and wall quenching.

Heat flux from the flowing hot gases in the combustor channel to the ambient air

can be computed using this simple 1-D steady state computation

47

 

A l l c. 1 [23]

 

 

 

From equation 23 we see that large thermal conductivity of the structure (SIC)
the solid conduction terms is very small and negligible at these small scales, also
conduction through air is small compared to radiation.

Preheating the mixture will help in sustaining combustion in lengths smaller than
quenching distance but it may also result in auto ignition at the inlet port. Also,
preheating reduces the mass charge density of the incoming charge thus
reducing the potential net power output of the device.

Because of the small size, most micro devices operate at a relatively uniform
temperature. Due to this reduced thermal gradients, we have reduced thermal

expansion stresses and subsequent misalignments in moving parts.

4.4 Combustion at micro-scale

The basic condition for combustion to take place at a micro scale is that the
physical time available for combustion, also called the residence time must be
larger than the time required for the chemical reaction to occur i.e. combustion
time. In case of closed systems like the internal combustion engines, the size of
the chamber as well as the rpm of the engine determines the residence time. For
micro scale combustion, small chemical times are needed which could be
attained using high combustion temperatures. This can be achieved by

minimizing heat losses, pre Increasing the reactants temperature, using

48

stoichiometric mixtures or by using high energy fuels which might be a bit more
expensive.

Due to a decrease in combustion volume and scale, the surface to volume ratio
increases which increases the surface heat losses and causes the waste of
radical species at the wall. These factors could lead to quenching and various
thermo chemical techniques like the use of excess enthalpy combustors, having
insulated temperature boundary condition, establishing high temperature ceramic
walls and using surface coatings, [23, 24, 22] could help overcome quenching.
Higher operating temperatures of the combustion channel walls helps reduce the
chemical time and thus reduce quenching [15]. Ceramic materials like $102, SiC,
Si3N4, can withstand temperatures of around 1700K and this makes them an
excellent candidate for micro combustion or micro channel materials. Also the
smaller size and compactness reduces the chances of fracture.

The quenching distance magnitude reported in the literature is considered often
as the limiting scale for micro-scale combustion. “T his is a conceptual error,
because the quenching distance depends on the reaction rate, and thus on the
temperature, species and radical concentration (it is related to heat and radicals
losses to the wall). The problem of wall quenching can be reduced or prevented
by increasing the wall temperature (the quenching distance is approximately
inversely proportional to the square root of the temperature), or equivalently
preventing the heat losses to the wall (adiabatic wall)”, [15].

Additional time and volume would be needed for fuel evaporation and mixing if

the fuel is not premixed and if the fuel is liquid. This is an important factor since

49

we are moving towards miniaturization. As compared to the gaseous premixed
residence time, the time can be more because of the evaporation and less mixing
due to smaller Reynolds number.

Some interesting alternatives to spray combustion are been researched. They
include the concept of burning the liquid fuel while forming a liquid film along the
wall of the combustion chamber or channel, [25]. The wall film reduces heat
losses from the combustor (a channel in our case) as it keeps the combustor
walls at a lower temperature (liquid boiling point), while reducing wall quenching.
While designing for micro combustion one should realize that although the
increase of the surface to volume ratio of the channel or the combustor favors
catalytic combustion over gas phase combustion. “Although the catalytic reaction
is generally slower than the gas-phase reaction, and surface heat loss is a
problem that also affects the catalytic reaction. The relative increase of surface
area and the lower temperatures of the catalytic reaction suggest that micro-
scale combustors using catalytic reaction may be easier to implement than those
using gas-phase reactions”, [15].

The potential solutions for the shorter residence times and lower temperatures
could provide us with some operating models but a more thorough understanding
of low temperature chemical kinetics is needed. Development of highly energetic
reactive fuels could also help achieve this goal.

Even though the field of micro scale power generation by using combustion is
relatively new, different research groups around the world are well advanced and

the state of art is available widely. Some of them are shown below

50

TE Generator

    

 

 

(b)

Fig 79 (a) Integrated catalytic combustor-thermoelectric micro power generator, [26], (b) MEMS
fabricated array of “Digital-Propulsion” micro-thrusters, [27]

51

CHAPTER 5: 2-D NUMERICAL SIMULATIONS AND DESIGN

VERIFICATION OF A WAVE ROTOR

This chapter discusses the numerical design verification using the commercially
available Computational Fluid Dynamics (CFD) software FLUENT®6.2. The
researchers at the Turbomachinery Laboratory, Michigan State University
College of Engineering have been working on manufacturing a Wave Rotor Test
Rig, a California department of energy grant project. As a part of this project, a
universal analytical design procedure for pressure wave machine or the wave
rotor to enhance gas turbines and internal combustion engines in a topping or a
bottoming cycle has been developed. This is done by Ludek Pohorelsky and
Pranav Ajit Sane, two researchers at the Turbomachinery Laboratory, MSU. As
verification for the porting angles, which were a result of this code, a numerical

solution was developed in order to verify the results.
5.1 Wave Rotors

Unsteady flow devices have been around for a while and widely studied. But the
design process of such machines is quiet complicated and intensive. The
dynamic pressure exchange taking places due to unsteady flow conditions
causing pressure wave and expansion waves yields higher compression
efficiencies and also improves the overall efficiency. The construction of a wave

rotor involves an array of channels arranged around the axis of a hollow

52

cylindrical drum. As shown in figure 25 , this channel drum rotates between two
stationary end plates or in some designs the end plates rotates around the
stationary rotor. Depending on the design and type of cycle each endplate has a
few ports or manifolds, controlling the fluid flow through the channels. As the
rotor rotates or vice versa, the channel ends are periodically exposed to differing
port conditions like pressures and temperatures, initiating compression, and

expansion waves within the wave rotor channels.

' Hpgfrst‘k'i 21"." w

 

Fig 80 Schematic showing the rotor and ports, [6]
The number of ports and their positions depend on the type of applications and
flow conditions and thus has to be computed precisely for each specific
application. By carefully selecting their locations and widths to generate and
utilize wave processes, a significant and efficient transfer of energy can be
obtained between flows in the connected ducts. Thus, pressure is exchanged
dynamically between fluids by utilizing unsteady pressure waves. Wave rotor

accomplishes compression and expansion within a single component as

53

compared to the steady flow turbomachines. Since such devices are very
sensitive to back pressures, the port timings are very crucial. Also to reduce
leakage the gap between the channels and the end plate has to be minimal but
without contact with the rotor under all operating and thermal expansion

conditions.

   

 

r End Plates with
Inlet and Outlet
Pons

 

 

 

Fig 81 A 3 D model developed in Catia to model the wave rotor test rig. Showing the arrangement
of face plates and rotor over a shaft, [28]

The figure shows a 3 D model of the wave rotor and face plates assembly over
the shaft. The wave rotors have two basic flow configurations, through flow and
reverse flow. This project has been based on the through flow design as shown
in this figure with air outlet port and exhaust outlet. For this configuration air and

exhaust gases enter from one side while the other side has the high pressure air

54

and exhaust gases leaving the system. More details are widely available in the

literature, [6,8,12].

5.2 Formulation of the Analytical code

The analytical code for the 1 D through flow wave rotor model was based on
shock wave theory and linear gas dynamic principles. The through flow wave
pattern is shown in the figure which has the channel length as the ordinate (x
axis) and the time is projected on the abscissa (y axis). The design of porting is
based on the understanding of the expected wave pattern which in turn depends
on the operating conditions.

As this was a through flow configuration, the flow area was divided in two zones,
high pressure zone (HP) and low pressure (LP) zone. For development of the
code and for better understanding of the flow zone, this area was further divided
into ten zones, [28]. An expected pattern of wave flow has been visualized they

have been explained.

55

 

 

 

 

 

 

 

Fig 82 Wave Patter in a through flow wave rotor configuration, [28]

l- Zone of the rotor filled with ambient air or a mixture from the previous
cycle. This is the initial stage of the through flow cycle.

ll - Zone created by the first shockwave (S1) which propagates due to the
high pressure at the exhaust inlet (El) port and travels towards the air outlet (AO)
port.

56

Ill - Zone created by the second shockwave (S2) which increases the Zone lll
pressure and propagates from the AO port to the El port

IV - Zone created by the first expansion wave (E1). This zone separates the
HP region from the LP region after the first expansion wave, E1. The air-gas
components of the zone expand to the zone pressure due to E1.

V - Zone created by the second expansion wave (E2) which is created by the
sudden opening of zone IV to the E0 port. E2 propagates in the low pressure
region from the E0 port towards the Al port.

VI - Zone created by the third expansion wave (E3). E2 rebounds at the air
inlet (Al) port and propagates towards the exhaust outlet (EO) port as a weak
expansion wave.

Vll - Zone created by the first pressure wave (P1) which is a low strength shock
wave. As the returning wave E3 opens directly into the E0 port, it returns as a
weak pressure wave P1.

Vlll - Zone created by the fourth expansion wave (E4). Because the Al port is
still open, P1 is reflected as E4 and propagates from the Al port to the E0 port.

IX - Zone created by the second pressure wave (P2) which travels from the
E0 port to the AI port due to similar interactions as before. Pressure and
expansion waves in low pressure part are weak.

X - This zone is created by the fifth expansion wave (E5). The mixture of fresh
air and exhaust gas expands through E5 to reach the same condition as the
beginning of the cycle. If any exhaust gas recirculation is present from the

previous cycle, it is exhausted to the AO port.

57

For the analytical model, the governing equations were the normal shock wave
relationships and methods of characteristics expressions as developed in section
3.1.

The shock wave relationships for the pressure ratio, f'ls between two zones were:

_ p behind shockwave _ p”
”s - - [24]
p ahead of shockwave pl

 

The local change of temperature across two zones was given by:
K \
+ 1
7 + 71' s
T, y — 1

[25]
T” 1+[7+1]fls
\ 7-1 7

with the local speed of sound being

 

 

 

 

 

 

yRT [26]

From there relationships we can find the induced velocity of the fluid due the

3% -1) I i/yfl) [27]
y V775 (y 1/(7+1)i

and the shock wave velocity is given by

W, = a\/l + ((71' 1X45 ’ 1)ij [28]

The assumptions behind this code were

shock wave is

 

L15:

 

 

58

- Isentropic flow behavior

- No heat transfer through the walls

- Fixed initial pressure and temperature at the start of the cycle

- Flow direction to be normal to the ports

- No leakage

This made us achieve higher than practically possible results but gave a quick
method to develop the porting design.

According to the code, the following porting angles were arrived by using the
following boundary conditions:

P1: Pressure of fresh air at Al: 0.995 bar

P2: Pressure of compressed air at E0: 1.88 bar

P3: Pressure of exhaust gas at El: 1.5 bar

P4: Pressure of exhaust has at E0: 1.01 bar

Boundary conditions for temperatures were:

T1: 300 K

T2: 600 K

Computed temperatures were:

T3: 1100 K

T4: 860 K

59

 

Fig 84 Outlet side, orange showing the exhaust gas outlet (E0) and blue showing the
compressed air outlet (AO) angle

Figures 28 and 29 showing the porting angles which were used to develop the
10 code and 2D simulations.

60

5. 3 Development of the CFD Model

For the development of the CFD model, this porting geometry was used. This
was laid out on a 2D plane. The length on the rotor was computed from the
average radius of the rotor, 36 mm and the total length of the channel were taken
to be 113 mm. This was divided into 24 channels of 5 mm width each with the
wall thickness taken to be approximately 0.5 mm. The length of the channels was
93 mm. The leakage was 0.25 mm and was divided between the face plate and
the rotor plane, at 0.125mm on each side.

The technique used was straight fonNard. For the rotor channels, a large
rectangle (113 x 93.25) was made and then another rectangle of 0.5 x 93mm
placed in the middle. By default GAMBIT places this rectangle at the origin. Now
this smaller rectangle (wall thickness) was placed 26 times along the length of
the bigger rectangle at a gap of 5mm which was the assumed channel thickness.
Please note that the default unit of scale in GAMBIT is meters but since we will
later be scaling the model in FLUENT into millimeters, the description given here
is in mm’s. These channels are then subtracted from the bigger area to give us
channels and a 0.125 mm leakage on both sides.

The mesh was developed on the FLUENT preprocessor, GAMBIT. For the
meshing, pave style technique was used, with the interfaces being much finer as
compared to the center of the channel.

The operation modeled is a periodic process. For this, prior to the meshing, the
periodic edges on the left end plate, rotor channel, and the right end plate were

first linked. After meshing, appropriate boundary conditions were given. For the

61

periodic boundary conditions, the two linked edges have to be selected together
and assigned the periodic boundary condition. When giving the interface
boundary condition, we just have to be careful while naming, as a mistake while
selecting the interface in FLUENT could give us errors.

The El and Al were given the pressure inlet conditions at the port edges and the
port length corresponded to the porting angles given by the analytical code team,
Pranav and Ludek, reference. The distance of the port edge to the interface was

kept small as to minimize the pressure drop across that distance.

62

 

Fig 85 A 20 grid showing the channels and the porting.

63

 

 

 

 

 

 

 

 

 

 

 

 

L} -
.i
L}: : z :
L
I T T .77
r“ 7 A i
I A .
[a . ,4 7 4
(a)
L ' . u ' :
4 _ > . 4 .
‘ r I g l
t v I
v I
v I I
. I v
I I . I
. . I .
' t - 1 . A
I
1' 7 T
I
I I ‘

 

 

 

(b)
Fig 86 (a) 8. (b) showing the mesh entry and the leakage area

5.4 Setting up FLUENT simulations

This grid was then exported to FLUENT solver. A 2D double precision solver was
chosen. The grid was scaled to the millimeter scale. FLUENT is arranged in
such a scale as to go from left to right in order. An unsteady flow, 1st order
upwind scheme with coupled energy equation was selected. Since the analytical
model did not account for viscous effects, an inviscid model was chosen for the
formulation. The boundary conditions were chosen as per the analytical model.
The interfaces were defined as a couple.

The rotor mesh was a moving mesh and had to be given a ‘y’ velocity. This was
computed using the average radius and the rotational speed at which the
analytical model was computed. They were 39 mm and 13,000 rpm respectively
and the y velocity was computed to be 49 m/s.

For the solution, a PISO solver was selected. PISO stands for Pressure Implicit
Splitting of Operators. This is recommended for time dependent problems like
this. The solution was initialized at the ambient conditions prescribed in the
analytical model. The four ports were then ‘patched’ by the initial temperatures
and pressures for cycle initialization.

The time step was chosen based on the commonly used Crank Nicholson
Scheme for Implicit solutions. 10 E-6 was the time step at which different

computations was performed.

65

5.4 Numerical Results

After about 30 cycles, a steady state solution was expected and is presented.
Contours of static and total pressures along with temperature profile showing

clear recirculation is shown.

 

 

 

 

 

I i45e+oz
L_.I .06e+0£
.67e+oz

Fig 87 Static pressure (pascals) contours showing the wave pattern in a through flow
configuration

 

 

66

2 126905

 

_.
no
it’
a
0
0|

3:
O
3

 

 

- 8 8M4
L 8 50e¢04
8 11e+04

 

Fig 88 Total pressure (pascals) contours showing the wave pattern in the channels

1 179*03

 

_.
o
0
ID

6
I»

 

 

 

Fig 89 Static temperature profile showing the flow pattern and the exhaust gas recirculation in the
exhaust outlet, E0

67

m 1 17e+03

l 1 14e+03

 

 

2 92e+02

 

Fig 90 Total temperature profile showing the flow pattern and the exhaust gas recirculation in the
exhaust outlet, E0

The area near the exhaust outlet shows the area of exhaust gas recirculation. It
could decrease the emission NOx because of lower combustion temperature, but
on the other side, lack of oxygen causes problems during ignition of fuel air
mixture.

The wave pattern using the exact same porting and boundary conditions from the

MATLAB analytical code is shown below.

68

x 1.3-3 Wave Diagram

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2.5 I I I l I I
_—-d_’_d_dd—d_'—__ ‘.l‘-
2 b f“—~H‘fi____——_— "do A
a“ 4
E_%_ ‘-O’
“acre—~3—
—__’___——-__#_—.‘+"
1.5 ” 5““!er -
E "1"...“ ____,__——J—'—P—-’_d——:
a". —'—’—_’_
OJ ‘.—_.. 4——f_— .4
E ...k________ . ,,,,, ..
'— E—E " IIII
‘r' a
1 '- E‘h _
0'5 ,- Hfi .‘.' 4
Wha— ,0". 0‘...“
__ ‘ o :. . j
M...“ N ”a :
D‘I-"“- ' FL—
‘O‘HHI :....
0 mil—“'4 4 I I 1 I
-0.02 0 0.02 0.04 0.05 0.08 0.1 0.12

Channel Length [m]

Fig 91 1 D Analytical model results showing the wave behavior , the red dots showing the gas air
interface and the green traces showing the net flow velocities, [28]

This figure shows a very good comparison between the analytical and the
numerical code wave pattern.

Now for another comparison, and to see the flow behavior, we will compare the x
velocities at different port, with the ones developed by the 1 D analytical code
developed in MATLAB.

The results are shown next:

69

-100

X Velocity, m/s

X Velocity, m/s
U1
0

 

 

140

120

100

80‘

60

4O

20

 

 

 

 

—2—D simulation

 

algebraic code

100 125 150 175

 

Fig 92: X velocity comparison of the Exhaust Inlet Port

TT— -'—' -”TTT—T' '7

 

 

 

100

   
  

Porting Angle, Degrees

"—7 ' 7210’ SEE-5&3?
——-—- -*- Algebraic code

 

 

 

 

 

125 150 175

Fig 93: X velocity comparison of the Air Inlet Port

70

X Velocity, m/s

120

80

X Velocity, m/s
5
o o

L
o

-120

 

 

 

 

Fig 94: X velocity comparison of the Exhaust Outlet Port

 

—Z-D s mulatlon
-—Algebrair. Code

 

1

 

 

A ,
I \ I

 

 

I’

 

 

 

0 l0 POFtAngle, 40 b0

Degrees

 

 

 

\

 

Fig 95: X velocity comparison of the Air Outlet Port

71

 

 

The result shows a correlation. Since the FLUENT model is more precise, and
has more data points it gives a nice curve where as the algebraic model shows
linear behavior. The channel walls can be accounted for the erratic behavior as
shown by the FLUENT results.

Figure 37 shows the X velocity pattern over the exhaust inlet length. It also
captures some back flow into the port; this might be caused due to the leakage.
The flow behavior is depicted in the figure below. The vectors plotted here are
the velocity magnitude and should be interesting to see how they compare with
the X velocity plots. Near the top edge of the port some circulation is clearly

visible.

c.27e+02 ' ' '. 1 I

 

 

Akhhkhhh
O
N
x‘
\ .
\
\
\\

2
o
+
o
N
\\ \
-e\
43:
i
/
,/
/
/
/

._ . :’/
- +
...e L\\'\:|l‘,//IIII//

 

N

.4
0
+

O

M
-_4_

‘53

Q

3
I‘/

x“ I/////////,
%;,//,,,

yer/:27 '
M

V
5
o

+++
o
N

[I

 

llllll

 

 

l."
e
§§§
ll
\1

 

_‘._

Fig 96: Velocity magnitude vectors showing the backflow in exhaust inlet port
The air inlet port comparison, figure 38 shows similar results. Higher X flow

velocity near the beginning of the port but it steadily falls down as the port is

72

closing. Figure 39 shows a close correlation between the two results. The flow
velocities steadily decrease across the Exhaust Outlet Port. Strong exhaust gas
recirculation is visible across the edges of the Air Outlet port in figure 40. This is
seen from the negative x velocities, showing the flow going back into the

channeL

5.5 Approach for modeling the Wave Disc Engine

The techniques from the wave rotor simulations can be extended to develop the
wave disc engine CFD model. As a wave disc engine also has periodic unsteady
flow, the same principle can be applied for modeling. There are just 2 ports
involved in the WDE engine design so that makes it less complicated than the
wave rotor. The most challenging task would be to model combustion in a

rotating channel, periodically.

For now, combustion can be modeled as sudden heat addition (sudden pressure
rise) in the channel. A more precise geometry could be developed in AutoCad
and imported in GAMBIT. In a more sophisticated approach, the channels could
be curved or in the form of spiral. This will increase the channel length. The
curved channel with greater lengths and different angles at inlet and outlet can
be used to extract work and self propel the disc. The varying angles at the inlet
and the outlet have to be precisely computed and modeled. The channel could
also be inclined at an angle with respect to the radii. Some of the different disc

designs and the variation of channel angle is shown in the figure 42 below.

73

 

 

(b)

Fig 97 (a) Examples of some wave discs, (b) Curved channel variation, [14]

The progression of compression and expansion wave can be simulated in exactly
the same way as done for the wave rotor. Modeling of combustion taking place
periodically in a rotating channel should be a much more intensive task. The
porting can be fine tuned using the flow pattern and the rotational speed of the

disc.

74

 

CHAPTER 6 2 PRELIMINARY ANALYTICAL RESULTS FOR

WAVE DISC ENGINE

To develop a preliminary understanding of the wave disc flow cycle and to arrive
at a possible first porting design, an analytical approach was used. This was
done by modifying the wave rotor code for the wave disc engine. Since the most
significant unknown would be the pressure and temperature right after
combustion, a whole range of pressures and temperatures were used to develop
an understanding of the flow pattern. The pressures ranged from 2 - 20 bar and
the temperatures were assumed from 700 — 2000 K. By calculating the induced
flow velocities at every expected compression and expansion state, an estimate
was made of the pressure and temperature range within which we could

reasonably move further in our design.
6.1 Results and Discussion

The results presented below show the patterns of induced flow velocity at
different compression and expansion states, and their behavior at different
temperatures and pressures.

In Up’x’, the x signifies the particular zone in which the wave travels. This is
shown in figure 43. Similar approach has been used to develop the low pressure

part of the wave rotor.

75

Flow velocity, m/s

Time
Roman” Exhaust (3) 7

lllllliiiiiiW///__

 

 

3' X7
f Xb §
\
If kavvdocfly
Inlet (Air + Fuel)

Fig 98 Wave pattern on Time v/s Distance plot

Up5 behavior at different pressures

1800 749~
1600
1400 , ,
1200
1000 §

800 .,

 

600 ‘

 

 

0 fr ,, A *1 ,_ r. v < fl, , » —— ,,, ___E i

 

600 800 1000 1 200 1400 1600 1800 2000 2200
Temperature, K

Fig 99 Temperature and Up5 velocity distribution for various pressures

76

Up6 Behavior at different pressures

600 1 7 ~ ~~~ ~~ ’~-~ -—- ~W__ -u-,44_--__r_h- -

550 ~'-~~ 7 _

 

soo

 

450

 

400 *

350

 

 

 

300

Flow Velocity, m/s

100 z . i I
600 850 1100 1350 1600 1350 2130

l i l

Temperature, K

Fig 100 Temperature and Up6 velocity distribution for various pressures
Up7 Behavior with different pressures

150:, ,1 , ,, ,,

 

Flow Velocity, m/s

 

8 Bar

-1ooI-** , ,. - .
650 900 1150 1400 1650 1900 2150

Temperature,K

Fig 101 Temperature and Up? velocity distribution for various pressures

77

Flow velocity, m/s

1?":

lb

25

'25

-75

-125

Flow Velocity, m/s

Up8 Behavior at different pressures

 

 

 

 

Temperature. K

Fig 102 Temperature and Up8 velocity distribution for various pressures

Up9 behavior at different pressures

 

100 . 7 7 7 77 7 7 7 7
i *1»-.. g
1 r
| — 1“ '—. can.“
so I y “‘7' 7 7 7 —-
i ‘- l \
C. l _. _ _
I
—-2 bar
-100 t m4 bar
" 1.1-5 bar
I Bbar
'ISC' I 1 A -,
i
_ i
‘400 f T” "’1 ‘ " ’ ’ i ’ ' r 1-, "'7 1 ’*' 1, fir .1, *-
600 850 13.00 1350 1600 1850 210(

Temperature. K

Fig 103 Temperature and Up9 velocity distribution for various pressures

78

8, . i 9910 Behayiegat éifiereezezs§§9rss__ -

60 7 7 —, ,Zbar

‘r' —— 4 bar
40 7 7 “:77.“ 12.1,. 777 7 7 7 7 7 7777 7
! 7...: ‘ WP -— 6 bar

-40 L

Flow Velocity, m/s

-60 i

-80 ~,

 

7100 7 7 7 777 7

-120 +- 7 77- 7 7 7.77777 7 7 e
600 850 1100 1350 1600 1850 2100

Temprature. K

Fig 104 Temperature and Up10 velocity distribution for various pressures

The idea of this exercise was to arrive at an intelligent approximation of pressure
and temperature range after combustion and also to understand how the flow
velocities in Al and E0 ports react to the change in these conditions. Up5 values
were expected to be highest as it’s induced by the strongest expansion wave E1.
While observing Up5 and Up6 at pressures ranges 2-8 bar, and temperature
range from 800—1400K, the flow velocities ranged between 200 to about 1000
m/s. Before arriving at conclusions we must understand that this code did not
take into account the work extraction of the system. Nevertheless such high
velocities seemed unrealistic and the range of interest was further narrowed
down. Higher than 8 bar pressures were neglected as the constant volume
combustion at such small scale might not produce pressures of that magnitude.

79

Also, such high pressures will increase the probability of leakage between the

disc and the ports.

Observing Up7 and Up8, figure 46 and 47 we see a drastic loss in the net flow
speeds due to exhaust. For higher temperatures, above 1400 K we see negative
velocities, thus suggesting that to prevent backflow, port has to be closed or
perhaps we can neglect the possibility of having higher than 1400 K temperature
arising in a micro channel. Another observation we see from this plot is that 2 bar
flow velocities are significantly lower than the 4 bar and 6 bar velocities for about
700 — 1200 K range. This could be even lower after accounting for the work

extraction due to exhaust.

Narrowing down our range further to 4 and 6 bar between 800 — 1200 K range,
we observe Up9 and Up10 shown in figure 48 and 49. The flow velocities show a
sudden dip for 6 bar in this temperature range and while accounting for work

extraction, could result in back flow in this zone.

After these observations a pressure of around 4 bars and a temperature range of
800 - 1100 K were taken to be the appropriate conditions after combustion for the
preliminary design of the geometry. Now from these conditions, a gas — air
interface was plotted to arrive at a preliminary porting design. Results are
computed for a 2mm long channel. For the complete temperature range the

interface is plotted for 4 bars and 8 bars. This is shown in figure 50 and 51.

80

0.07 ,7 7 7 77 77 - 1 1 11- 111-111 1
1 Gas air interface for 4 bar post combustion

    
  
 
  

 

006 F pressure
’ |
+X7 Interface Point
.05 7 1 1 , _ .1
E O +X8lnterlace Porn:
‘ I.
.c
E i {a +X9 Interface Pom:
: 0.047 77 7.“ 7 1 , 1
3 I ‘3‘ ., ,
_ I a»... *3“ fl‘ENfi -—X10lnlwfdce PUIIII.
3 “11.7,. "I!
c 0.03 + — ~ —-—— — Htmtflfl 1 _
2 ‘”_.s:‘r
U
002
I $ : ¢ ¢ ¢ ;" A A “ * A A A A A A ‘3‘“. 3‘13}!
am i .7 7 _. . . . .- - .'_.-.' 1'1: '1' ' .Vi1 __,1_1
I
l
01 77 7 e7 77 1-11 11 1.111,

750 850 950 1050 1150 1250 1350 1450 1550 1050 1750 1850 1950 2050 2150
Temperature, K

Fig 105 Gas air interface distribution for a 4 bar post combustion pressure

The interesting observation which can be made from these two plots as we can
see how the interface travels within the channel for a particular range of
temperatures and pressures. The channel length is 2 mm and the interfaces
points for x8 and x9 are beyond the channel length up to 1950 K for a 4 bar
pressure. This means that complete scavenging has already occurred and we
should not be concerned about the wave reflections VII, Vll, XI and X. The
porting design is made accordingly.

But as we see figure 51, we see that for 8 bar post combustion temperature, we
see the interfaces (or the wave reflections) takes place till about 1500 K. The
directions of the interfaces shows us back flow and thus exhaust gas

recirculation.

81

0.09 7 7 777 77 7 777 7—7—777—77777-77-77777777777—7—777-77 — 77

Gas air interface for 8 bar post combustion

   
 
    

 

 

 

008 190155019- 1_ 1 1 1- 1 11 __ _, , ,
0,07 7 ~ 77 7 77 77 7
I +X7 Interface
Point
006 T 7— 7- 7777 77- , 7 7~ 777 77 7 7 7 7 7
l +X8 Interface
‘ Point
“.057 1 1 11 1 111-1
E .
-C’ i
a l
c 0.04 - 7 7 7 7
(D
-‘ |
E
c 0.03 77 77 7 77 7 7
(U
.c ' , J
O ; ‘1‘
0.02 i .111- . -11- 111.... - .. 1. _ 11 1 _ 11L”)‘ 1 . 11- 1-111, 11____ ___1__,_ __ 111111
0.01 7 7 7 7
0 . 7 7
i
-001 41 - .. _1 -111 1 ,. . _,_1_ . r, 1.. ,_ ...1 .11 1- 1 .,__.11 ...11 ,__ . __
700 900 1100 1300 1500 1700 1900

Temperature, K
Fig 106 Gas air interface for a 8 bar post combustion temperature

While designing the porting angles we have to take in to account these factors as
this will affect scavenging and chances of EGR, which in turn will affect the
overall device efficiency. Centrifugal forces also affect the scavenging and a

more sophisticated code should take into account of this effect.

82

CHAPTER 7: FRICTION FACTOR STUDIES IN

MICROCHANNELS

While designing unsteady flow micro devices or MEMS, it is important to
understand the flow characteristics and micro fluidic behavior. One such fluid
flow characteristic is the friction factor. Friction factor calculations were
preformed for three different microchannels machined inside a silicon substrate
and compared with previous work. Experimental results were computed for
pressure drops across micro channels with uniform rectangular cross sectional
area. Channels dimensions were 3000 x 360, 1500 x 180, 750 x 90 with depth
360, all units in micrometer. Deviations of the experimental values are seen for

Reynolds numbers 100 — 1000.

 

(a) (b)

Fig 107 Silicon microchannels: (a) front view, (b) back view, [8]

Figures 52 the channels machines in Silicon and topped with glass. Fig 53

shows some images taken from Scanning Electron Microscope (SEM).

83

 

(C) (d)

Fig 108 Channels visualized with SEM: a) 90pm and 180 um wide channels; b) 360 um and 720
um wide channels, [8]

Some of the first studies on friction factor were performed by Wu and Little [29]
where Darcy friction factors were calculated for microchannels etched in silicon.
The observed friction factors were larger than the predicted by the classical
macro scale theory. The findings here verify these results as the experimental
values are greater by around 22% than the theoretical values for hydraulic
diameters 114um, 240um and 360nm. Standard properties of air were taken at
one end of the channel. The temperature is assumed to be constant throughout
the channel (isothermal flow). This assumption has been made considering the
high coefficient of thermal conductivity of silicon, 148W/mK, although, a recent
study shows no significant effect of heat transfer on the compression efficiency in

silicon microchannels [8].

7.1 Theory

The two non dimensional flow parameters are often used to characterize the fluid
flow are the Reynolds number Re and the Darcy friction factor f. The viscous
effects of the flow are characterized by Re.

84

Reynolds number is given by:

lovavg Dh
0

Re:

The dynamic viscosity was taken to be constant at 25 degrees Celsius.

_4xA

D, P

 

The Darcy friction factor relates roughness effects to pressure drops in ducts and

channels. It’s defined as

 

pVavg
Using this relation and combining it with the energy and the momentum equation
for the fully developed flow, the Darcy Weisbach equation is obtained, which

holds for both laminar and turbulent flow.

h _vamg2
f— thg

 

Solving the continuity and momentum equation, the solution for the laminar flow
in the Hagen-Poisseuille flow problem is found and is commonly known as the
Darcy friction factor [8] as shown.

__ 2D,,Ap
11V 2

avg

f

Analytically the laminar friction constants can be found out using the aspect ratio,

0, which is the smaller of the ratios width/height and height/width so that 05. 0 S1.

85

The friction coefficient C can be represented as a function of 0 by the polynomial

correlation

C = 96(1—1.35a +1.950r2 —1.70a3 + 0.960:4 — 0.250(5)
Where
C = f X Re
The classical theory of laminar flow relates the friction coefficient to be
proportional to the Reynolds number and it’s given by

_64

HT.

7.2 Experimental setup

Ambient conditions were used for the channel entry. Pressure drop across the
channel was determined using the experimental set up shown in Fig. 4. The flow
exit velocity was computed by measuring the volume flow rate of the water.

Estimates of pressure drops can be made using the traditional theory and
correlations. However, accurate prediction of pressure drops in microchannels for

non-slip flows is not yet possible [30].

86

 

"__1 Si Chip with

 

 

 

microchannels
Ambient
Conditions, A I R
F atmospheric WATER
WATER
U Tube with
1"rwater "'" vair Hg

Volume of water collected
and measured

Fig 109 Experimental setup
The results for Friction coefficients C are more conveniently shown using the

normalized friction coefficient

a:

= f Re exp erimental
f Re

 

theorecrical

Entry and exit losses were calculated based on the standard expression for
minor losses in flow. 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

V
AP=kP—2—

87

Where the entry loss coefficient, k is considered to be 0.5 for a contraction with
sharp 909 corners [3131] . The losses were computed as head losses at entry
and exit and the sharp bends using the standard minor flow losses relationships

[32] as shown by the equation below.

7.3 Results

The following table gives the experimental results for the pressure drops, friction
factors, normalized friction coefficients and Reynolds number for all three

channel sizes.

 

 

 

 

 

 

 

 

 

 

 

 

 

m(kg/s) AP(Pa) f 0’ Re
E-6
1.147 3466 0.309 1.326 274
2.057 6933 0.179 1 .375 491
2.403 8532 0.155 1 .399 574
2.403 8532 0.1 55 1 .399 574
2.859 12932 0.151 1.618 683
3.010 14665 0.149 1.674 719
3.307 17732 0.138 1 .714 790

 

88

 

 

3.640 21065 0.125 1.703 871

 

 

 

 

 

 

 

Table 1: Experimental data for the smallest microchannel (750um x 90pm x 360um)

 

m AP(Pa) f 0* Re
(kg/s)

 

4.753 5466 0.090 1.344 946

 

6.369 10398 0.086 1.716 1268

 

6.409 8532 0.073 1.458 1276

 

6.608 14132 0.100 2.067 1316

 

7.519 14532 0.079 1.851 1497

 

 

 

 

 

 

 

Table 2: Experimental data for (1500um x 180um x 360um) microchannel

 

m AP(Pa) f C‘ Re
(kg/8)

 

9.636 7199 0.064 1.445 1439

 

8.299 5599 0.091 1 .777 1239

 

6.994 4266 0.136 2.21 1037

 

5.863 3066 0.208 2.85 876

 

 

 

 

 

 

 

89

Table 3: Experimental data for (3000um x 360nm x 360um) microchannel

The plot in Fig. 5 shows the variation of the normalized friction factor, with

different Reynolds Numbers. It is always greater than 1.

 

 

 

 

 

 

 

 

 

 

 

 

 

3
‘ O 750 x 90
I 1500 x 180
A 3000 x 360
2.6
7.5.
:g 2.2 A
5 I
o
0
g 1.8 A '
.2 o 7 9.
E O
.t' 1.4 ‘4
E o l
E
o
z
1 l r T
0 500 1000 1500 2000

Reynolds Number, Re

Fig 110 Plot showing Reynolds number versus the Normalized friction coefficient for three
different micro channel dimensions

As shown above, the normalized coefficients show a marked deviation from the
laminar flow values. Another important factor verified during the analysis was the
rarefaction effect occurring during flow in micro channel. A considerable change
in density is observed due to the formation of viscous boundary layers during the

gaseous flow in micro channels. This fall in density due to viscous dissipation is

90

also termed as the rarefaction effect. Figure 7 verifies the viscous dissipation and

rarefaction studies previously under taken [32].

 

 

)5 77777777777 77 77 7- 77 77 77 77 7 77 7 777— .
. 9750x233 i
l I1500x180
l ,. A3000x360 ‘
101 7 77 777 7777 77777 77- -- 7 77—7 7 7— 77- 7-7 77 i
I 6
.\° , l
a , l
157777 7777 7 7 7— 7 7 7 7-777 7
a l
. o
E i ' I l
U l . l
a l *
310I 7 7 7 7 7 7 7 7 7 777 7'7 7 77 77
0 :
o , o I
l 0 ‘
5-: a _ z _ z z a an”.-- _____A _ _ _ -
i A
l . A
l
0 1 "7' ‘ “‘ T 7"" " —” _ ‘ 7' ‘ "i T "W ‘ f '1 '77 ’—“”_“'-"—— " '- 'T ""- ‘ "’“H‘Tw— ’—_ '_‘fl E
l
o 200 400 £00 80:) 1000 1200 1400 1600 l
Reynolds Number, Re i

 

 

Fig 111 Plot showing the percentage of density change for different channel lengths and for
different Re

Friction factor results were verified by previous experimental findings. We find
comparable variations of the laminar friction coefficients for a given pressure
difference compared to the macro scale theoretical predictions [30]. The results
also confirm the micro scale effects in low aspect ratio microchannels, however
further work is required to identify and quantify these effects. Another important
factor the “initial length effect’ plays a very important role for the flow in micro

scale.

91

Further work will deal with this aspect where it is shown that flow is not fully
developed yet as the micro channel length is about 5 -8 °/o of the fully developed
channel flow length. This is true for most micro channel flows. Because of the
greater pressure losses in such a case in comparison with the "normal" laminar
flow the normalized friction coefficient calculated for the full length must be
obtained greater then theoretical (C*>1) and this has been verified by our

findings above.

92

CHAPTER 8 CONCLUSION

The area of power MEMS has been in considerable focus in the past decade as
research groups around the world work towards developing ideas for generating
power at the micro level. This work has been an attempt to present one such
idea and the lays down a first ever design approach for an internal combustion
wave disc engine. Using the unsteady flow and pressure exchange principles, an
idea for an engine was presented and explained.

This work has discussed and covered the following:

. The principle of operation of a wave disc engine has been extensively
discussed. Wave patterns and state plane diagrams have been presented
for this model. A linear gas dynamic model using the powerful technique of
method of characteristics has been developed, and also the governing
equations have been shown. This work also discusses the assumptions
for such approach and the simplifications to develop a preliminary model.

The observations have been discussed and presented.

93

Numerical simulations of a unsteady flow periodic machine, wave rotor
were successfully performed. The results were used as a comparison for a
1 D algebraic code developed by fellow researchers. Porting design were
calculated and verified using these two simulations and they are now
manufactured as a part of the wave rotor test rig. Techniques employed
for performing these simulations will be used to model the wave disc
engine. Further work has been suggested as to how to improve the
numerical methods and the possible challenges while modeling the wave

disc with internal combustion.

Micro combustion inside a micro channel could be the biggest challenge
so far. Thermal, fluidic and combustion aspects of a micro scaled
combustion is discussed and presented. Expected problems along with

the available solutions are discussed.

A preliminary analytical model analytical model for the wave disc engine
has been made as a 1 D algebraic code and was run for a wide range of
post combustion temperatures and pressures. Its affect on the design
parameters like the induced flow velocities after all the expansion and
compression wave, and also the behavior or the gas air interface was
studied and shown. Interesting observations were made regarding the
affect of post combustion temperatures and pressures and also for a 20
mm channel length the interfaces were calculated for a wide range of

94

temperatures. This could be used to develop the first ever porting design
for the wave disc engine. Several different disc design were shown from

the available literature.

0 Experimental work on microfluidic behavior was conducted at the
University of Technology, Warsaw, Poland. Four different channel lengths
were machined in a silicon wafer and friction factors were computed for all
four of them using a simple volume flow rate measuring technique. The
results showed good comparison to the available data in the literature.

Change of density or rarefaction of the gas was also seen and plotted.

Using the presented work, a more sophisticated model of the Internal combustion

wave disc engine will be developed and then eventually manufactured and

tested.

95

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98

99

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