Direct Energy Conversion: Fundamentals of Electric Power Production

275 Pages·1996·5.051 MB·English

by  Reiner Decher

DIRECT ENERGY
CONVERSION
Fundamentals of Electric
Power Production
Reiner Decher
New York Oxford
Oxford University Press
1997
Oxford University Press
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Copyright© 1997 by Oxford University Press, Inc.
Published by Oxford University Press, Inc.,
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All rights reserved. No part of this publication may be reproduced, stored in a retreival system, or trans
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Library of Congress Cataloging-in-Publication Data
Decher, Reiner.
Direct energy conversion : fundamentals of electric power
production I Reiner Decher.
p. em.
Includes bibilographical references and index.
ISBN 0-19-509572-3 (cloth)
1. Direct energy conversion. I. Title.
TK2896.D43 1996 96-4842
CIP
Printing (last digit): 9 8 7 6 5 4 3 2 I
Printed in the United States of America
on acid-free paper
CONTENTS
PREFACE, VII
SYMBOLS, X
1. HEAT ENGINES, 1
1.1. Common features of all heat engines: thermodynamics, I
1.1.1. Efficiency, 3
1.1.2. Specific work, 3
1.2. Practical cycles and ideal processes, 3
1.2.1. Temperature limits, 6
1.2.2. Peak cycle temperature, 7
1.2.3. Other limits, 8
1.3. Irreversible work processes, 10
1.4. Irreversible heat transfer processes, 12
1.5. Part-load performance, 13
1.6. Shaft power, 15
1. 7. Energy conversion not involving heat engines, 17
2. FLOW WITH ELECTROMAGNETIC INTERACTION, 22
2.1. Electromagnetic forces, 23
2.1.1. Drift velocity: Motion of a collisionless charged particle, 23
2.1.2. Induced electric field, 24
2.1.3. Cyclotron frequency, 25
2.1.4. Combined E and B fields, 25
2.1.5. Ohm's law, 26
2.1.6. Applications, 28
2.2. Gaseous working fluids: Plasma, 30
2.2.1. Electric charge density, 31
2.2.2. Electric current, 31
2.3. Electromagnetic fields, 32
2.3.1. Faraday's law and the E field, 32
2.3.2. Ampere's law and the B field, 34
2.3.3. Electromotive force, 37
2.3.4. Maxwell's equations, 38
2.3.5. Work interactions, 39
2.4. Fluid mechanical equations, 39
2.4.1. Fluxes, 39
2.4.2. Mass conservation, 40
2.4.3. Momentum equation, 40
2.4.4. Energy equation, 42
2.4.5. Entropy equation, 42
2.4.6. Enthalpy equation, 43
2.4.7. Interaction parameter and interaction length, 44
iv DIRECT ENERGY CONVERSION
3. PLASMAS AND ELECTRICAL CONDUCTIVITY OF GASES, 46
3.1. Debye length: Neutrality scale, 46
3.2. Ohm's law: Momentum equation for the electron gas, 48
3.2.1. Scalar conductivity, 49
3.2.2. Tensor conductivity, 49
3.2.3. Collision frequency, 50
3.3. Magnetic Reynolds number, 52
3.4. Lorentz theory of the electron gas: Electrical conductivity of an
ionized gas, 54
3.4.1. The Lorentz gas approximation, 56
3.4.2. Force fields, 56
3.4.3. Encounter geometry, 56
3.4.4. Momentum changes, 58
3.4.5. Motion in the c vector and atom plane, 62
3.4.6. Collision force integral, 67
4. MAGNETOHYDRODYNAMICS, 77
4.1 Crossed-field devices, 77
4.1.1. Current flow and electric field constraints, 78
4.1.2. The MHD terms in the dynamical equations, 79
4.1.3. Continuous electrodes generator, 80
4.1.4. Segmented electrode generator, 81
4.1.5. Hall generator, 84
4.1.6. Diagonal Faraday generator, 89
4.2. MHD channel flow gas dynamics, 90
4.2.1. Characteristic velocities, 90
4.2.2. Sears-Resler diagram, 92
4.3. MHD accelerators, 96
4.3 .1. MPD thrusters, 97
4.4. Gaseous and liquid metal working fluids, 98
4.4.1. Pumping of incompressible, conducting fluids, 100
4.4.2. The MHD flow meter, 100
4.5. Gas-phase power systems, 101
4.5.1. Gaseous MHD analysis model approximations, 102
4.5.2. Maximizing conductivity of a gaseous plasma, 103
4.5.3. Ion collisions, 106
4.5.4. Temperature and pressure dependence of conductivity, 108
4.5.5. MHD generator flow Mach number, 109
4.5.6. Enthalpy extraction, 110
4.5.7. Minimum interaction length, 112
4.5.8. Viscous effects, 117
4.5.9. Flow area variation, 118
4.6. Cycle implementation, 118
4.7. Concluding remarks, 119
5. ELECTROHYDRODYNAMIC POWER GENERATION, 123
5.1. The EHD generator, 123
5.2. Analytic description, 123
CONTENTS v
5.2.1. E field and voltage distributions, 124
5.2.2. Current, 126
5.2.3. Power density, 127
5.3. E field limit, 129
5.4. Fluid mechanics, 130
5.4.1. Efficiency, 131
5.4.2. Flow velocity and current, 131
5.5. Remarks, 132
6. HEAT TO ELECTRICITY VIA FREE ELECTRONS: THERMIONIC
POWER GENERATION, 134
6.1. The thermionic diode, 134
6.2. Thermionic emission, 134
6.2.1. Physics of metals, 135
6.2.2. The Fermi-Dirac distribution function, 137
6.2.3. Emission Current, 141
6.2.4. Emission heat transport, 143
6.3. Space charge effects, 144
6.3.1. Emission across a small gap, 144
6.3.2. Space-charge-limited current, 146
6.4. The thermionic diode, 148
6.4.1. Open circuit voltage, 149
6.4.2. Cell current, 150
6.4.3. Saturation current, 151
6.4.4. Voltage-current characteristic, 151
6.5. Performance, 153
6.5.1. Efficiency, 153
6.5.2. Losses, 158
6.6. Plasma diodes, 159
6. 7. Technology, 160
7. CHEMICAL ENERGY TO ELECTRICITY:
ELECTROCHEMISTRY, 162
7.1. Galvanic efficiency in electrochemical reactions, 162
7 .2. Cells, 163
7.3. Chemical reactions, 164
7 .4. Elementary cell performance, 166
7.4.1. Capacity, 166
7 .4.2. Ideal cell potential, 168
7.4.3. Temperature effects on cell performance, 169
7 .4.4. Cell internal resistance, 170
7.4.5. Energy density of batteries, 171
7 .4.6. Lead acid battery, 173
7 .5. Fuel cells as energy converters, 174
7 .5.1. The hydrogen-oxygen cell, 175
7 .5.2. Chemical and electrochemical potentials, 178
7.5.3. Half-cell potentials, 180
7.5.4. Hydrocarbon fuel cells, 182
vi DIRECT ENERGY CONVERSION
7.5.5. Solid electrolyte cells, 184
7.6. Cell system performance, 187
7 .6.1. Voltage-current characteristic, 187
7 .6.2. Efficiency, 190
7.6.3. Other issues, 191
8. SEMICONDUCTORS: PHOTOELECTRICITY, 194
8.1. The photoelectric effect and cells, 194
8.1.1. Doped semiconductors, 196
8.1.2. The p-n junction, 198
8.1.3. Photon energy and voltage, 201
8.1.4. Dark current, 202
8.2. Review of radiation physics, 204
8.2.1. Blackbody cavity, emissivity from solids, 205
8.2.2. Emission spectra of real surfaces, 207
8.2.3. Physics of radiation interacting with matter, 208
8.3. Spectral aspects of electric power from photocells, 210
8.3.1. Photon flux and current, 211
8.3.2. Photovoltaic cells, 216
8.3.3. Losses in cells, 218
8.3.4. The equivalent circuit 219
8.3.5. Cell performance, 225
8.3.6. Temperature effects, 226
8.4. Radiant conversion power systems, 227
8.4.1. Solar power, 227
8.4.2. Nuclear radiation and heat, 228
8.4.3. Thermal radiation, 228
8.5. Infrared photovoltaic systems, 229
8.5.1. Thermodynamics of heat generation by combustion, 230
8.5.2. Radiative transfer to cells, 232
8.5.3. Radiator tube length, 233
8.5.4. System characteristics, 236
9. HEAT TO ELECTRICITY VIA BOUND ELECTRONS:
THERMOELECTRICITY, 240
9 .1. Physical phenomena in thermoelectric interactions, 240
9 .2. Thermoelectric power generation, 243
9.2.1. Efficiency and power, 244
9.3. Alkali metal thermoelectric conversion, 248
9.3.1. Voltage and current, 250
APPENDIX A: Maxwell-Boltzmann distribution function, 253
APPENDIX B: Fundamental physical constants, 255
INDEX, 256
PREFACE
The intent of this book is to acquaint the technically trained reader to under
stand the physics and practical limitations of methods that might be employed
for the production of electrical power, that most useful of all power forms.
The conversion of energy in its many forms occurs naturally and is caused to
happen deliberately by industrial man in processes for a variety of reasons and
purposes. The production of electromechanical power is dominated by the
exploitation of heat resources by means of heat engines and of mechanical
power resources available in nature. The utilization of heat resources is, in
tum, dominated by the thermodynamics of the heat engine and its limitations.
For some cycles, the limitation is due to the fuel energy content; for others,
the usable temperatures allowed by the materials in the engine are critical; and
for still others, the characteristics of the thermodynamic cycle working fluid
limit the cycle performance.
Thermodynamics, physics, and chemistry also govern the direct conversion
of energy in various forms to electrical energy. Direct energy conversion is
concerned with the transformation of energy to electrical power without the
use of the heat engine and the associated rotating electrical generator. These
methods are characterized by an electrical circuit wherein molecular scale
charge carriers complete the circuit rather than electrons in the conductors of
the rotating machinery. This offers the potential for production of electric
power with long-lived, reliable, and durable power systems from such
resources as heat, chemical energy, flow kinetic energy, as well as photon
radiation. The conversion of these energy forms to electric power is limited to
varying degrees by the Second Law of Thermodynamics.
The greater purpose of this book is to provide an understanding of the crit
ical physical phenomena involved in designing an energy conversion device or
system around a laboratory effect. This book is limited to those devices that
have or were thought to have a realistic chance of becoming commercially
successful or may be particulary useful in a special application niche. The top
ics covered therefore do not include all energy conversion methods. For an
appreciation of some of other methods that have been investigated as well as
a good overview of the governing concepts associated with irreversible ther
modynamics, the reader is encouraged to see other texts on the same subject.
Works by Angrist (Ref. 1-8), Soo (Ref. 5-1), Sutton (Ref. 1-9), as well as oth
ers are often very good and complementary to the study here. In fact, a par
ticular author's interest in a specific subject often reflects a disproportionate
effort spent on writing about the ideas involved and its details. This is prob
ably true here and with other authors. Thus the reader may wish to read in
greater depth elsewhere about some topics that are omitted or touched on only
briefly here.
viii DIRECT ENERGY CONVERSION
Chapter 1 is a review of the characteristics of heat engines as an extension
to that in Ref. 1-1. Some discussion there is also devoted to the production of
solar cell electric power. Of interest always are factors that determine power
output (specifically power density or compactness), complexity (or cost), and
the efficiency of the conversion of heat to power. By virtue of their function
in meeting a user's needs, most engines must operate for some fraction of
their operating lives at power levels less than full power. The variation of the
performance characteristics, specifically the efficiency, is often of great inter
est under these circumstances.
Chapter 2 is a discussion of flows with electromagnetic interactions, the
singular and practical method of obtaining work from a gas with kinetic
energy by means of a volumetric, rather than surface (on the airfoils of a tur
bine, for example), force interaction. The description of magnetohydrodynamic
(MHD) devices requires reviews of classical electricity and magnetism and of
the fluid equations of motion. A specialized review is provided here. The
background covered also serves the development of electrohydrodynamics
reviewed in Chapter 5.
Chapter 3 addresses determination of the principal property of materials
asked to carry electric current: the electrical conductivity. In gases, the mag
nitude of this transport property is critical to the successful design of power
machinery. The mathematical development yields valuable insight into the
physics of MHD and similar plasmas. This background is important for under
standing the design and performance of the devices discussed in Chapter 4.
Finally, it sets the stage for understanding the electrical conductivity in other
materials: metals (Chapter 6), electrolytes (Chapter 7), and semiconductors
(Chapters 8 and 9).
Chapter 4 describes direct removal of work from a moving fluid as elec
tric power. The interaction involves passage of a high-speed, conducting gas
through a magnetic field. Study of this form of energy conversion is an impor
tant aspect of MHO, the study of gas dynamics with significant flow interac
tion. The MHO generator described is similar to a very high-temperature
turbine whose contribution to the performance of the conversion system is crit
ical. The characteristics of this process are examined in detail. The reader is
referred to Ref. 1-1 for an examination of the integration of this generator into
a heat engine power system.
The forced convection of charges may be used to generate an electric
field and thus a current. The electrohydrodynamic interaction is covered in
Chapter 5.
The physics of metals and the ability of hot metals to transfer charges into a
vacuum or low-pressure space and to a receiver at an elevated potential is
described in Chapter 6. This forms the basis for the analytical description of
thermionic converters whose physical and performance characteristics are covered.
Chapter 7 is a discussion of chemical cells (batteries and fuel cells) where
the conversion of chemicals of one type to another takes place. Since chemi
cal reorganization involves the valence electrons of the constituents, the cells
can force the transfer of electrons to occur through an external load circuit
where their energy may be usefully employed. Such a conversion circumvents
PREFACE ix
the transformation of the chemical energy to heat, and thus the conversion
efficiency is not constrained by the Carnot cycle limitation, which afflicts heat
engines. This attractive feature is balanced by the lower power density. This
chapter describes ionic conduction of charges through electrolytes and the
most interesting types of fuel cell systems. Liquid and solid electrolyte cells
are considered. Fuels cells are promising alternative to heat engines, especially
with simple fuels such as hydrogen or methane. Batteries, as a close relative
to the fuel cell, will continue to play an important role in energy storage,
especially in the transportation sector. Methods for calculating the energy den
sity are described together with examples of practical systems.
Chapters 8 and 9 deal primarily with semiconductors. In Chapter 8, the
photovoltaic effect is described where photons interact with the electrons in a
semiconductor junction, resulting in the production of electron-hole pairs. The
electrons are elevated to a higher potential energy. The physical phenomena
described apply to the design of solar cells covered here and in ref. 1-1 and
to infrared cells for power systems using fuels. A review of the physics of
radiation precedes a discussion of the system design, power density, and effi
ciency. In Chapter 9, the thermoelectric effects are described, together with
the characteristics of devices designed to exploit them.
It is the author's view that a phenomenon or result is made much more
understandable if it can be modeled mathematically because one can readily see
the effect of the parameters involved. Thus the reader will find a quantitative
emphasis on fundamentals carried to the point where important conclusions
regarding performance characteristics can be drawn. Detailed design character
istics and statements regarding performance of specific devices are avoided
because these will change in time, while the fundamental underpinnings will not.
It is expected that the reader be competent in calculus, physics, and chem
istry. For the discussion of MHD devices in particular, the student should have
had an introduction to the dynamics of compressible fluid flow. This text is
suitable for senior-level undergraduates or graduate students in engineering. A
limited number of problems are given at the end of the chapters.
ACKNOWLEDGMENTS
The author gratefully acknowledges the contribution of colleagues who con
tributed material or agreed to review various chapters and thus improve not
only the book but my understanding as well. These include Lewis Fraas,
Thomas Mattick, Dan Schwartz, Uri Shumlak, Eric Stuve, Gene Woodruff,
and the students who had to put up with early versions of this work. The
work on MHD (Chapters 2-4) is influenced in no small way by interactions
with many colleagues. Among these are Jack L. Kerrebrock, Gordon C. Oates,
Myron A. Hoffman, James P. Reilly, Jean F. Louis, and Thomas R. Brogan.
Finally, sincere thanks to my wife Mary for being so understanding of my
need to focus "elsewhere" while completing this endeavor.
Seattle Reiner Decher