Thermodynamic Diagrams for High Temperature Plasmas of Air, Air-Carbon, Carbon-Hydrogen Mixtures, and Argon

189 Pages·1971·3.41 MB·English

by  H. Kroepelin

H. Kroepelin
K.-K. Neumann
K.-U. Hoffmann
R. Kuthe
Thermodynamic Diagrams
for High Temperature Plasmas of Air,
Air-Carbon,
Carbon-Hydrogen Mixtures,
and Argon
Diagramme zur Chemie und Thermodynamik
yon Hochtemperaturplasmen fur Luft,
Luft mit Kohlenstoff,
Kohlenstoff-Wasserstoff-Gemische
und Argon
Pergamon Press · Vieweg
Oxford · Edinburgh · New York
Toronto · Sidney · Braunschweig
Pergamon Press Ltd., Headington Hill Hall, Oxford
Pergamon Press (Scotland) Ltd., 2 & 3 Teviot Place, Edinburgh 1
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Pergamon Press (Aust.) Pty. Ltd., 19a Boundary Street, Rushcutters Bay,
N. S.W. 2011, Australia
Vieweg + Sohn GmbH, Burgplatz 1, Braunschweig
ISBN 08 017581 3 (Pergamon)
ISBN 3 528 08306 9 (Vieweg)
No part of this publication may be reproduced, stored in a retrieval system or transmitted mechanical,
photocopying, recording or otherwise, without prior permission of the Copyright holder.
1971
Alle Rechte vorbehalten
Copyright © 1971 by Friedr. Vieweg + Sohn GmbH, Verlag, Braunschweig
Library of Congress Catalog Card No. 74-150704
Satz: Friedr. Vieweg + Sohn GmbH, Braunschweig
Druck: E. Hunold, Braunschweig
Buchbinder: W. Langelüddecke, Braunschweig
Umschlaggestaltung: Peter Morys, Wolfenbüttel
Printed in Germany
Vorwort
Im Laufe der Jahre sind in meinem Institut viele Werte für thermische
Plasmen im Gleichgewichtszustand errechnet worden. Wir hielten es für
geboten, diese Werte für die Konzentration der Komponenten als Funk-
tion von Temperatur und Druck, Enthalpie, freie Enthalpie, Entropie
usw. zu vervollständigen und in Form von Kurventafeln zu veröffent-
lichen. Wir hoffen, damit den an diesem Gebiet Interessierten eigene
Rechenarbeit zu ersparen. Die Kurven sind im Original meist in der
Größe bis DIN A 1 gezeichnet und dann auf einheitliches Format ver-
kleinert worden. Wer die Originalzeichnungen benötigt, kann Pausen
davon bei uns anfordern.
Ich habe allen im Laufe der Jahre auf diesem Gebiet tätigen Mitarbeitern
zu danken. Es waren dies in zeitücher Reihenfolge: Prof. Dr. E. Winter,
sowie die Doktoren K.-K. Neumann, R. Kuthe, D. E. Kipping, H. Piel·
ruck, E. T. T. Hasibuan, P. Kalthoff, F. Weigang, K-U. Hoffmann und
R. Hoffmann.
Das Hauptverdienst am Zustandekommen dieses Buches hat Dr. K. -K
Neumann. Die Zeichnungen wurden von Frau E. Galler sorgfältig ausge-
führt. Sie hat auch die mühsame Arbeit der Retusche der Drucknegative
zusammen mit Fräulein K. Zieling unternommen.
Nur die anfängliche Unterstützung seitens des Herrn Bundesministers
für wissenschaftliche Forschung und die langjährige der Fraunhofer-
Gesellschaft sowie die Mithilfe des Rechenzentrums der T. U. Braun-
schweig (Prof. Dr. H. Herrmann) machten es möglich, die umfangreichen
Arbeiten zum guten Ende zu bringen.
Braunschweig, im Juni 1970 H. Kroepelin
V
Preface
For many years we have been interested in chemical equilibria at high
temperatures, and in the course of our work we have collected together
much thermodynamic data, e. g. enthalpies, free enthalpies, entropies and
so forth. We feel that this material should be published and thus be made
available to other researchers in plasma physics and chemistry.
Our results were originally presented in diagrams in the format DIN Al
(approximately 84 x 59 cm). Although these diagrams have been here
reduced to the size of this book, full-size copies of the original diagrams
can be supplied, if needed, by the Chemical Technology Department of
the Technical University of Braunschweig.
I should like to take this opportunity to thank all my colleagues who have
worked with me in this field since 1956: through the years these were
Prof. E. Winter, and Drs. K.-K. Neumann, R. Kuthe, D. E. Kipping,
H. Pie truck, E. T. T. Hasibuan, P. Kalthoff, F. Weigang, K.-U. Hoffman
and R. Hoffmann.
Special thanks are due to Dr. K.-K. Neumann who contributed much to
this book. Mrs. E. Gatter very carefully prepared the diagrams and was
assisted by Miss K. Zieling in the most tedious task of retouching the nega-
tives.
Our research was made possible by the sponsorship of the Ministry of
Scientific Research of the Federal Republic of Germany and by the
Fraunhofer-Gesellschaft. We are indebted to Prof. H. Herrmann, Head of
the Computing Department at the Technical University of Braunschweig,
for his assistance.
Braunschweig, June 1970 H. Kroepelin
VI
Zum Geleit
Durch seine Theorie der thermischen Ionisation und Anregung hat
M. N. Saha vor einem halben Jahrhundert gezeigt, wie man in das Ge-
biet der Gasplasmen, als des vierten Aggregatzustandes der Materie
rechnerisch vordringen kann. Aber erst mit der Entwicklung neuzeitiger
Rechenanlagen konnten die sehr umfangreichen Rechenprogramme
mit erträglichem Aufwand bewältigt werden. Nur dadurch wurde es
möglich, das experimentell schwer zugängliche Verhalten hochtempe-
rierter Gasplasmen systematisch zu untersuchen und vorauszusagen.
Der Arbeitskreis um Professor Dr. H. Kroepelin im Institut für Chemische
Technologie der Technischen Universität Braunschweig befaßt sich seit
anderthalb Jahrzehnten experimentell und theoretisch mit dem Ver-
halten von Kohlenwasserstoffen im elektrischen Lichtbogen, d.h. im
Gasplasmazüstand. In der vorliegenden Monographie wird ein Teilergeb-
nis dieser umfangreichen Untersuchungen der Öffentlichkeit übergeben.
Das mit großer Sorgfalt erarbeitete Material gibt Auskunft über die
Eigenschaften von Plasmen im Gleichgewicht, die aus Kohlenwasser-
stoffen, Luft ohne Argon, reinem Argon und Luft mit Kohlenstoff bei
verschiedenen Drucken, Temperaturen und Molenbrüchen entstehen
können.
Zur Speicherung der Informationen wurde die diagrammatische Dar-
stellung gewählt, welche im Vergleich mit Zahlentafeln raumsparend
und übersichtlich ist. Das schätzt man unter anderem bei der Unter-
suchung von Zustandsänderungen, wo man mit wenigen Linienzügen
einen besseren Überblick über den Verlauf gewinnen kann, als das mit
reinen Zahlenangaben möglich ist.
Mag auch die aufgewendete Mühe allein nur bedingt für den Wert eines
Werkes bestimmend sein, so sei dennoch die außerordentliche Leistung
der Mitarbeiter, vor allem von Dr. K. -K. Neumann hervorgehoben, die
zur Vollendung der vorliegenden Monographie aufzubringen war.
Durch die zunehmende Bedeutung der Gasplasmen in der Technik dürfte
aber auch der Kreis derer wachsen, die an den Ergebnissen der vorliegen-
den Arbeit interessiert sind und sie zu schätzen wissen werden, wodurch
schon allein deren Wert steigen dürfte.
Stuttgart, im Juni 1970 F. Bosnjakovié
VII
Preface
Half a century ago, M. N. Saha provided, in his theory of thermal ioniza-
tion and excitation, a method by which gas plasmas could be explored
mathematically as the fourth state of matter. However, only with the
development of modern computers could the complex numerical calcula-
tions involved be successfully carried out. In this way, it has become pos-
sible to estimate and predict the behaviour of high temperature gas plasma
in states not easily investigated experimentally.
During the last fifteen years, a team working under Professor H. Kroepelin
at the Chemical Technology Department of the Technical University of
Braunschweig has been studying, both experimentally and theoretically,
the behaviour of hydrocarbons in an electric arc, i. e. in gas plasma state.
Some of the results of this extensive work have been summarized in the
present monograph.
This carefully prepared material provides information relating to the pro-
perties of equilibrium gas plasmas formed from hydrocarbons, from air
without argon, from pure argon and from mixtures of air and carbon at
various compositions, temperatures and pressures. The data are presented
in graphical rather than tabular form, since this was considered not only
to be more economical of space and the reader's time, but also to provide
a clearer picture of the plasma processes investigated.
Although the effort spent on a book cannot necessarily serve as a criterion
for its value, the tremendous amount of work done by the contributors,
and in particular by Dr. K.-K. Neumann, deserves mention.
Gas plasmas enjoy a growing importance in modern technology. It is likely
that this will increase the number of readers interested in and appreciating
the results presented in this monograph.
Stuttgart, June 1970 F. BoSnjakovié
νπι
I. Introduction
High temperature plasmas are becoming more important The thermodynamic data for the mixtures considered were
today both in science and technology. In the study of computed frpm the calculated equilibria (see explanation
plasma processes, a knowledge of the characteristics of below). The properties included are enthalpy, entropy, free
these plasmas, and in particular their thermodynamic energy, density, the compressibility factor, the degree of
properties, is important. ionization, and the ratio of the effective specific heats.
Thermodynamic equilibrium was assumed for the thermo-
The thermodynamic diagrams, which are presented in this plasmas considered. That is, stationary non-equilibrium
book, are the results of our calculations. We have limited conditions, such as those found in the corona of the sun
ourselves to a temperature range in which the plasma is or in gas nebula, were eliminated. Changes in conditions
essentially molecule-free and up to 100000 K. Computa- whose rates were of the same order of magnitude as those
tions for higher temperatures are basically the same so of the related chemical reactions were also eliminated.
long as the temperatures are below the electron gas region, Interactions between the particles, such as the Van-der-Waals
i. e., as long as ionization has not ceased (see Hund [1936]). forces or Coulomb forces for the ions, were neglected
(exceptions to this are indicated below). In the majority of
calculations, equilibrium with the black body radiation
The equilibrium constants for ionization equilibrium are
contained in the plasma was assumed. Results calculated
calculated from tabulated values for the ionization energies,
for a hypothetical, "radiation-free" plasma are also reported.
electron activation energies, and the related summed
angular momenta for the neutral atoms and ions. The Calculations were made at constant total pressure ; tempera-
values for mixtures are based on these calculations. The ture values and total composition of the mixtures were
calculations for such simultaneous equilibria (for multi- assumed. The equilibrium compositions stated throughout
component mixtures) require extensive numerical computa- are on a volume basis. The Joule was used throughout as
tions. a measure of energy.
English by P. B. Ledermann and I. F. Miller, Polytechnic Institute of Brooklyn.
Kuthe/Neumann 1
1. Einleitung
Hochtemperatur-Plasmen gewinnen heute in Wissenschaft Aus den Eingabedaten und den errechneten Gleichgewichts-
und Technik zunehmend an Bedeutung. Für die Erfor- zusammensetzungen (siehe zum Begriff der Gleichgewichte-
schung und die technische Beherrschung von Vorgängen, Zusammensetzung weiter unten) haben wir dann thermodyna-
an denen Plasmen beteiligt sind, ist die Kenntnis der Ei- mische Daten für die verschiedenen von uns betrachteten
genschaften dieser Plasmen, insbesondere ihrer thermody- Gemische ausgerechnet : Enthalpie, Entropie, freie Enthalpie,
namischen Zustandseigenschaften, wichtig. Dichte, Kompressibilitätsfaktor, Ionisierungsgrad, Verhältnis
der effektiven spezifischen Wärmen.
Wir haben für die von uns betrachteten thermischen Plasmen
In dieser Schrift teilen wir Ergebnisse einiger von uns durch-
stabiles thermodynamisches Gleichgewicht vorausgesetzt,
geführter thermodynamischer Berechnungen für thermische
d. h. es werden sowohl stationäre Nichtgleichgewichtszu-
Plasmen in Diagrammform mit. Wir beschränken uns dabei
stände ausgeschlossen, wie sie z. B. in der Sonnenkorona und
auf den Temperaturbereich, in dem das Plasma praktisch
in Gasnebeln vorkommen, als auch Zustandsänderungen,
molekülfrei ist und teilen Rechenergebnisse mit bis zu ei-
deren Geschwindigkeiten in die Größenordnung der Reak-
ner Temperatur von 100 000 K. Am Rechenansatz ändert
tionsgeschwindigkeiten der betreffenden chemischen Reak-
sich für noch höhere Temperaturen grundsätzlich nichts,
tionen kommen. Wir vernachlässigen femer Wechselwirkungs-
solange man nicht in das Zustandsgebiet des Elektronen-
kräfte zwischen den Teilchen, wie van der Waals-Kräfte
gases kommt, d. h. solange die Ionisation noch nicht abge-
oder die Coulomb-Kräfte der Ionen (Ausnahme hierzu siehe
schlossen ist (siehe dazu Hund [1936]).
weiter unten). Bei der Mehrzahl der Berechnungen haben
wir Gleichgewicht mit der im Plasma eingeschlossenen
Wir haben, ausgehend von tabellierten Werten für die Ioni- schwarzen Strahlung angenommen. Daneben teilen wir auch
sierungsenergien und für die elektronischen Anregungsener- Rechenergebnisse für ein hypothetisches „strahlungsfreies"
gien und die dazugehörigen Drehimpulse für neutrale Atome Plasma mit.
und Atomionen, die Gleichgewichtskonstanten für die Ioni-
Wir haben durchgehend für konstanten Gesamtdruck ge-
sierungsgleichgewichte ausgerechnet und daraus die Zusam-
rechnet und daneben Temperaturwerte und die Elemen-
mensetzung für Gemische, die aus mehreren chemischen
tarzusammensetzung des Gemisches vorgegeben. Die Gleich-
Elementen aufgebaut sind. Die Berechnung solcher Simul-
gewichtszusammensetzung beschreiben wir mit Rauman-
tangleichgewichte für Vielkomponentengemische erfordert
teilen. Als Energiemaß wurde durchgehend das Joule ver-
umfangreiche numerische Berechnungen.
wendet.
13
II. Theoretical Basis
Calculations were made using a system of equations derived In our method of calculation for "radiation-free" plasmas
from quantized Boltzmann statistics. This was supplement- as well as for plasmas where radiation is considered the
ed for the radiation portion by addition of Bose statistics. Eggert-Saha equation applies (Eggert [1919], Saha [1921].
This equation is applicable when both elementary plasma
The particles of matter are a non-degenerate gas in the
ionization and recombination processes (namely, those due
region considered (the thermal energy of the ions and
to collision and radiation) occur. It is also valid if only
electrons is large compared to the reference energy at zero
collision processes and no photon induced processes take
temperature). The theory of relativity does not enter into
place. On the other hand it is valid if only photon induced
the calculations at temperatures considered (velocity of the
processes and no collision ionization or recombination
electrons is small compared to the velocity of light). There
takes place (Elwert [1952a]). The equation is no longer
is no condensed phase in the mixtures at the temperatures
applicable when plasma generated radiation escapes without
and pressures considered.
radiation induced ionization taking place (Knoche [1961]),
Equilibria were calculated as if the plasma had reached
a situation which often results in lower measurements in
thermodynamic equilibrium, i. e., the calculations are based
laboratory generated plasmas. The equation is inapplicable
on a model in which equilibrium exists between the particles
when collision ionization and radiation recombination occur,
and the surrounding black body radiation. This theoretically
as for example in the sun's corona (Elwert [1952b]). The
important boundary condition cannot be realized under
Eggert-Saha equation is also inapplicable when the tempera-
terrestrial conditions. The plasma would have to absorb
ture acting on the plasma - also, eventually "diluted-radia-
and emit radiation continously throughout the whole
tion" (analogous to grey radiation) - is greater than the
spectral region while at the same time absorbing incident
temperature of the plasma ; this occurs in gas clouds (Elwert
radiation of any wavelength. The mean free path of the
[1952a]). The three previously discussed cases do not fall
photons would then have to be small compared to the
within the limits for the plasmas calculated, namely, plasmas
dimensions of the plasma.
in which radiation is in equilibrium and those in which
Equilibrium values between particles, without consideration particles are in thermodynamic equilibrium and in which no
of any radiation, are presented only for argon-free air. Such radiation occurs.
a stationary condition based on a totally thermodynamic
In a few expanded thermal plasmas the thermodynamic
point of view can exist in many plasmas. The plasma
equilibrium can also be disturbed by diffusion of the charge
considered is one in which ionization and recombination
carrier, or heat conduction processes (Frie and Maecker
take place only through collision processes and equilibrium
[1961], [1962]. If these disturbances are large, such plasmas
exists in the sense that in a given time period the number
will deviate from the calculated values.
of ionizations and recombinations are equal. Interactions
with the radiation field do not exist in these plasmas; this The validity of the ideal gas law is assumed after Finkelnburg
can be achieved in practice with very small expansions or and Maecker [1956]indicated the reasonableness of this
very low density plasmas. Even an expanded plasma can assumption for the thermal plasma region. Therefore, despite
approach these conditions more closely than a model which the coulomb effects, at high temperatures the translational
considers black body radiation, when the plasma being movement of the particles can be calculated based on an ideal
considered contains only particles which absorb radiation gas. The interaction effects must not, in comparison, be
of a few wave lengths. Small additions of gas impurities e. g., neglected in the computation of the partition function.
The expansions for these partition functions must be
argon in air, would cause the plasma to appreciably depart
truncated after a specified term to prevent them taking
from this idealized model (Knorr [1958]).
on an infinite value. The formula of Unsoeld [1948] was
The radiation in the temperature region considered is
used to calculate the limit to which the partition function
almost entirely terminal and recombination radiation. For
was always summed :
practical applications, it is important to note that the
percent of the radiation absorbed reaches 99 % when the Eg = E - 5,615 . lu"3 (Z2 . r · Ng)^ (1)
ion eff e
thickness of the plasma layer is 26 times as large as the
mean free absorption wavelength. (Saenger [1957]). where Ei = ionization work in cm"1 ; E = activation
on g
The properties of real plasmas will Ue between the extremes energy of the highest term included in the computation in
calculated for the two cases. This is true when the intensity cm"1 ; re = volume fraction of the electrons ; Ng = total
of the radiation is less than the black body radiation at the particle number ; Zeff = effective nuclear charge.
temperature of the plasma and all other equilibrium condi- This equation is only really applicable for hydrogen. A
tions are present. It is not unusual in real plasmas for other small error in the computation of the function will not
properties besides the radiation not to be in equilibrium. influence the final result significantly because the contribu-
In these instances other methods of calculation based on tion of the partition function to the ionization constant
non-equilibrium thermodynamics must be used. is of the order of magnitude of only several percent.
2
In the actual calculation, the fact that not all possible terms denser and hotter the plasma. The bandwidths are larger
for the electron excitation have been used has a somewhat the higher the electron level, so that above a certain level,
greater influence on the value of the partition function than the bands overlap and the width of the pattern becomes
the summation. The quantum numbers are established, but greater than the distance of the true series limit continuum.
the excitation energies are not. These latter values can only Electrons in these bands behave more like free electrons
be crudely estimated by comparison with other species. than bound electrons. Further, it is possible that during a
Therefore, these terms have been neglected. collision an electron from a highly energized ion wanders to
a neighbor (tunnel effect). This exchange imparts to the
The work of ionization for isolated particles, which are in
electrons, below the ionization threshold, properties of the
an infinite volume, are tabulated. The ionization energy can
free electron. For example, these electrons form a conducting
be lowered as a result of the microfield surrounding each
plasma, although in these calculations they are not considered
particle. The work of ionization can be lowered by the
to be free electrons. Traving [1960] discusses this question
Stark effect, which is related to the principle quantum
thoroughly.
numbers, and the quantum-mechanical tunnel effect.
The various values presented for the amount of decrease To calculate the statistical weights, the idea of Russell-
in the ionization work as a function of other plasma para- Saunders coupling was used for all terms. For high energy
meters are still very much in dispute. Ecker and Kroell [1962] levels, which are close together, this scheme is often in-
present rules which result in smaller decreases than those applicable. The error introduced into the present computa-
presented ; they take strong issue with contrary points of tions, however, is very small.
view. The ionization energies were not decreased in these
As normally, the nuclear spin portion of the partition
computations.
function was not included as the spin energy contribution
Closely related to the question of the lowering of the
is practically always constant until very high temperatures
ionization potential is the question of which electrons
are reached. Spin energy may be considered by multiplying
should be taken as "free electrons". In our computations,
the partition function by characteristic factors for each
every electron is considered to be bound, that is, relative
chemical element and adding a value to the entropy.
to one ion, at an energy level that is lower than the ioni-
zation energy for an isolated ion. However, the discrete The necessary initial values (ionization energy, electron
quantum levels of the bound electrons are spread out into activation energy and the related angular momentum) were
energy bands. This charge in quantum levels is stronger the taken from the tables of Moore [1949 etc.]).
3