Measurement and calculation of thermodynamic properties of the

Transkript

Faculteit Ingenieurswetenschappen
Vakgroep Toegepaste Fysica
Voorzitter: Prof. Dr. Ir. G. Van Oost
Measurement and Calculation
of Thermodynamic Properties of Plasma
in the Waste Pyrolysis Reactor
door
Adinda van den Berg
Promotoren: Prof. Dr. Ir. G. Van Oost, Dr. Ir. M. Hrabovsky
Scriptiebegeleiders: Dr. Ir. T. Kavka
Scriptie ingediend tot het behalen van de academische graad van
Burgerlijk Ingenieur in de Natuurkunde
optie Toegepaste Natuurkunde
Academiejaar 2006–2007
i
Introduction
In recent years the price of fossil fuels has increased dramatically. The governments are
not only concerned with economics but also with the amount of fossil energy, which is
decreasing rapidly. It is believed that the use of fossil fuels for a several decades has caused
serious pollution and Global Warming. All this combined with the increasing population,
who wish to live comfortable lives as we do in the West, is cause for concern. Therefore
there is a great need for alternate methods of hydrogen gas production, which is sustainable,
and also for a way of waste disposal that is not harmful to the environment.
The pyrolysis or the gasification of waste with plasma could be a good way to solve part
of these serious problems. Plasma technology does not incinerate the waste. Due to this
process there is less use of oxygen and nitrogen, and so less production of greenhouse gases.
Therefore it is much easier to remove the hazardous components from the waste. Waste
is generally composed of organic and inorganic components. The organic component will
transform into gas by chemically reacting with O2 , while the inorganic component will be
turned into lava. This lava can still contain some hazardous materials, but the quantity is
so low that it is considered safe.
Using thermal plasma (with its higher temperatures than non-thermal plasma) to destroy the waste makes sure that no complex molecules are left in the composition of the
gas. In this process the temperature is kept lower than the atomization temperature, to
keep the syngas useful.
For pyrolysis the plasma itself supplies the energy for the material conversion. In the
gasification process a small amount of oxygen is added to oxidize the surplus of carbon in
the material. There are some definite benefits to the usage of plasma for waste disposal:
High reaction rates (saves time)
Less reactor volume needed (saves space)
Better control of the composition of the syngas
High calorific value of the syngas
High amounts of hydrogen in the syngas
Less production of tar
The results obtained so far pertaining to the production of hydrogen and the low levels
of CO2 found in the exhaust of the plasma reactor, are very promising.
The hybrid torch used in these experiments is relatively new when compared to the
water-stabilized and the gas-stabilized torch. Its characteristics have therefore not been
fully defined. It is suspected from previous experimental results that the hybrid torch will
have an enthalpy flux comparable to that of the water stabilized torch but that it will have
a higher mass flow rate. In this work the thermodynamic properties of the hybrid torch
used in the reactor experiments will be measured and calculated. The calculations will
be made using an equilibrium model. Because there is little data for ionized gas below
20000K I will calculate the thermodynamic properties of the ions which are suspected to
be present in the plasma gas coming out of the torch. These values will then be used to
compute the energy balance and the mass balance of the argon-water-stabilized torch used
at the IPP for different experiments conditions.
TOELATING TOT BRUIKLEEN
iii
Toelating tot bruikleen
“De auteur geeft de toelating deze scriptie voor consultatie beschikbaar te stellen en delen
van de scriptie te kopiëren voor persoonlijk gebruik.
Elk ander gebruik valt onder de beperkingen van het auteursrecht, in het bijzonder met
betrekking tot de verplichting de bron uitdrukkelijk te vermelden bij het aanhalen van
resultaten uit deze scriptie.”
Adinda van den Berg, juni 2007
Measurement and Calculation
of Thermodynamic properties of
Plasma
in the Waste Pyrolysis reactor
door
Adinda van den Berg
Scriptie ingediend tot het behalen van de academische graad van
Burgerlijk Ingenieur in de Natuurkunde:
optie Toegepaste Natuurkunde
Academiejaar 2006–2007
Promotoren: Prof. Dr. Ir. G. Van Oost, Dr. Ir. M. Hrabovsky
Scriptiebegeleiders: Prof. Dr. Ir. C. Leys
Faculteit Ingenieurswetenschappen
Universiteit Gent
Vakgroep Toegepaste Fysica
Voorzitter: Prof. Dr. Ir. C. Leys
Summary
In this thesis the thermodynamic properties of a hybrid plasma torch are calculated. This
plasma torch is used in a waste pyrolysis reactor. The Mach number,the enthalpy flux and
mass flux are then calculated with these thermodynamic properties.
Trefwoorden
thermodynamic properties, plasma torch, hybrid torch,mach number
Measurement and calculation of Thermodynamic
properties of the hybrid torch used in the waste
pyrolysis reactor
Adinda van den Berg
Supervisor(s): Tetyana Kavka
Abstract—This article shows the characteristics of the hybrid torch and
how it bridges the gap in characteristics between the water-stabilized torch
and the gas stabilized torch.
Keywords— thermodynamic properties, mach number, energy balance,
mass flow rate.
the plasma from the first chamber (also called the cathode chamber) and creates an overpressure, which accelerates the plasma
towards the exit.
I. I NTRODUCTION
T
HE hybrid torch is used today in the waste pyrolysis reactor at the IPP. From several experiments the difference
between the water-stabilized and the gas stabilized torch was
ascertained. The high enthalpy values achieved by the waterstabilized torch are very useful when considering the formation
of a useful syngas. But one would also like a higher mass flow
rate. The hybrid torch offers the possibility of having things
both ways. The high enthalpy achieved by the water stabilized
part, and the higher mass flow rate due to the use of Argon as a
stabilizing gas.
Fig. 2. Scheme of hybrid torch
The anode is made of copper and rotates to prevent hole burning by the plasma.
The cathode is made of Tungsten. The electrons are emitted
by thermionic emission. We use thoriated tungsten for its high
electron emission ability and its low erosion rate. Both the anode
and the cathode are water cooled to slow down erosion.
Because the anode is external there are some difficulties in
preventing the plasma jet from intensively mixing with the surrounding air. This can be a problem in spraying systems.
Fig. 1. comparison of power versus mass flowrate between gas and waterstabilized torches
II. T HE HYBRID TORCH
The hybrid torch has a gas-stabilized part near the cathode
and a water stabilized part in the chamber next to this. As with
the liquid-stabilized torch the water moves in a swirl around the
arc. The last part is a free jet of plasma.
In the first chamber the gas is injected through the cathode
vortex and stabilizes the arc there. Through the nozzle the
plasma then flows to the second chamber, where it is stabilized
by the water. The stabilization occurs through vortex flow of
water in three cylindrical chambers. The arc column interacts
with the water vortex and the water evaporates to steam. The
mixture of gas and steam forms plasma. The steam mixes with
Usually the gas used in the hybrid torch is Argon. This gas
only needs a low voltage to sustain the arc column. Because
of the low thermal conductivity k the arc will be narrow and
therefore it will have a high temperature. Sometimes hydrogen
is mixed with the argon for reducing and oxidizing effects. It
also increases the heat content and transfer in the gas stabilized
chamber.
Because of the low enthalpy, heat conductivity, absorption coefficients and radiation intensity of the Argon the arc will have
the thermal characteristics of the water-stabilized arc. Only the
characteristics controlled by mass balance such as velocity, momentum flux and plasma density will change considerably. This
can be seen in the graph below.
The only problem here is that the mass flow of argon can not
be easily determined. The amount of steam is very large compared to the amount of argon present. This is why theoretical
calculations must be made to determine these values.
III. C ALCULATION OF THERMODYNAMIC PROPERTIES
This calculation was done in several steps. First the thermodynamic properties of the components of the plasma gas were
calculated seperately. Then the properties were calculated for
the entire gas using the Gibbs free energy minimization and the
NASA method for the solving of the set of equations.
The thermodynamic properties such as the enthalpy h, the entropy s and the frozen specific heat capacity were computed by
using the statistical function Q, the partition function.
X
Q=
gs exp(−E/kT )
(1)
s
The thermodynamic properties of a gas of plasma depend
strongly on the composition. This is because, if we consider
a mixture of particles which has a dynamic equilibrium between
dissociation, recombination and ionization, the total energy will
be a function of the energy of the different particles and of the
possible chemical reactions between these particles. This composition for equilibrium was calculated using the Gibbs free energy minimization and the NASA method for the solving of the
set of equations.(work done by Petr Krenek)
IV. E NERGY AND M ASS BALANCE FOR THE HYRBID TORCH
We can also measure the amount that is lost to the water cooling system. From this information we can calculate the amount
of argon in the plasma jet. The problem for the water can be
handled much in the same way. The water is vaporized when
in contact with the plasma. When it is in contact with the water
cooling system it will partially condensate. The gas coming out
of the cooling system is measured and the water which condensates will not be taken into account. This makes the calculations
for the amount of water less precise.
To find the flow rate of the plasma out of the jet we have the
following information. We know the power flow into the jet
( I*U = current times the voltage). We also know the power
loss to the cooling system by measuring the mass flow and the
temperature difference between two points so that
Qloss = ṁwater cp ∆T
In this formula Fplasma can be calculated from the energy balance (formula 1.35). M is independent of the radial co-ordinate
at the exit nozzle, if we neglect the radial pressure gradients and
if radial velocity is small compared to the axial component. If
we know the Mach number M, we can also calculate the mass
flow rate out of the torch.
ZR
mplasma = M
(2πr)ρcdr
(6)
0
For gas stabilized torches the flow rate can be changed independently, but a minimum value must be maintained for a certain arc power. For water stabilized torches the mass flow
rate is determined by the evaporation rate of the stabilizing
wall,mevaporation .mplasma = mevaporation L(7)The main stabilizing part of the hybrid torch is also water-stabilized. Therefore I will use this equation for the calculation of the mass flow
rate in the hybrid torch. The Mach number can be calculated
when the integrals of the thermodynamic parameters are known.
(see chapter 3)
The formula for M is:
M=
L(IE − Qev )
RR
RR
2πrρchdr + (λ + Cw (TB − Twater )) 2πrρcdr
0
0
(8)
For the Mach number I found the following numbers
TABLE I: Table with calculated Mach numbers
I
300
400
M ,A=12.5
0,62987752
0,81058386
M,A=22.5
0,794485
0,92299
And for the mass flow rate and the Enthalpy flow of the hyrbid
torch I found :
(2)
TABLE II: Power and Mass flux for the hybrid torch
With these two values we can calculate the flux of the plasma
jet.
Fplasma = IU − Qloss
(3)
The formula for the enthalpy flux of the theoretical calculation
plasma is:
ZR
Fplasma = ρvh(2πr)dr
(4)
I and Ar
I=300A,Ar=12.5 slm
I=300A,Ar=22.5 slm
I=400A,Ar=12.5 slm
I=400A,Ar=22.5 slm
enthalpy flux(W)
37404,10037
39170,89665
59653,75005
62261,64153
mass flux(g/s)
0,317536183
0,463799877
0,343389738
0,422498781
0
In this formula we have used the fact that the exit of the plasma
jet is circular. We also know that throughout the plasma jet the
mach number M is constant and we know that M=v/c, where c
is the speed of sound. If we put this into formula 4 we find that
the flux of the plasma jet is :
ZR
Fplasma = M
(2πr)ρchdr
0
(5)
When we compare the characteristics of the hybrid torch with
those of the water stabilized torch we see that the mass flow rate
is somewhat higher. The density is also higher because argon
(39,9 g/mol) is heavier than hydrogen (1 g/mol) and oxygen (16
g/mol). The density is higher for larger input amounts of argon. For higher currents the density is lower in both the waterstabilized and the hybrid torch. In the hybrid torch the mach
number is higher for a higher argon flow. This is because when
the argon flow increases the plasma flow increases. Argon does
not influence the energy transfer to the walls. The water evaporation is therefore not influenced by a higher flow of argon. No
difference in water evaporation flow rate and a lower speed of
sound results in a higher mach number for the hybrid torch. The
lower enthalpy value of the hybrid torch for 300A suggests that
the gas stabilized part of the torch has a greater effect than at
higher currents. At higher currents the evaporation rate will be
larger and therefore have a greater effect than the gas stabilized
part.
TABLE III: Comparison of characteristics for the water-stabilized and
hybrid torch
current (A)
Argon in(slm)
power in(kW)
mass flux(g/s)
mean h(MJ/kg)
mean v(m/s)
mean ρ(g/m3 )
Mach number
water-stabilized
300
400
84
0,204
157
1736
4,15
0,317
106,8
0,272
185
2635
3,64
0,445
300
12,5
74,8
0,368
127
2875
5,8
0,630
hybrid torch
300
400
22,5
12,5
72,8
107
0,464 0,343
95,2 192,6
3143 4692
7,6
3,8
0,794 0,811
V. C ONCLUSION
We see that the hyrbid torch has a higher mass flow rate than
that of the water-stabilized torch, and that it’s enthalpy is a lot
higher than that of the gas-stabilized torch. The hybrid torch is
therefore a good way to bridge the gap in characteristic between
the gas and the water-stabilized torch.
R EFERENCES
[1] Bart Lannoo, Didier Colle, Mario Pickavet, Piet Demeester, Optical Switching Architecture to Implement Moveable Cells in a Multimedia Train Environment, Proc. of ECOC 2004, 30th European Conf. on Optical Communication, vol. 3, pp. 344-345, Stockholm, Sweden, 5-9 Sep. 2004.
[2] Michael
Neufeld,
Ashish
Jain,
Dirk
Grunwald,
Nsclick::
bridging
network
simulation
and
deployment,
http://systems.cs.colorado.edu/Networking/nsclick/
[3] The Click Modular Router Project, http://www.read.cs.ucla.edu/click/
[4] NS – Network Simulator, http://nsnam.isi.edu/nsnam/
400
22,5
108,6
0,422
161,2
5000
4,5
0,923
CONTENTS
viii
Contents
Toelating tot bruikleen
iii
Overview
iv
Extended abstract
v
Content
1 Plasma
1.1 What is Plasma . . . . . . . . . . . . . . . . . .
1.2 Thermal Plasma . . . . . . . . . . . . . . . . .
1.3 How plasma is made : The plasma torch . . . .
1.3.1 The electric arc . . . . . . . . . . . . . .
1.3.2 The different types of plasma torches . .
1.4 Thermodynamic properties of plasma . . . . . .
1.4.1 Energy and mass balance . . . . . . . . .
1.4.2 Flow rate of the plasma and composition
1.4.3 Gibbs Free Energy Minimization . . . .
viii
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2 Explanation of the reactor system and the instruments used
2.1 The system . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Diagnostics for thermal plasmas: . . . . . . . . . . . . . . . . .
2.2.1 Optical methods . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Probe methods . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 Acoustic and electrical signal processing methods . . . .
2.2.4 Thermocouples . . . . . . . . . . . . . . . . . . . . . . .
2.2.5 Pitot tube . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.6 The Quadrupole mass spectrometer . . . . . . . . . . . .
2.2.7 The Gas chromatograph . . . . . . . . . . . . . . . . . .
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CONTENTS
ix
3 Explanation of programs and results
3.1 Measured results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Calculation of the thermodynamic properties of the separate components
3.3 Calculation of the thermodynamic properties of the plasma . . . . . . . .
3.4 Program for the Calculation of the Mass flux and the Energy flux . . . .
3.5 Calculation of the amount of Argon present in the plasma jet . . . . . . .
3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A Thermodynamic properties for the seperate
A.1 Argon . . . . . . . . . . . . . . . . . . . . .
A.2 Argon 1+ . . . . . . . . . . . . . . . . . . .
A.3 Argon 2+ . . . . . . . . . . . . . . . . . . .
A.4 Argon 3+ . . . . . . . . . . . . . . . . . . .
A.5 Argon 4+ . . . . . . . . . . . . . . . . . . .
A.6 Argon 5+ . . . . . . . . . . . . . . . . . . .
A.7 Argon 6+ . . . . . . . . . . . . . . . . . . .
species
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for argon
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B Thermodynamic properties for the seperate
B.1 Oxygen . . . . . . . . . . . . . . . . . . . .
B.2 Oxygen 1+ . . . . . . . . . . . . . . . . . .
B.3 Oxygen 2+ . . . . . . . . . . . . . . . . . .
B.4 Oxygen 3+ . . . . . . . . . . . . . . . . . .
B.5 Oxygen 4+ . . . . . . . . . . . . . . . . . .
B.6 Oxygen 5+ . . . . . . . . . . . . . . . . . .
B.7 Oxygen 6+ . . . . . . . . . . . . . . . . . .
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C Thermodynamic properties for the seperate species for hydrogen
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C.1 Hydrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
D Tables for the calculation of the Mach number
115
D.1 Table of net power and Cooling water temperature . . . . . . . . . . . . . 115
D.2 Table of calculated Mach numbers . . . . . . . . . . . . . . . . . . . . . . . 120
E Programs for matlab
123
E.1 Program for calculation of Partition function,Enthalpy, frozen specific heat
and Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
E.2 Program for calculation of integrals . . . . . . . . . . . . . . . . . . . . . . 127
Bibliography
131
List of Figures
133
CONTENTS
List of Tables
x
135
CONTENTS
xi
Symbols and abbreviations used in
this thesis
The notation adopted below is used throughout this thesis, unless otherwise specified.
atm :
T:
L:
r:
v:
A:
t:
h:
m:
k:
E:
I:
J:
V:
C:
c:
x:
y:
p:
slm:
n:
kB :
me :
ρ:
atmosphere=101325 Pa
temperature (Kelvin or degrees Celsius, see context)
length (m)
radius (m)
velocity (m/s)
cross section (m2 )
time (s)
enthalpy (J/kg)
mass flow rate (kg/s)
thermal conductivity (W/mK)
electric field intensity(V)
current (A)
current density (A/m3 )
potential (V)
specific heat (J/kgK)
speed of sound(m/s)
mass fraction
molar fraction
pressure (Pa)
standard liter per minute= 1.666667 m3 /s
particle density (particles/m3
Boltzmann constant=1.38 10−23
mass of electron = 9.11 10−31
Density (kg/m3 )
CONTENTS
xii
σ :
η :
Electric conductivity (V/mK)
efficiency
PLASMA
1
Chapter 1
Plasma
The most exciting phrase to hear in science, the one that heralds new discoveries, is not
”Eureka!”, but rather, ”hmm,...that’s funny...”.Isaac Asimov
In this chapter I will give an explanation about what plasma is, and what its main
characteristics are. I will then go into more depth about thermal plasmas. In the next
section I will describe some methods used to create and stabilize the plasma.
1.1
What is Plasma
Although a lot of people might not even know it exists, just about 99% of the universe
consists of plasma. The space between the stars, lightning, the sun, all of us see plasma
every day, but most of us go through our entire life without realizing it is even there.
Plasma is a fourth state of matter, next to the solids, liquids and gases. The difference
between the first three is mainly the way the particles are ordered in the material. The
particles in solids are positioned in a solid lattice and therefore cannot move, but they can
vibrate. The interaction between the particles is strong. Above the melting temperature
this lattice dissolves and the material liquifies. The particles are closely packed together and
can move over each other, interacting only weakly. Beyond the vaporization temperature
the interaction between the particles practically vanishes completely, the material is in
its gas state. Now I will come to the fourth state. Plasma can be described as a high
temperature gas where the particles are ionized, meaning that they can conduct electricity.
Even if only a small fraction of the particles have been ionized the gas can show plasma-like
behavior. This as opposed to ”normal” gas, where the particles are electrically neutral.
Plasma can be formed in different ways, but the most common way is electric discharge.
This will be explained in 1.3.
1.2 Thermal Plasma
2
Plasma is generally divided into two large groups:
1. Cold, non-thermal, or non-equilibrium plasma
2. Hot, thermal or equilibrium plasma
Both types of plasma consist of different types of particles: electrons, ions, neutral particles in ground and excited states and photons. For an electrically conducting gas to be
considered a plasma the number of ions has to balance the number of electrons. In other
words, there has to be a charge balance such that the plasma is electrically neutral:
ni = ne
(1.1)
where ni is the number of ions and ne is the number of electrons.
Plasma can display luminosity, which is partially explained by excited neutral particles
falling back to the ground state and thereby emitting a photon.
One speaks of cold plasma when the charged particles have a much higher kinetic energy
than the neutral particles. This is because the energy of the charged particles is lost to
the boundaries of the plasma, before it can be transferred to the neutral particles through
collisions. The temperature of the electrons is in the order of tens of eV.
Thermal plasma is used in the reactor at the institute of plasma physics in Prague
(IPP) and I will therefore go into more detail about this type of plasma in the following
section.
1.2
Thermal Plasma
This information was taken from [6], [7] of which I used several chapters. As was men in the
previous section 1.1I will explain a bit more about thermal plasmas. Thermal plasmas are
partially ionized or strongly ionized gases. The plasma can be created by different methods,
but is usually created by an electric arc at atmospheric pressure. The temperature in this
plasma is high, typically 5000 up to 50000K. Because of this high temperature the enthalpy
and the thermal conductivity of the plasma will be significantly higher than that of gas.
The electric field in the plasma remains rather low and the particle density is quite high,
about 10 20 m−3 . Under these conditions it is assumed that the particle velocities follows
the Maxwellian distribution.
dnv = nf (v)dv
(1.2)
mv 2
4 2kT 3/2 2
) v exp(−
)
f (v) = √ (
2kT
π m
(1.3)
1.2 Thermal Plasma
3
For most calculations (except for transfer coefficients) the electron energy distribution
function can be considered to be Maxwellian.
Energy is built up in the plasma mostly by the Joule effect1 .
This energy is primarily absorbed by the lightweight and highly mobile electrons, which
pass it on to the other particles through collisions. Because of the high electron density
ne the rate of elastic collisions is very high and this leads to an isotropic distribution of
the energy in the plasma. In a first approximation we will assume thermal equilibrium,
meaning that all the particles have the same temperature. This condition is never achieved,
because even with perfect collisional coupling with high collision frequency the temperature
Te of the electrons will always be different from the temperature of the heavier particles Th .
This approximation will prove useful when calculating the thermodynamic properties by
simplifying the computations without creating too large errors. The condition for thermal
(or kinetic) equilibrium is:
2
Te − Th E
(1.4)
T
p
Here E is the electric field and p is the pressure.
In the plasma the electrons are not only responsible for the many elastic collisions but
also for the inelastic collisions, that cause ionization, excitation, recombination, etc. These
reactions are reversible because of the inversion symmetry of the Maxwell distribution.
Again, because the particle density is high, the number of collisions will be high as well and
a statistical equilibrium will be established among the particles. The electrons will transfer
the energy, which was received from the electric field per unit time, to the heavier particles
in the same amount of time This means the particle densities will obey the equilibrium
laws. (Boltzmann, Saha2 . Guldberg- Waage3 ). This is in very good agreement with the
experiments for high temperatures, such as in the centerline of the arc. In the colder
regions we have to take into account the radiation effects. These effects, combined with
the existence of temperature gradients and gradients in the density of the particles, show
that the plasma is in fact not in complete thermal equilibrium. That is why the term Local
thermal equilibrium (LTE) is introduced. In this approximation the equilibrium laws can
be used, but the Planck law regarding radiation cannot be applied here, as the radiation
is not in equilibrium with the particle density. The LTE is sustained through continuous
collisions between the plasma particles, so thermal plasmas are usually produced at high
pressures. (Close to or higher than 1atm) In short, the plasma needs to fulfill the following
1
2
3
This effect is the increase of the heat (or energy) due to the current passing through a conductor
Equations for the ionisation/recombination equilibrium
Equations for the dissociation/ association equilibrium
1.3 How plasma is made : The plasma torch
4
requirements to be in the LTE state:
1. There is a Maxwellian distribution function for the velocity (steady, uniform isotropic)
2. E/p is small enough so the temperature of the electrons is high and the same temperature can be taken for all the species in the plasma.
3. There is chemical equilibrium so that we can calculate the concentration of the particles present in the plasma.
4. Ionization and excitation is achieved mainly by electron collisions, the corresponding
particle densities follow the Saha equations, Boltzmann equations, respectively.
5. Local gradients of temperature, density, heat conductivity, etc. are small enough so
that the diffused particles have enough time to reach equilibrium.
There are some definite benefits to using thermal plasmas:
1) High temperatures can be reached: 5000-50000 K
1. They have a high energy density and a high energy transfer rate
2. The reaction time for chemical reactions in the plasma is low
3. There is a wide choice of plasmas mediums; at these high temperatures any material
can become plasma.
Due to all the experiments done in the past decades we now know that LTE in plasma
should not be readily assumed. The main reason for this is that there is no excitation
equilibrium. There is an overpopulation of the higher states and an under population of
the lower states due to the high radiative transition probability in these lower levels. In the
bulk of the plasma the effect of excitation is negligible, and therefore we can still assume
LTE. In the fringes of the plasma the deviation from LTE will be greater.
In high velocity plasma flow the chemical reactions can not follow the macroscopic
movement of the plasma, so the chemical equilibrium is broken.
1.3
How plasma is made : The plasma torch
Plasma is usually generated in an electric arc. By running a current through a gas or
a vacuum, a conducting path will form between the electrodes. This process is called
5
breakdown. This method is easy to set up and to keep up. In this section I will explain the
different parts and the operation of the different types of plasma torches. The information
for this section was found in [10], [1], [2].
1.3.1
The electric arc
The information for this section was found in [10], [1], [2].
An Electrical arc is a self-sustaining discharge between two electrodes. It is produced
when the air (or another gas) is ionized, by high temperature or high voltage, and is
therefore able to carry current. It has a low burning voltage and low cathode fall voltage.
The burning voltage is the voltage over the electrode gap. The arcs have very high current
density and a high luminosity and emission of radiation.
The arc is generated between two electrodes, the anode and the cathode. Some of
the main characteristics of the arc can be differentiated on sight. The arc is homogeneous
throughout the distance between the two arcs and it is constricted. This constriction of the
arc increases near the electrodes. The electric arc can thus be divided into three different
areas: the cathode region, the anode region and the arc column itself.
The arc voltage (the voltage between the two electrodes) depends on the radius of the
arc and whether or not the walls are “sensed” by the arc. If the influence of the walls is
small, we will have a descending volt-current characteristic. If the walls influence the arc
either a part of its energy will be absorbed by the wall or the walls will confine the arc to
a certain diameter, and a current rise will cause a voltage rise.1.2
Now I will give some more information about the different regions in the arc. This
information was found in [5] and in [18]
Figure 1.1: potential distribution along the arc
6
Figure 1.2: voltage (Volt) and current (Ampere) of the arc in a channel 1.smaller diameter; 2.
larger diameter
The Cathode region
The cathode is an electron emitter, it provides the electrons which will then be accelerated by the electric field. The cathodes are classified by the way they emit the electrons:
thermionic emission or field emission (cold cathodes).
Thermionic emission (also known as the Edison effect) is the flow of charged particles
from a heated charged conducting surface. The particles will have the same charge as
the surface from which they are emitted. In this case the cathode will have a certain
surface temperature, which is sufficiently high to provide enough electrons. To assure
this, refractory materials are used, sometimes with addition of materials with a low work
function. This causes more electrons to be emitted by the material at a lower temperature.
Cold cathodes are usually made up of water-cooled metal. The electrons are supplied
by the evaporation and ionization of metal in a very small cathode spot (this is the highly
energetic emitting area).
The electrons are emitted and then accelerated by the electric field. The injected gas is
then heated through the Joule effect. Because the electrons are such light particles, they
can accelerate more than the heavy neutral atoms, and ionize these atoms. These positive
ions will then accelerate towards the anode and release their energy.
The current density in this region can be very high (107 – 108 Am−2 ) and the widening
of the arc column will create a strong cathode jet, which has a stabilizing effect on the arc.
The Anode region
The anode can be put either perpendicular to or parallel with the axis of the arc.
Because the thermal flux in the arc attachment to the anode can reach very high values
7
the anode must by cooled. Because of the turbulent nature of the plasma jet, there are
fluctuations in the arc. Through extensive measurements of the voltage, three different
operating modes of the arc were discovered: the re-strike, takeover and steady mode. The
most important variable for the occurrence and transferring of a mode is the thickness
of the layer of cold gas (Duan et al.). Another division was made by Pfender et al., they
divided the turbulent region into three sections: a region where the cold gas is engulfed with
eddies into the plasma, a region where these eddies are broken down, and a fully turbulent
region. This very different theories show that the behavior of the arc is quite complex.
The fluctuation of the arc voltage and the movement of the arc root are considered to be
the main reason for energy fluctuations. If we would try to fix the arc root erosion could
occur and it would still not ensure a stable arc. The theory for this region is very complex
and will not be mentioned further.
The arc column
The arc column is where the energy is deposited and where the gas is heated. The voltage
drop over the arc is determined by its length, width, conductivity of the plasma in the arc
and the arc current. If we assume the arc flow to be fully developed4 ,radially symmetric
and stabilized by the wall, the flow can be described by the Ellenbaas-Heller equation:
dT
1 d
rk
+ σEz2 − Pradiation = 0
(1.5)
r dr
dr
Where r is the radial coordinate, k is the thermal conductivity, σ is the electrical conductivity, Ez is the axial component of the electric field and Pradiation is the power loss due
to radiation. This equation shows the balance for heat lost by conduction and radiation
and added through Joule heating. When the current increases the temperature and the
electrical conductivity increase while the potential difference will decrease. The arc diameter will increase with an increase in current, because the energy loss is proportional to the
diameter of the arc. Because the arc is wall stabilized the arc diameter is limited and the
temperature and the electrical conductivity will increase. But a higher potential difference
will be needed due to the increased heat loss to the wall.
This shows that for lower currents the V-A characteristic will be descending when the
arc widens, and for high currents the V-A characteristic will be ascending because the loss
of heat through conduction through the walls will have a greater effect.
4
The variables are independent of the axial distance
1.3.2
8
The different types of plasma torches
A plasma torch generates plasma and stabilizes the arc. The electric arcs are unstable by
nature; they will avalanche if they are not inhibited by current limiters. The discharge
is very turbulent and the arc will oscillate. This means the arc could come close to and
possible touch the walls (when they are metallic). This would lead to a decrease of the
length and of the power of the arc. This is an undesired effect, as we want to operate
in steady state if it is possible. Through stabilization we create and maintain certain
boundary conditions and also contain the arc. This containment helps the steady flow
of the current through the arc. When an arc is stabilized it does not mean the arc is
stationary, it can still rotate or move along the electrodes. So stabilization of an arc means
that the arc can move along a well defined path determined by the stabilization method
[10]
There are several ways to stabilize an arc. We can use a solid wall of heat conducting
material around the arc. When the arc deviates from its equilibrium position the wall will
ensure the temperature drops through heat conduction to the wall. This will diminish the
conduction in the fringes of the plasma and cause the arc to return to its former position.
As plasma is electrically conducting we can also use a magnetic field to stabilize the arc.
The torch used in the experiments is a hybrid torch. This is a combination of a gas
stabilized and a water stabilized plasma torch. This type of stabilization uses convective
heat transfer. In this case the arc is confined to the center of a tube by an intense vortex
of gas or liquid which is maintained in the tube. The centrifugal forces caused by the
vortex movement will push the cold liquid or gas towards the wall, which is thus thermally
protected. There is also a superimposed axial fluid flow, which continuously introduces
new cold gas or liquid into the tube and stability can be achieved.
The gas-stabilized torch
The information about the gas-stabilized torch was found in [18].
In a gas stabilized torch the arc is formed between the anode and the cathode.
The gas flows along the cathode and in between the anode, which forms a constricting
nozzle. As mentioned in 1.3.2 the anode has to be sufficiently cooled, this is done by using
pressurized water. To prevent the overheating of either side of the anode the cathode has
to be perfectly centered with respect to the anode opening. The gas enters the torch either
tangentially or axially. The amount of gas has to be sufficient to ensure a layer of cold gas
of certain thickness between the cathode and the nozzle, otherwise the arc will overheat
the walls of the chamber. The tangential flow will then run in a vortex around the arc.
9
This vortex pushes the cold gas to the walls of the chamber through centrifugal forces. The
hot gas will remain in the center. The axial component of the vortex is larger than the
radial component. At the exit of the nozzle the radial component will be suppressed and
the jet will flow axially. This kind of constriction makes for high energy density and high
temperatures in the chamber. The enthalpy (calculated as the ratio of the useful power to
the arc and the flow rate of the plasma forming gas) is mostly between the 1-100MJ/kg.
These values are limited because the walls are protected from thermal overloading by the
flowing gas. That is why there will be a minimum gas flow rate for a certain arc power.
Figure 1.3: : Scheme of the Gas stabilized torch
If water is ised instead of gas we would have evaporation near the arc and a cooling
through the water. Then higher enthalpy and temperatures can be reached without the
problem of overheating. (Ideal for thermal plasma)
The water-stabilized torch
The information for this part was taken from [3], [14] and [12].
In a water-stabilized torch the arc is ignited in the center of the water vortex. This
vortex is created by tangentially injecting the water into a cylindrical arc chamber.
The vortex evaporates and thereby cools and constricts the arc in the chamber. Because of the overpressure created in the chamber the arc plasma is accelerated to the exit
nozzle.The main advantage here is that there is no need for gas supply because the plasma
is generated by the heating and ionization of the steam evaporated from the vortex.
The material properties of the plasma medium and the dimensions of the arc chamber
influence the arc characteristics. Let us write the energy balance for internal energy to
10
analyze this effect. (Cylindrical coordinates)
∂(ρvz hA)
∂T
− mh(R) = AσE 2 + 2πR(k
)r=R − 4πεn A
∂z
∂r
(1.6)
In gas-stabilized arc chambers m is 0.
Here ρ is the plasma density,vz is the axial velocity, h is the enthalpy, m is the mass
flow rate from the chamber per unit length, σ is the electric conductivity, k is the thermal
conductivity, T is the temperature, εn is the net emission coefficient and E is the electric
field intensity. The emission coefficient represents the power loss due to radiation. A is
the cross section of the chamber and R is the radius. If we average the quantities over the
cross section A then we use the following equation:
1
X=
πR2
ZR
2πXrdr
(1.7)
0
If we approximate the derivatives in equation 1.7 as f rac∂ρvz hA∂z = f racρvz hAL and
RT
∂S
S
)
=
(
)
=
−
.
Here
S
is
the
heat
flux
potential
S
=
(k ∂T
kdT and L is the arc
r=R
r=R
∂r
∂r
r
T0
length. The enthalpy at the edge of the arc chamber h(R) = h (Tb) =0 where Tb is the
boiling temperature of water. The equations for electric field intensity E and arc current
I are then derived as:
s
1
Gh
(1.8)
E=√
+ 2πS + 4π 2 R2 εn
L
πσR
s
√
Gh
I = πσR
+ 2πS + 4π 2 R2 εn
(1.9)
L
Here G is the total mass flow rate and is calculated as G =
RR
2πrρvz dr = πR2 ρvz . From
0
these equations we can see that we can calculate E, I and the temperature, for the known
ratio of G/L and radius R. From the calculations we see that the water-stabilized arcs have
high electric field intensity, high arc powers, and also high enthalpy.
The main difference between the two torches is the process that determines the mass
flow.
In the gas torch the mass flow is determined by the flow rate of the gas. In liquid
torches arc processes determine it. A part of the power input IE is dissipated by Joule
heating in the core of the arc.Another part is absorbed into the water-body or into the
chamber walls. From there the dissipated energy travels radially to the water vortex. The
steam produced by the evaporation of the water in the vortex heats up, ionizes and forms
11
plasma. The steam is heated by conduction, turbulent transfer and radiation. So the mass
flow cannot be independently altered as in the gas torch.
Figure 1.4: : comparison of power versus mass flowrate between gas and water- stabilized
torches
As can be seen in the graph 1.4 the gas-stabilized torches achieve much higher mass flow
rates than the liquid torches. The mass flow G to the length L is low in water stabilized
torches and so high enthalpy and high temperatures can be achieved.
The characteristics of the two torches are quite different. If we want to achieve a high
torch enthalpy, high mass flow and energy density, we have to look somewhere else.
The hybrid torch is a solution to this problem. As it has a higher mass flow due to the
gas stabilized part and a high enthalpy due to the water stabilized part.
Let us now take a closer look at this hybrid torch
The hybrid torch
The hybrid torch has a gas-stabilized part near the cathode and a water stabilized part
in the chamber next to this. As with the liquid-stabilized torch the water moves in a swirl
around the arc. The last part is a free jet of plasma.
In the first chamber the gas is injected through the cathode vortex and stabilizes the
arc there. Through the nozzle the plasma then flows to the second chamber, where it is
stabilized by the water. The stabilization occurs through vortex flow of water in three
cylindrical chambers. The arc column interacts with the water vortex and the water
evaporates to steam. The mixture of gas and steam forms plasma. The steam mixes
12
with the plasma from the first chamber (also called the cathode chamber) and creates an
overpressure, which accelerates the plasma towards the exit.
The anode is made of copper and rotates to prevent hole burning by the plasma.
The cathode is made of Tungsten. The electrons are emitted by thermionic emission.
We use thoriated tungsten for its high electron emission ability and its low erosion rate.
Both the anode and the cathode are water cooled to slow down erosion.
Because the anode is external there are some difficulties in preventing the plasma jet
from intensively mixing with the surrounding air. This can be a problem in spraying
systems.
Usually the gas used in the hybrid torch is Argon. This gas only needs a low voltage to
sustain the arc column. Because of the low thermal conductivity k the arc will be narrow
and therefore it will have a high temperature. Sometimes hydrogen is mixed with the
argon for reducing and oxidizing effects. It also increases the heat content and transfer in
the gas stabilized chamber.
Because of the low enthalpy, heat conductivity, absorption coefficients and radiation
intensity of the Argon the arc will have the thermal characteristics of the water-stabilized
arc. Only the characteristics controlled by mass balance such as velocity, momentum flux
and plasma density will change considerably. This can be seen in the graph 1.5.
The only problem here is that the mass flow of Argon can not be easily determined.
The amount of steam is very large compared to the amount of argon present. That is why
theoretical calculations must be made to determine these values.
Figure 1.5: Scheme of hybrid torch
1.4 Thermodynamic properties of plasma
1.4
13
Thermodynamic properties of plasma
When describing a physical state of thermodynamic equilibrium in plasma, we use pairs
of state function: (T,V); (s, p); (T, s). Here T is temperature, s is the entropy, p is the
pressure and V is the volume. The thermodynamic properties of plasma include the mass
density ρ , the internal energy u, the enthalpy h, the specific heat and the entropy s. If
we then need other thermodynamic properties, they can easily be calculated using the
thermodynamic equations. For example: the Gibbs free energy can be calculated by:
G = H − TS
(1.10)
If we consider a mixture of particles which has a dynamic equilibrium between dissociation,
recombination and ionization, the total energy is a function of the energy of the different
particles and of the possible chemical reactions between these particles. This is why the
thermodynamic properties depend so strongly on the composition. The local composition
is a function of the local temperature, pressure and the concentrations of the chemical
elements. The composition can be calculated by the minimization of the Gibbs free energy
for given pressure p and temperature T. Since we use gases in a wide range of temperatures
(from room temperature up to 20000 K) we need to consider a wide range of particles.
If we were to consider a plasma generated in a mono atomic gas, such as Argon, we
can describe the composition with three types of particles: the neutral atom, the positive
ion and the electron. For these three types we have three equations, the Eggert- Saha
equation, Dalton’s law and the quasi neutrality condition.
ne ni
2Qi
=
n
Q
2πme kT
h2
3/2
Ei
exp −
kT
(1.11)
p = (ne + ni + n)kT
(1.12)
ne = ni
(1.13)
In formula 1.11 Q and Qi are the partition function of the neutrals and the ions, respectively and h is the Planck constantand Ei is the ionization energy. These partition
functions are the link between the microscopic coordinates of the system and the macroscopic thermodynamic properties. The partition functions are given by:
P
Qi = gi,s exp(−Ei,s /kT )
Ps
Q = gs exp(−E/kT )
s
(1.14)
14
With these equations the composition can be calculated for a given pressure.
For plasma generated by a molecular gas we can use equations similar to the EggertSaha equation. The thermodynamic properties can be calculated from the sum of the
”frozen” property (where reactions are not taken into account) and the reaction property.
Although a lot of the relationships in plasma are based on the uniformity of the plasma, it
is difficult, if not impossible to obtain a completely uniform plasma. Due to this fact the
plasma will have gradients in temperature, number of particles etc. and thus there will be
fluxes present in the plasma. The transport coefficients in the flux equations are difficult
to calculate. One of the most important transport coefficients for thermal plasmas is the
thermal conductivity coefficient k. Its importance lies in the fact that it determines the
heat flow through conduction.
1.4.1
Energy and mass balance
The power that is transmitted to the arc by the electric unit through current and voltage,
is not entirely transferred to the plasma in the arc. The efficiency of power throughput
is about 60%. Other power losses are those to the cooling water and to the walls. The
exact calculation of the power losses to the walls is difficult to asses, as the thickness of
the chamber walls is not uniform.
The power losses to the cooling water can be found by the following equation:
Q = Cp mH2 O (Tin − Tout )
(1.15)
Where Cp is the heat capacity of the water (kJ/kgK), GH2 O is the mass flow rate of the
water (kg/s), Tin is the temperature before the cooling water enters the system.
1.4.2
Flow rate of the plasma and composition
The calculation of the flow rate in the hybrid torch is not as straight-forward as in the
water-stabilized torch. The amount of argon used is very small compared to the larger
steam flow, and therefore difficult to determine exactly. This is why we will have to
consider each step separately.
With the balance of power we can calculate the amount of plasma coming out of the
jet. We know the amount of argon going into the plasma jet.
We can also measure the amount that is lost to the water cooling system. From this
information we can calculate the amount of argon in the plasma jet. The problem for the
water can be handled in much the same way. The water is vaporized when in contact
15
Figure 1.6: illustration of mass balance for Argon
with the plasma. When it is in contact with the water cooling system it will partially
condensate. The gas coming out of the cooling system is measured and the water which
condensates will not be taken into account. This makes the calculations for the amount of
water less precise.
To find the flow rate of the plasma out of the jet we have the following information.
We know the power flow into the jet ( I*U = current times the voltage). We also know
the power loss to the cooling system by measuring the mass flow and the temperature
difference between two points such that
Qloss = ṁwater cp ∆T
(1.16)
With these two values we can calculate the flux of the plasma jet.
Fplasma = IU − Qloss − mevaporation Qevaporation
(1.17)
The formula for the enthalpy flux of the plasma with the evaluation in thermodynamic
properties is:
ZR
Fplasma = ρvh(2πr)dr
(1.18)
0
16
In this formula we have used the fact that the exit of the plasma jet is circular. We also
know that throughout the plasma jet the mach number M is constant and we know that
M=v/c, where c is the speed of sound. If we put this into formula 1.18 we find that the
flux of the plasma jet is :
ZR
Fplasma = M (2πr)ρchdr
(1.19)
0
In this formula Fplasma can be calculated from the energy balance (formula 1.35). M is
independent of the radial co-ordinate at the exit nozzle, if we neglect the radial pressure
gradients and if radial velocity is small compared to the axial component. If we know the
Mach number M, we can also calculate the mass flow rate out of the torch.
ZR
mplasma = M
(2πr)ρcdr
(1.20)
0
For gas stabilized torches the flow rate can be changed independently, but a minimum value
must be maintained for a certain arc power. For water stabilized torches the mass flow
rate is determined by the evaporation rate of the stabilizing wall,mevaporation .mplasma =
mevaporation L(1.21)The main stabilizing part of the hybrid torch is also water-stabilized.
Therefore I will use this equation for the calculation of the mass flow rate in the hybrid
torch. The Mach number can be calculated when the integrals of the thermodynamic
parameters are known. (see chapter 3)
The formula for M is:
L(IE − Qev )
M= R
(1.22)
R
RR
0
0
In this formula λ is the latent heat capacity for vaporization and Cw is the specific heat
for water. The real problem is that ρ, c and h are dependent on the temperature, which
in turn is dependent on the radius (these variables are also dependent on the pressure
but we assume the pressure is constant at 1 atm or 105 Pa) . The numbers also depend
on the amount of argon being used. It is clear that a method is needed to calculate the
composition of the plasma at different temperatures. The method which is most widely
used is the Gibbs free energy minimization.
1.4.3
Gibbs Free Energy Minimization
This method calculates the composition of a plasma. It needs the chemical potentials of
all the chemical particles present.
17
At high enough temperatures we can use the statistical functions known as the partition
functions. These functions use the internal energy levels of the different species, which can
be calculated through spectroscopy. The easiest calculation is for plasma in CTE. This
can not be assumed and most calculations will need the consideration of two different
temperatures, Te for the lighter particles, and Th for the heavier particles.
Figure 1.7: Composition of gas containing H vs temperature
The amount of particles for each of those chemical species is divided over the different
energy levels. In the formulas Ni is the number of particles of a certain species and Ni,s is
the number of particles of species i in state s. These numbers are linked by the following
formula:
−Ei,s
g
exp
i,s
kT
Ni,s
= K
(1.23)
P
Ni
−Ei,s
gi,s exp kT
i
Ei,s is the internal energy level at quantum level s. The denominator of this equation is the
atomic or molecular internal partition function. For a given particle two types of energy
will be considered: the translational energy and the energy for the internal degrees of
freedom. For an atom this will be the excitation energy of the electrons, and for molecules
the vibrational and rotational degrees of freedom will be included.
18
When using the Boltzmann statistical treatment the Boltzmann hypothesis has to be
fulfilled. This states that the number of quantum levels should exceed the number of
particles, so that the probability of finding two particles in the same state is negligible.
The energy of the system is the sum of the energies of all the separate particles. The
partition function Q is then
Q Ni
Qi
i
(1.24)
Q= Q
Ni !
i
For this formula to be valid all the interconnected energy levels must be referred to the
same energy level.
When we calculate these levels there are some corrections which must to be taken into
account.
1. the Debye correction
2. the virial correction
The Debye correction is a correction for the interaction energy that is introduced by the
long range Coulomb interaction. Because of high temperatures the density of ion particles
will increase. These higher densities will cause the Coulomb interaction to take on a more
significant effect and this leads to an interaction energy, which will have to be added to the
thermodynamic functions. The value of this energy remains small (2 or 3% of the normal
value) so that it is usually not taken into account.
The virial correction takes into account the interaction of two atoms in the vicinity of
each other. If we examine the Morse potential we see that two atoms will attract until
they are too close (order of an angstrom) when they will repulse each other. When the
mean free length is larger than the average distance between the atoms this correction is
negligible. For the pressures at which the jet operates here this is the case.
System states can either be characterized by the pressure and the temperature, or the
volume and the temperature. If a system is described in the p,T system the equilibrium is
reached when the Gibbs free energy is at a minimum or, dG=0. For a spontaneous reaction
the derivative of the Gibbs free energy is smaller than zero, or dG<0.
G(T, p) =
n
X
µi Ni + G0 (T, p)
(1.25)
i=1
In this formula µi is the chemical potential. G0 is the part of the Gibbs free energy which
does not depend on the composition. The chemical potential can be found using the
19
partition function with the following formula:
Qi
0
µi = −kT ln
+ E0i
Ni
(1.26)
The second term is the energy needed to reference each level to the same reference level.
We want to know the composition for the equilibrium state of the system so we calculate
the differential of the Gibbs free function, which must be equal to zero.
dG =
n
X
µi dNi +
n
X
i=1
Ni dµi = 0
(1.27)
i=1
According to the Gibbs-Duhem relationship (Fowler Guggenheim 1956)
n
P
Ni dµi = −SdT +
i=1
V dP the second term is equal to zero for isobaric (atmospheric pressure) and isothermic
conditions (equilibrium state is assumed here). So the equation that remains to be solved
is :
n
X
dG =
µi dNi = 0
(1.28)
i=1
This equation is solved by finding the Ni ’s that fulfill the equation, and which also satisfy
Dalton’s law and the law of conservation of chemical elements (the number of moles of the
elementary species is conserved). Dalton’s law states that the total pressure is the sum of
the partial pressures of the different species.
p=
n
X
pi
i=1
For the different species present in the system we will write the different chemical
equations. From these equations we will use Hoff’s law for stoichiometric coefficients to
solve 1.6. The rate of production of a certain species is proportional to its stoichiometric
coefficient, and its sign is positive for the species which are produced. (the values of the
stoichiometric coefficients can be found from each chemical reaction equation)
After considering these equations we are left with relations between the chemical potentials of the different species. At this point we will use Dalton’s law to further eliminate
the unknown variables. The partial pressure in the Dalton’s law can also be written as
Ni
pi = P
p
n
Ni
i=1
Because of the complexity of the system (with the different ions of each species) I will
use a simplified system. To illustrate the forms of the next few equations we will use a
20
system of nitrogen. In this system the nitrogen dissociates and then ionizes.
N2 2N
N N + + e−
(1.29)
If we then calculate the mass action laws through the partial pressure equilibrium constants
we find that
p2N
1
0
0
Kp (N ) =
= exp −
2µN − µN2
(1.30)
p N2
kT
ppN + e−
1
+
0
0
0
Kp (N ) =
= exp −
µ + + µe− − µN
(1.31)
pN
kT N
These are the equilibrium constants for dissociation (1.30) and for ionization (1.31)
To calculate the composition for a mixture of several species, it becomes obvious that we
will need to solve a set of non-linear equations. For this a numerical computer technique can
be used. Brinckley’s way to tackle this problem is to solve the equations for conservation of
chemical elements, the equation for electrical neutrality and the partial pressure equilibrium
constants for dissociation and ionization, using a method which will lead to equations which
can be solved by a more applicable method. One of these methods is the NASA method.
The first step is to provide an estimation of the composition, so a value for the amount
of each species present in the system, and also the total number of particles. These values
are not likely to satisfy all the conditions (mass action laws, chemical conservation laws,
Dalton’s law) so the method then tries to improve the initial guesses.
The NASA method uses three differences. The first is ∆g which is the differences in the
mass action laws. For a change in temperature of a few hundred degrees, the composition
for the case of a disappearing or generated species can change by orders of magnitude. To
account for these steep variations in the composition we will use logarithmic coordinates.
Expressing the equilibrium constants as functions of the particle numbers we find that
N
N
∆g(N ) = 2 ln N
− ln NNT2 + ln p − ln Kp (N )
NT
N
N
∆g(N + ) = 2 ln NNT+ + ln NNTe − ln N
− ln p − ln Kp (N + )
NT
(1.32)
In these formulas Kp is the theoretical value for a certain p,T and NN , NN + , Ne , NN 2 and
NT
are the initial guesses.
The next difference is ∆a. This is the difference in the conservation laws.
2N
N
∆a(N ) = N
+ NNT 2 +
NT
N
∆a(e) = NNTe − NNT+
NN +
NT
−
Nav
NT
(1.33)
21
The third and final difference is the ∆p : the difference between the actual pressure and
the sum of the partial pressures.
Ne
NN
N N 2 NN +
∆p =
+
+
+
p−p
(1.34)
NT
NT
NT
NT
Equilibrium is reached when all three differences equal zero. The problem can be solved
by using first order linearization to find a set of particle number corrections. This set will
give new values for the three differences. This iteration can be continued until we find a
desirable accuracy.
This problem can also be solved by using logarithmic corrections. If we consider ∆g:
−∆g(N ) = 2d (ln NN ) − d (ln NN2 ) − d (ln NT )
−∆g(N + ) = 2d (ln NN + ) + d (ln Ne ) − d (ln NN ) − d (ln NT )
(1.35)
Considering the fact the NN and Ne are the fundamental species through which other
species can be expressed, we can write d(ln NN 2 ) and d(ln NN + ) as functions of d(ln NN )
and d(ln Ne ). Introducing these expressions into the three differences we achieve a set of
linear equations. These can be solved through iteration until convergence. This was done
in the program written by Petr Krenek.
If we consider the species in the jet of the hybrid torch we have those present in steam
and vapor. In this case we must consider H2 , O and A. At the high temperatures in the
jet the H2 will already have dissociated(see figure, calculated with T&T winner program)
and the oxygen and argon will have formed ions. The ionization temperature of H is very
high so we will not consider hydrogen ions. In total 15 different chemical species will be
considered.
The figure shows the temperature dependence of the equilibrium composition. We can
see from the figure 1.8 that when the temperature rises the number density of the argon
drops, and the particle density for the argon ion A+ increases. For higher temperatures
this number will also decrease when the presence of A++ increases and so on. For oxygen
the same processes will be considered. We will have the following chemical processes in the
mixture: For dihydrogen there will first be a dissociation reaction and then a ionization
reaction.
H2 2H
H H+ +e−
22
Figure 1.8: composition of Argon gas for temperature range 10000K to 50000K
For argon and oxygen we will only have to consider subsequent ionization reactions.
A A+ + e−
A+ A++ + e−
A++ A+++ + e−
···
O O+ + e−
O+ O++ + e−
···
With the program of Petr Krenek the composition was calculated. This composition was
then inserted into a second program which calculated the thermodynamic properties of
the gas containing those elements that were found in the first program. This program also
used the thermodynamic properties for the individual elements, which were determined
using my program. These programs will be explained in chapter 3.
EXPLANATION OF THE REACTOR SYSTEM AND THE INSTRUMENTS USED
23
Chapter 2
Explanation of the reactor system
and the instruments used
In this chapter I will explain how the reactor system is set up at the institute. The figures
will help to clarify the actual situation. I will also describe the systems used for the
diagnostics of the plasma device.
2.1
The system
Information for these sections was taken from [4]and [3].
The system used in the experiments is shown in figure 2.1 Waste is fed into the waste
reactor by means of a screw feeder. Once it is in the reactor is decomposed into noncomplex molecules due to the thermal energy and so syngas is produced. The plasma
torch inside the reactor provides the energy needed for the gasification. Next the syngas
is rapidly quenched by the water-cooling system. This prevents any formation of complex
molecules with possible harmful effect, such as CO2.
In the combustion chamber the syngas is then burned.
The reactor: The reactor is cylindrical and has a certain inclination to make sure all
the waste input goes through the plasma jet to be gasified.
The outer wall is made out of 5 layers of steel. The different layers procure a low
thermal conductivity between the reactor core and the outside of the reactor. The wall is
also water-cooled. The inner wall is made of refractory ceramics to reduce the power loss
in the reactor. This ceramic layer has a very high melting point and is therefore very well
adapted to the high temperatures in the reactor.
The most important measurements are those of the temperature, pressure and the flow
2.1 The system
24
Figure 2.1: : Scheme of the reactor system
rate and composition of the syngas. How these units are measured will be explained in the
section about Plasma Diagnostics see section 2.2.
The temperature is measured by thermocouples. This of course poses a problem if we
want to know the exact temperature of gas. The most common problems for error are the
radiation losses, the conduction error and the reactions between the plasma gasses and the
metallic surface of the probe. The thermocouples are made of different types of metals
each with their own range of use.
Tungsten for example, is used from the range of 600 up to 2134K. Theoretically this type
could be used for temperatures starting from 0 degrees Kelvin, but in the low temperature
range there is a sinus shaped voltage, which causes problems for an accurate measurement.
After about 50K the voltage measured is only still microvolts, so measurements should be
amplified. That is why the tungsten thermocouples are only used from 600K upward in
practice.
The pressure is measured at different points. The most important points are those
where the pressure of the syngas is measured.
The flow is measured by Pitot tube flow meter. This tube has to be able to resist the
high temperatures in the gas. That is why it is made out of Inconel. Again the problem is
2.1 The system
25
Figure 2.2: : Input and output for the reactor system
the exact measurement of the flow of the gas see section 3.4.
In some experiments the anode chamber (top part of the reactor) is also injected with
argon gas, not only for the arc, but also to prevent the back-flow of soot.
Before the reactor is started there is a period of preheating. If we would just ignite the
arc in the reactor, the ceramic lining would crack, resulting in great power losses. This
preheating is done by a propane gas burner. The manufacturer of the ceramic lining gives
a certain angle, which the curve portraying temperature to time may have, so the lifetime
of the lining would not be shortened by the heating.
The water that is used for cooling comes from an outside system. This system only has
one controlling pump, which does not operate constantly, and therefore we have fluctuations
in the flow to our cooling system. This results in oscillating temperatures.
A spray of water (low flow rate) quenches the hot syngas; this spray is needed to cool
down as much of the syngas as possible. At the top of the quenching tower the water is
therefore mixed with a small amount of air so a larger area is cooled at once.
The best temperature to work with depends on the composition of the syngas. If
we want to get rid of the complex molecules, the temperature needs to be high enough.
According to the following graph, the best temperature to work with for our needs is about
1300K. This then results in a syngas primarily composed of hydrogen (43%) and carbon
(47%)monoxide.
The problem for the measurement of the flow rate of the syngas is that it requires the
knowledge of the density of the gas. This does not only depend on the pressure, but also on
2.2 Diagnostics for thermal plasmas:
26
Figure 2.3: Detailed schematic of measuring points in the system
Figure 2.4: Composition of the syngas in Molar fraction in relation to the Temperature
the temperature and the composition of the gas. The temperature of a gas is not easy to
measure, especially of a hot gas like the syngas. The composition of the gas is not known
at every point in time. Therefore we assume the density to be a constant, namely, ρ= 0.35
kg/m3. (a value derived from experiments)
2.2
Diagnostics for thermal plasmas:
Information was taken from from [10] and [1] Diagnostics of the thermal plasma is needed
to study and control the plasma proces. The methods used for these diagnostics have to
be well adapted to the high temperatures and the high velocities, which occur within these
plasmas.
27
Several methods have been developed for the diagnostics of thermal plasma. Here I
will briefly overview these methods and then explain the ones that have been used in the
experiments in more detail.
2.2.1
Optical methods
These methods are most commonly used in diagnostics.
Emission/Absorption techniques
these methods use absolute line spectroscopy, Boltzman plots, Stark broadening1 and twopoint light emission correlation techniques. This method is widely used in plasma diagnostics. The apparatus is located outside the torch andthe measurements do not influence
the plasma. Spectroscopy can have very good resolution. Analysis of this data can provide
information about the physical states of the species present.
Laser induced techniques
such as LIF2 Thomsom and Rayleigh Scattering and Coherent Antistokes Raman spectroscopy. These methods are based on the analysis of radiation emitted from the plasma
after illumination by high power lasers
Flow visualization
uses high-speed photography, laser interferometry and schelieren techniques.
High speed photography
High-speed photography is used to capture events that occur in time spans smaller than
the human eye can perceive (ms or even µs). This method uses cameras with very short
exposure times and very high sample rates. Because arc jets show strong fluctuations
in time and in space, this method can give information about the shape, stability and
movement of the jet. Usually the samples are taken at specific times specified by the
controlling computer.
1
Even if there is no macroscopic electric field, the ion will feel the electric field caused by the neighbouring charged particles in the plasma. The broadening of the lines can be used to determine the density
of the plasma
2
Laser induced fluorescence: if plasma contains ions that fluoresce the temperature, density and flow
can be determined.
2.2.2
28
Probe methods
These methods have become more widely accepted of the past ten years. The most commonly used probes are the Langmuir and the enthalpy probe, which will be discussed in
the following section.
The enthalpy probe
Information was gathered in [11] and [10]. The enthalpy probe is a device commonly used
in the experiments. The advantages are that it is a low cost appliance, and the velocity and
enthalpy of the plasma can be measured directly. The disadvantage is that it may perturb
the plasma. Experiments have shown (Rahmane et all 1995)however that the plasma is
only cooled down about 3% in the centerline by inserting the enthalpy probe. This error
is comparable to the one found in other techniques; such as emission spectroscopy. It is
found that for the enthalpy probe to still be accurate, it can be used for temperatures up
to 10.000K. And even that for these temperatures the enthalpy probe is more accurate
than emission spectroscopy.
Figure 2.5: : Enthalpy flux (right) and density(left) vs the radius for the water stabilized torch
and the hybrid torch measured at the nozzle
The enthalpy probe is constructed of three concentric tubes. It is water-cooled. The
probe measures the stagnation pressure and takes gas samples. There are three thermocouples present. One measures the temperature of the gas at the probe end, and the two
others measure the temperature rise in the cooling water.
29
Figure 2.6: Schematic of the enthalpy probe system
The local specific enthalpy of the plasma hi can be derived from the combined energy
balance of the cooling-water flow and the gas sample. The plasma enthalpy can be found
Cp (∆TGF − ∆TN GF ) + hexit
by the following equation:htip = mmwater
gas
htip is the enthalpy at the tip of the probe, hexit is the enthalpy at the exit of the probe.
∆TGF is thee temperature rise of the cooling water if there is gas flow, ∆TN GF when there
is no gas flow (tare measurement). mwater is the mass flow of the cooling water, mgas is
the mass flow of the gas, Cp is the specific heat of the water and is assumed constant. The
flow of the gas has to be in accordance with the isokinetic sampling law. This law states
that the velocity in the measuring tube must be as close as possible to the free stream
velocity. In this equation mwater has to be altered to make sure the temperature difference
(∆TGF − ∆TN GF ) is large enough to measure, but it is constant during the measuring
cycle. If the mass flow of the gas is increased the ratio of the mass flows decreases, but the
heat flux to the cooling water increases. These two effects cancel each other out, so the
plasma enthalpy is independent of the mass flow of the gas within a certain range. hexit is
calculated from the temperature at the exit of the probe and it does not vary significantly
with the mass flow. If the gas composition is known at the probe exit, the mass of the gas
can be calculated through the mass flow rate. The plasma temperature T can be calculated
from the dependency of htip on the temperature. For a mixture we can use the Favre law
for the calculation of the temperature, if the composition of the gas or plasma is known.
hmix (T ) =
N
X
xi hi (T )
(2.1)
i=1
Here N is the number of the different species in the mixture. Xi is the mass fraction, which
yi M i
is calculated as xi = P
, where yi is the molar fraction, Mi is the molecular weight.
N
yj M j
j=1
30
Figure 2.7: Schematic of tare and sample tests for enthalpy probe
The calculations of quantities such as temperature, enthalpy. . . with computer programs
usually assume Local Thermal Equilibrium. This approximation assumes that the Maxwell
distribution can be used to describe the translational distribution of the species, and the
Boltzmann distribution can be used to describe the atomic excitation.
Figure 2.8: : Temperature range for different diagnostic measures (left); enthalpy probe in
plasma (right)
Because the density of the plasma is very low and the exit velocity is very high, there
will be a lot of interaction with the ambient air near the jet nozzle. These fluctuations
have high frequency time constants up to 100 kHz. Near the exit nozzle, highly coherent
oscillations are formed, which decay near downstream in the jet. Due to the external anode
there is an interaction between the plasma flow and the flow in the anode. This interaction
causes deflections and the whipping of the jet.
2.2.3
31
Acoustic and electrical signal processing methods
Here information is gathered through a simple spectrum analysis of the acoustic noise,
which is emitted, by the DC arc discharge, and/or the fluctuations of the voltage of this
discharge.
2.2.4
Thermocouples
Thermocouples are thermo-electric temperature sensors [19], made up of two metallic wires
of a different type, which are put together at the tip of the probe and extended to a reference
probe with known temperature. The change in the voltage measured at the reference tip3 is
then used to calculate the temperature difference between the probe tip and the reference
junction. The absolute temperature is then derived by making the difference between the
reference temperature and the temperature difference as calculated above.
Figure 2.9: schematic of a thermocouple
Because of the Seebeck effect the voltage can be used to determine the temperature if
we connect a different conductor to the first one at the hot end of the wire. This second
conductor will then also sense a temperature gradient and will also generate a voltage, different from the first one. The voltage difference will increase with increasing temperature.
The relation between the temperature and the voltage is given by the following polynomial
expansion:
N
X
T =
an v n
(2.2)
n=0
The cold junction is mostly used as the reference junction.
3
Due to the Seebeck effect: any conductor which has a temperature gradient will generate a voltage
32
There are different types of thermocouples, depending on which metals are connected.
The different types are classified by letters. At the institure we mainly used type K
and B. Thermocouple types B, R, and S are all noble metal thermocouples and exhibit
similar characteristics. They are the most stable of all thermocouples, but due to their
low sensitivity (approximately 10 µV/˚C) they are usually only used for high temperature
measurement (>300 ˚C).
The sensitivity of the thermocouples depends on the wire size. If higher lifetime is
needed a thicker wire should be used, but this negatively affects the precision of the measurement.
The length of the thermocouple must be sufficient to minimize the conduction effects
of the hot end of the thermocouples, but not too large so it will not disturb the plasma
flow. There is also a correlation between the probe size and the settling time4 of the probe.
The bigger the probe the longer the settling time will be.
Also the insertion of the thermocouple must be enough to read out exact temperatures.
This can present a problem when working with thermal plasma. The probe must be able
to withstand the intense heat and still be able to read out the exact data. The other
problem comes with the radiation and the conduction of the thermocouples, which impede
the exact measurement of the temperature in the plasma.
Type K
This type is made of Chromel (Ni-Cr alloy) and alumel( Ni-Al alloy). This thermocouple is
used for temperature between -200˚C and 1200˚C. It is a low cost thermocouples, which
is used for general measurements.
Type E :Chromel / Constantan (Cu-Ni alloy)
Type E has a high output (68 µV/˚C), which makes it well suited to low temperature
(cryogenic) use. Another property is that it is non-magnetic.
Type J
(Iron/ Constantan) Limited range (-40 to +750 ˚C) makes type J less popular than type
K. The main application is with old equipment that cannot accept modern thermocouples. J types cannot be used above 760 ˚C as an abrupt magnetic transformation causes
4
Time needed to reach a steady state temperature read-out in case of a sudden change in the discharge
temperature
33
permanent decalibration. Type J’s have a sensitivity of ∼52 µV/˚C
Type N : Nicrosil (Ni-Cr-Si alloy) / Nisil (Ni-Si alloy)
High stability and resistance to high temperature oxidation makes type N suitable for
high temperature measurements without the cost of platinum (B, R, S) types. They can
withstand temperatures above 1200 ˚C. Sensitivity is about 39 µV/˚C at 900˚C, slightly
lower than a Type K. Designed to be an improved type K, it is becoming more popular.
Type B: Platinum-Rhodium/Pt-Rh
Suited for high temperature measurements up to 1800 ˚C. Strangely enough type B thermocouples (due to the shape of their temperature-voltage curve) give the same output at
0 ˚C and 42 ˚C. This makes them useless below 50 ˚C.
Type R: Platinum /Platinum with 7% Rhodium
Suited for high temperature measurements up to 1600 ˚C. Low sensitivity (10 µV/˚C)
and high cost make them unsuitable for general-purpose use.
Type S: Platinum /Platinum with 10% Rhodium
Suited for high temperature measurements up to 1600 ˚C. Low sensitivity (10 µV/˚C)
and high cost make them unsuitable for general-purpose use. Due to its high stability type
S is used as the standard of calibration for the melting point of gold (1064.43 ˚C).
Type T: Copper / Constantan
Suited for measurements in the -200 to 350 ˚C range. The positive conductor is made
of copper, and the negative conductor is made of constantan. Often used as a differential
measurement since only copper wire touches the probes. Type T thermocouples have a
sensitivity of ∼43 µV/˚C
2.2.5
Pitot tube
The Pitot tube does the measurement of the plasma flow rate. This is a differential
pressure flow meter. The Pitot tube uses the Bernoulli equation for the calculation of the
flow velocity. Bernoulli found that when a fluid hits a constriction (for instance in a tube) it
accelerates. The energy it needs for this acceleration is given by the stagnation pressure (or
34
total pressure). At the constriction there is a pressure drop, which is partially recovered in
the unrestricted section. The Bernoulli equation states that: stagnation pressure = static
pressure + dynamic pressure, and so we find for the velocity:
s
(p − p0 )
v=k
(2.3)
ρ(T )
Here k is the discharge coefficient of the element, which depends on the ratio between the
diameter of the constriction and that of the unrestricted pipe, and the Reynolds number.
The flow rate is then calculated as:
G = vρA
(2.4)
Where A is the cross sectional area of the pipe.
Figure 2.10: : Laminar flow and turbulent flow velocity profiles in a tube
For the calculation of the flow rate we need to know the density of the plasma at
that point. The density of the plasma not only depends on the temperature, but also on
the composition of the plasma. These two things can usually not be exactly determined.
The dependency on the temperature may be determined by the use of the ideal gas law,
we then get ρ = ρ0 T0 /T , and the unknown temperature is then determined by emission
spectroscopy. Also the penetration of the plasma in the pitot tube can change the fluid flow
velocities. But if the Pitot tube is placed close to the anode, the disturbance is minimal.
There is also some heat transfer between the Pitot tube and the plasma.
For the calculation of the error if constant density is assumed there are several things
to consider. The density depends on the temperature, the pressure and the composition
of the syngas. Also, when we measure the pressure difference we measure these pressures
at different point in the plasma. In the calculations we then assume that the plasma
parameters do not change.
35
Actually the plasma has a typical flow profile depending on whether the flow is laminar
of turbulent. For laminar flow we have a parabolic flow profile (usually laminar flow is
assumed). To determine the plasma pressure at different point along this profile a five-hole
pressure tube is used.
The problem for the hybrid plasma torch is that the amount of argon used is very small
compared to the large amount of water steam. The measurement of the amount of argon
out of the jet is therefore hard to determine. And we have to use a more theoretical method
of calculation
2.2.6
The Quadrupole mass spectrometer
Information was taken from [8] The quadrupole mass spectrometer is comprised of four
rods with hyperbolic (or cylindrical) shape. These rods are placed parallel to each other
and arranged so that the beam of ions passes axially between them. Then a voltage with
a DC component U and a radio frequency component V cos ωt is escerted on the adjacent
rods.
Figure 2.11: : schematic of the quadrupole mass spectrometer
When the ions reach the quadrupole, they oscillate in the x and y direction because of
the high frequency electric field. The stability of the oscillating ions is then determined by
the magnitude of two parameters,
a=
8eU
mion ro ω 2
(2.5)
4eV0
(2.6)
mion ro ω 2
Here r0 is half the distance between opposing rods, mion is the mass of the ion and ω is
the radial frequency. For certain values of a and q the oscillations will remain stable. If
q=
36
the oscillations are not stable, the ions will hit the rods and will dissipate. Only a very
restricted range of values for a and q allow the mass spectrometer to work in a stable
mode. The range of masses can be scanned by changing U and V0, but by leaving their
ratio invariant.
Figure 2.12: : schematic of the inner workings of the mass spectrometer
The problem with the mass spectrometer is that, even though there is a vacuum pump,
there is still some water collecting on the walls, and there is a slight leakage of N2, so
we have to consider this in our measurements. Also there is a problem with molecules,
that have the same mass like N2 and CO. With the mass spectrometer there is no way of
separating the two. For this we need a gas chromatograph. Because there is a freezer to
block water from entering the spectrometer, we cannot measure H2 O.
2.2.7
The Gas chromatograph
This is called a specific test because it can determine the exact species present in a gas.
There is a carrier gas in the mobile phase ( mostly inert gasses like helium or nitrogen)
and a microscopic layer of liquid in the column in the stationary phase. The column is a
thin capillary fiber (the internal diameter is only a couple tenths of millimeters) through
37
which the gas molecules pass with a different rate according to their physical and chemical
properties. At the entrance of the column a liquid or a gaseous species is injected into the
column. This is then pushed through the column by the carrier gas. Not all the gas passes
through the column at the same rate. Some of the molecules are absorbed into the wall
or the packing material of the column wall. So the rate is determined by the adsorption
of the molecules, and this in turn is determined by the type of molecule considered. This
way the different components exit the column at different times. The exit of the column
is monitored by a detector which determines the component which exits and the quantity
of the component.
Figure 2.13: : Schematic of the gas chromatrograph
EXPLANATION OF PROGRAMS AND RESULTS
38
Chapter 3
Explanation of programs and results
In this chapter I will explain how the different programs work and why they were made. I
will then show the results of these calculations.
3.1
Measured results
Experiments were done to determine the energy balance of the hybrid torch. The temperatures of the cooling water was measured at the hot and the cold side of the two parts of
the chamber, the cathode and the anode. With this information the energy flow rate of the
water was calculated by using formula 1.16.This constitutes the power loss to the cooling
water.
By using the data one can also calculate the input voltage to the torch, Pin =I*U.
With all this information the plasma energy flow out of the torch was calculated.
The experiments used variations in different parameters. The current and the argon
flow rate into the system were varied, to determine their effects on the overall power of
the system. Below I will show some of the results of the experiments performed November
10th , 2006.
From this figure we can deduce that when the argon input is changed, only a small
difference in power is observed. A slightly bigger difference is seen for a current of 500
Ampere. There the voltage for a larger argon input will be slightly higher.
The arc power is the input power to the system. The net power is the arc power minus
the losses to the water cooling in the different parts of the torch. In these figures we can see
that when the argon flow is changed there are no noticeable differences in the net power or
the arc power. The current does influence the net power and the arc power considerably.
A higher current level will result in a higher arc and net power level
3.1 Measured results
39
Figure 3.1: The current-voltage levels for several argon inputs
Figure 3.2: The arc power (above) and the net power(below) vs the argon inpute for several
currents
Figure 3.3: Loss total enthalpy and the total power of the arc (J) vs the current for Ar=12.5
slm
40
slm
slm
41
If we compare these figures we can see that the argon input levels have a small influence
on any of the power levels. The water losses remain about the same with a maximum below
50 kW. Also the total power and the total enthalpy remain at the same levels. The biggest
variations can be achieved by differentiating the currents. Higher currents will result in
somewhat higher losses. But this difference is small when compared to the rise in enthalpy
and total power. We see that the total enthalpy starts at a value of about 40kW for 300
Ampere, and ends at about 85 kW. This is a doubling of the enthalpy level.
If we look at the efficiency of the process in function of the current in the hybrid torch
(figure below) we will see that the efficiency of the process at a current level of 500 Ampere
is about 62%, whereas the efficiency at 300 Ampere is found at around 55%
Figure 3.6: Efficiency of the water-stabilized part of the arc
If we then look at the efficiency for the process in function of the flow of argon into the
system we see a more noticeable difference than was expected when looking at the previous
figures.
This figure shows a difference for the different amount of argon injected into the system.
The efficiency for the highest current of 500 A varies from about 60 to less than 62 %. The
most obvious difference is found when 300A. There the efficiency varies from about 50 to
more than 54%.
This difference can be explained if we take a closer look at the losses to the stabilizing
water versus the argon flow input.
In this figure we can clearly see that for 300A the loss to the stabilizing water diminishes
when the amount of argon injected, rises. This diminishing effect is less visible for 400A
and for 500A the losses rise when the amount of argon rises.
42
Figure 3.7: Efficiency of the arc
Figure 3.8: Losses to the stabilizing water vs the amount of argon for different currents
3.2
43
Calculation of the thermodynamic properties of
the separate components
For the calculation of the partition functions we need the internal energies of the different
species in the gas. For the hybrid torch at its operation temperatures we took 15 different
species: H,Ar ,A 1+, Ar 2+, Ar 3+, Ar 4+,Ar 5+,Ar 6+,O,. . . ,O 6+. For these species
I took data about the levels and the total impulse moment from [20]. For these different
species the thermodynamic properties were calculated. Information can be obtained readily
in tables for molecules and atoms for temperatures below 20000K. For a gas containing
ions this is not the case. This is why these calculations were made.
With this program I calculated the thermodynamic properties for different temperatures (ranging from 10000 to 20000K). In the data I got from Viktor Sember there was
a temperature vs. radius profile. At the 35 different radial points the temperature was
measured. Also the molar fraction of argon present was calculated at these points. These
measurements were taken for two different current levels, namely 300 and 400A, and also
for two argon input levels: 12.5 and 22.5 slm.
Figure 3.9: molar fraction of argon for different currents and argon
From the figure above we can see that the amount of argon remaining in the jet is
higher for a current of 400 A than for 300A.
44
Figure 3.10: Temperature profile for different currents and amounts of argon input
The program reads the temperatures into a vector T. The energy levels and the total
impulse moments are put into a different vectors, Level and J respectively.
The internal energies of the different species in the formulas of the partition function
are determined through spectroscopy. The data I used in the program Ewas taken from
the website of nist [20].
The frozen heat capacity can also be found for the different species present in the
plasma flow: (formulas taken from [16])
Q(T )
∂ ln Q(T )
S = R ln
(3.1)
+ RT
N
∂T
H(T ) = H(0) + RT 2
∂h
Cpf = ∂Tf
∂ ln Q(T )
∂T
so
2
Q(T )
Cpf = RT 2 ∂ ln
+ 2RT ln Q(T )
∂T 2
(3.2)
(3.3)
Q(T )
)
The derivative of ln(Q) can be written calculated as ∂ ln∂T
= Q1 ∂Q(T
This frozen thermal
∂T
capacity is just a part of the total heat capacity. In the frozen heat capacity we did not
3.3 Calculation of the thermodynamic properties of the plasma
45
include the several chemical reactions that can occur. These reactions cause extra heat
transfer so the heat capacity changes.
The enthalpy for the different species can be calculated using :
H = RT (2.5 + Qp
)
Q
P
Q = (2J + 1) exp − cE
T
P
cE
Qp = (2J + 1) cE
exp
−
T
T
(3.4)
Here Q is again the partition function (only the internal part), Qp is an expression for
the derivative of Q to T times T. We can see that if we compare Q with the other formula in section 1.14 that we have taken g = 2J+1, the rotational state described by
the quantum number J (total angular momentum). The c in the formula 3.4is used to
get the correct dimensions of the temperature T [K] and the level energy [cm−1 ]. The
2.5 in the formula of the enthalpy is calculated using the translational partition function
3/2
Qtrans = f rac2pmkT h2 V where V is f racnkT p.
P
can now be easily calculated as we
The partition function Q =
(2J + 1) exp − cE
T
know the energy levels E, the temperatures T and the total impulse moments J.
Then the first and second derivatives to the temperature of the partition function are
calculated, respectively named Qp and Qpp in the program.
With these partition functions the enthalpy H, entropy S, and the frozen thermal capacity Cf (when no interactions are taken into account).
The results of these calculations are given in the appendix A and the following. The
enthalpy, entropy and frozen heat capacity versus the temperature for the O, H and Ar
atoms are given here.
[htbp] [htbp]
These values are then used to calculate the thermodynamic properties of the whole gas.
3.3
Calculation of the thermodynamic properties of
the plasma
The information here was given to me through personal communication with Petr Krenek
and from his article [17] This program uses the composition calculated with the Gibbs
free energy minimization method (see section 1.4.3) . This computation was done for
three different pressures: 0.9, 1 and 1.1 atm. These three values are needed to be able
to calculate the differentials. Using these compositions and the thermodynamic properties
of the separate species, the thermodynamic properties of the entire gas were calculated.
Figure 3.11: Thermodynamic properties of oxygen vs temperature
Figure 3.12: Thermodynamic properties of Hydrogen vs temperature
46
47
Figure 3.13: Thermodynamic properties of argon vs temperature
Because of the different value of argon at each point, the compositions were determined
for the 35 different positions.
The total molar mass was calculated by the summation of the products of the molar
fractions xi and the individual molar mass Mi .
M=
n
X
x i Mi
(3.5)
i=1
The total enthalpy is calculated as the individual enthalpy Hi and the formation enthalpy
times the molar fraction xi .
n
1 X
kJ mol
MJ
H=
xi (Hi + Hf i )
=
(3.6)
M i=1
mol g
kg
The total density is the sum of the masses of the individual species times their mass
fraction, or :
n
105 h g i
p X
ρ=
x i Mi =
M
(3.7)
RT i=1
RT
m3
Two different types of tables were calculated. The first was for temperatures from
500K up to 19500K. The second was from 10500 up to 49500K. These tables contained the
thermodynamic properties for different values of argon present in the gas (from 0 till 100%
in steps of 10%) and for the different temperatures.
3.4 Program for the Calculation of the Mass flux and the Energy flux
48
Why is this distinction made? Below 10000K there will still be molecules present. As
the temperature rises these molecules will dissociate. The temperatures below 10000K are
named the dissociation area. Above 10000K these molecules are no longer present. Here
the ionization process can work fully. There can be multiply-charged ions present. The
ionization process is more effective when there are still valence electrons present in the
atom. These electrons are in the outer orbital of the atom and are therefore easier to give
up than the electrons which are closer to the core and have a higher binding energy than
the valence electrons. For oxygen the maximum ionization is O6+, to achieve a higher
ionization level the temperatures would have to be almost a hundred times higher. If we
look at the figure 3.14 and following we see that this is indeed the case.
Below 5000K there are still molecules present, namely H2O, O2 and OH. These molecules
then dissociate into O and H. The ionization process starts above 10000K. No multiplecharged ions are present below 20000K.
This figure continues the figure above. We see that the O++ is formed at temperatures
above 25000K. O+++ is formed above 40000K.
Again we see that molecules remain until the dissociation process starts at about 5000K.
Ionization processes start above the 10000K mark. No multiple-charged ions are present.
Argon releases its second electron somewhat sooner than oxygen. This is because argon
has more overall electrons and eight valence electrons instead of six. The radius of the s
and p orbitals of these valence electrons is larger than the radius for the s and p for oxygen.
The binding energy of these valence electrons will therefore be smaller than that of the
oxygen valence electrons.
Further results can be seen in the article in [17]
3.4
Program for the Calculation of the Mass flux and
the Energy flux
This program uses the formulas explained in the section flow rate of plasma and composition
1.4.1.
Data for the temperature profiles and argon profiles were used to calculate the thermodynamic properties of the gas (see 3.9 and 3.10). The data I got from Petr Krenek
of the thermodynamic properties of the gas was ordered by the amount of argon present,
from 0 % up to 100% in steps of 10%. The two different types of tables (for temperatures
ranging from 500 up to 19500 and from 10500 up to 49500) were put into matlab. I then
interpolated this data to fit the several temperature and argon profiles. When I interpo-
Figure 3.14: Composition of pure steam for temperatures up to 10000K
Figure 3.15: Composition for pure steam for temperatures from 10000K up to 50000K
49
Figure 3.16: Composition for 50% Argon for temperatures up to 20000K
Figure 3.17: Composition for 50% Argon for temperatures from 10000K up to 50000K
50
51
lated the enthalpy for the different tables using interp1 I got a jump in the values. This
is because one table was calculated without multiple ions below 20000 and the other was
calculated with the assumption of no molecules present for temperatures from 10000K.
Because these two tables have overlapping values from 10000K and 20000K there is a jump
in the figure.(see figure 3.18)
Figure 3.18: Enthalpy (left) and Density vs the temperature for I=300A and AR=22.5 slm for
interp1
I then got interpolated values for the enthalpy, the speed of sound in equilibrium and
the density of the plasma with interp2, where the interpolation happens for 2 variables at
the same time. In this case the variables were temperature and argon level. The figure
3.19 shows that there is no more jump for the two different tables. This is why I used the
data which was interpolated with interp2 for the calculation of the integrals.
These values were then integrated to the radius range in which the measurements were
made. These results are given in the table below 3.1.
integral1 integral2
59.383
0,000504123
49.303
0,000583773
73.593
0,000423632
67.456
0,00045775
Table 3.1: Calculated intergrals
52
Figure 3.19: Enthalphy and Density profiles for I=300A and Ar=22.5 slm
When we look at section 1.4.1 we can see that we still need the input power and the
power losses to the water to calculate the Mach number M. We also need the temperature
of the water before it is cooled. This data was taken from the measurements used in section
3.1. The table in the appendix D.1 contains the input power minus the power losses to
the water cooling around the arc and to the anode and the cathode, it also contains the
temperatures of the cooling water for several experiment conditions (in °C). With this
data I then calculated the Mach number per unit length using equation 3.8. The boiling
temperature for water at atmospheric pressure is 100°C.
M=
(IE − Qev )
RR
0
RR
(3.8)
0
These values are given in the appendix . The calculated values were averaged and the final
mach numbers are given in the table below. These values were also put in the graph below
3.20.
From this figure 3.20 it is obvious that the mach number rises when the amount of
I
M ,A=12.5 M,A=22.5
300
0,630
0,794
400
0,810
0,923
Table 3.2: Table with calculated Mach numbers
53
Figure 3.20: Mach number vs current for different amounts of argon
argon is larger. Argon is a heavier particle than either hydrogen of oxygen. Because of
this the speed of sound is lower 3.4, which increases the Mach number because:
M=
speed
speedof sound
(3.9)
Now that we know the mach number per unit length, the mass flux per unit length and
enthalpy flux per unit length can be calculated with the values from table 3.1 containing
the values for the integrals
Z
2πrcρdr
and
Z
2πrchρdr
and 3.2.
If we look at the table 3.3 we see that the enthalpy flux is higher for a higher current
and also rises with the amount of Argon injected. The mass flux for the torch depends
mostly on the argon input. For a same amount of argon the mass flux is somewhat lower
for a higher current. This could suggest that the amount of energy for evaporation is higher
for higher currents.
We can also create a velocity profile using the temperature profile, the mach number
and the speed of sound.
Figure 3.21: Equilibrium speed of sound for different amounts of argon
I and Ar
I=300A,Ar=12.5
I=300A,Ar=22.5
I=400A,Ar=12.5
I=400A,Ar=22.5
slm
slm
slm
slm
enthalpy flux(W) mass flux(g/s)
37404
0,368
39171
0,464
59654
0,343
62262
0,422
Table 3.3: Power and Mass flux for the hybrid torch
54
55
Figure 3.22: Velocity (m/s] profile for different experiment conditions
For higher current and higher input of argon the velocity is higher. We can also see
that the velocity has a smaller variation to the radius for 300A.
3.5 Calculation of the amount of Argon present in the plasma jet
56
Table 3.4: Comparison of characteristics for the waterstabilized and hybrid torch
water-stabilized
hybrid
arc current (A) 300
400
300
300
Argon input (slm)
12,5 22,5
power input (kW)
84
106,8
74,8 72,8
mass flow rate (g/s) 0,204
0,272
0,368 0,464
mean enthalpy (MJ/kg) 157
185
127
95,2
mean velocity (m/s) 1736
2635
2875 3143
3
mean density (g/m ) 4,15
3,64
5,8
7,6
Mach number 0,317
0,445
0,630 0,794
torch
400
12,5
107
0,343
192,6
4692
3,8
0,811
400
22,5
108,6
0,422
161,2
5000
4,5
0,923
When we compare the characteristics of the hybrid torch with those of the water stabilized torch we see that the mass flow rate is somewhat higher. The density is also higher
because argon (39,9 g/mol) is heavier than hydrogen (1 g/mol) and oxygen (16 g/mol).
The density is higher for larger input amounts of argon. For higher currents the density
is lower in both the water-stabilized and the hybrid torch. In the hybrid torch the mach
number is higher for a higher argon flow. This is because when the argon flow increases
the plasma flow increases. Argon does not influence the energy transfer to the walls. The
water evaporation is therefore not influenced by a higher flow of argon. No difference in
water evaporation flow rate and a lower speed of sound results in a higher mach number
for the hybrid torch. The lower enthalpy value of the hybrid torch for 300A suggests that
the gas stabilized part of the torch has a greater effect than at higher currents. At higher
currents the evaporation rate will be larger and therefore have a greater effect than the gas
stabilized part.
3.5
Calculation of the amount of Argon present in the
plasma jet
A program was given to me by dr Kavka using mixing rules to calculate the mass fraction
of Argon present in the jet of the hybrid torch. I tested the use of these mixing rules by
comparing the mass fraction which was measured by dr. Sember with the calculated values
of the program.
The total mass flux can be written as
R
mplasma = 2πrρvdr = far + fsteam
v = Mc
R
mplasma = M 2πrρcdr
57
(3.10)
Here f ar is the flow of argon in kg/s and fsteam is the mass flow of the steam out of the jet.
R
The Energy flux is given by : M 2πrρhcdr
We know that the mach number can be calculated as:
M=
2π
R
Fe
R
rρchdr + (Cw (Tb − Twater ) + λ) rρcdr
(3.11)
In this equation Fe is the net-power .If we disregard the small value provided by the second
term in the denominator we find that:
R
Z
Fe rρcdr
Fe
far + fsteam = 2π R
rρcdr = R
(3.12)
2π rρchdr
rρchdr
So then we find that :
fsteam
Fe
= R
R
rρcdr
− far
rρchdr
(3.13)
If we write this in mass fractions :
xar =
If we use c =
q
far
xar
far
far + fsteam
(3.14)
γ ρp with γ the adiabatic constant and γ = 0, 2 ÷ 0, 8 and xar = 1, 37 ÷ 1, 55
R√
ρrdr
R
Fe √ρhrdr
We get
=
If we include the following mixing rules for the enthalpy :
hmix = xar har + xsteam hsteam = xar har + (1 − xar )hsteam = hsteam + (har − hsteam )xar (3.15)
And for the density:
ρmix =
=
xar
ρar
1
x
+ ρsteam
=
steam
xar
ρar
1
+ ρ1−xar
steam
ρar ρsteam
ρar +xar (ρsteam −ρar )
(3.16)
Now we can write the enthalpy flux as:
Fe =
far
xar
R
q
(hsteam + xar (har − hsteam )) ρar +xρarar(ρρsteam
rdr
steam −ρar )
Rq
ρar ρsteam
rdr
ρar +xar (ρsteam −ρar )
(3.17)
58
The value for xar is now calculated using these formulas in an iterative program. First a
preliminary value is chosen for xar . With this value Fe is calculated and compared with
the actual value of Fe . While these values are different xar is adjusted.
The thermodynamic properties for argon and steam were found in tables (these were
provided by dr. Kavka). The mass flow of argon was found using.
marg on = Ar%remaining ∗ Arinput (slm) ∗ 2.9 · 10−5
(3.18)
The last factor is the conversion factor from slm to kg/s. The values for the remaining
percentage of Argon and the net power were found in the table 3.5 (data received from dr.
Kavka)
Ar
% of ar remained
net power
I=300
12,5
36,6
37,3
17,5
45,8
38,9
22,5
49,3
39
I=400
12,5
33,5
59,7
17,5
42
61,3
22,5
45,5
62,2
Table 3.5: Remaining percentage of argon provided by dr Kavka
I tested the values calculated by dr. Kavka but my values were quite different from the
values measured by dr. Sember (see table 3.7 row 2). This could have been caused by a
wrong value for the remaining value of argon in the program.
From Victor Sember I got the argon profiles for different experiment conditions. These
values are the percentage of argon present in the jet of the hybrid torch. With these values
and the values for the mass flux I then calculated the percentage of argon left from the
initial input in the jet. For this I used the following formulas.
mplasma = marg on + msteam
xar =
marg on
mplasma
(3.19)
(3.20)
The values for the remaining Argon percentages were different than those provided by
dr Kavka.
I then recalculated the molar fraction using dr Kavka’s program. These values are
written in the third row of the table.
These values resemble the values measured by Viktor Sember. This is more so for the
higher current (I=400A) than for the lower current. A preliminary conclusion (awaiting
further data) from these differences is that the mixing rules can apply for calculation where
3.6 Conclusion
59
I=300
Ar
12,5
% of ar remained 37,4
net power
37,3
22,5
34,22
39
I=400
12,5
26,59
59,7
22,5
22,7
62,2
Table 3.6: Remaining percentage of argon and net power calculated using the measured values
I=300,Ar=12.5
x ar measured 0,368
x ar mixing 1 0,430
x ar mixing 2 0,440
I=300,Ar=22.5
0,4812
0,640
0,530
I=400,Ar=12.5
0,281
0,330
0,270
I=400,Ar=22.5
0,351
0,550
0,360
Table 3.7: mass fraction of Argon present in the hybrid torch jet: row 1: measured values, row
2: calculated with 3.5, row 3: calculated with 3.6
the temperatures are very high (average close to 20000K) and where the precision is of less
importance (e.g.: the initial calculations for the composition used 50 % of argon in the
jet). This conclusion has to be taken with caution, because there is only a small amount
of data available.
3.6
Conclusion
Using the energy levels and total impulse moments from NIST, I calculated the enthalpy,
entropy and specific heat capacity for the specified atoms and ions present in the hybrid
torch.The results I obtained for these thermodynamic properties of the seperate ions were
considered to be reasonable when compared to the data for individual atoms found in
tables for this temperature range. I then handed these tables over to Petr Krenek who
calculated several thermodynamic properties of the plasma gas, including the enthalpy,
speed of sound and the density of the plasma. I then used his data to calculate the energy
balance and the mass balance for the hybrid torch. The results I obtained for the Mach
number, the enthalpy flux and mass flow rate are in the range which was expected from
earlier experiments. The hybrid torch has a higher mass flow rate than that of the waterstabilized torch, and its enthalpy is a lot higher than that of the gas-stabilized torch. These
characteristics can be changed by altering the amount of Argon input to the torch. The
hybrid torch is therefore a good way to bridge the gap in characteristics between the gas
3.6 Conclusion
60
and the water-stabilized torch. Mixing rules were used to calculate the fraction of argon
present in the jet of the hybrid torch. These values were then compared to the measured
values of the mass fraction. One can assume that the mixing rules can be used when
the temperatures are high enough (close to 20000K). Because of small amounts of data
available for this subject no firm conclusion can be drawn from these calculations
THERMODYNAMIC PROPERTIES FOR THE SEPERATE SPECIES FOR ARGON
61
Appendix A
Thermodynamic properties for the
seperate species for argon
This appendix contains the thermodynamic properties calculated for the seperate species
of argon.
A.1
Argon
T (K)
9900
10000
10100
10200
10300
10400
10500
10600
10700
10800
10900
11000
Q
H (MJ/kg) Cpf (kJ/kgK) S (MJ/kg)
1,0001
205,8596
20,9132
227,5694
1,0001
207,9519
20,9336
227,7796
1,0001
210,0464
20,9567
227,9881
1,0001
212,1433
20,9828
228,1946
1,0001
214,2431
21,0124
228,3995
1,0001
216,3459
21,0458
228,6027
1,0001
218,4524
21,0833
228,8043
1,0002
220,5628
21,1254
229,0043
1,0002
222,6776
21,1725
229,2029
1,0002
224,7974
21,2251
229,4001
1,0003
226,9228
21,2836
229,596
1,0003
229,0544
21,3487
229,7906
Table A.1: Thermodynamic properties of Argon
Continued on next page
A.1 Argon
11100
11200
11300
11400
11500
11600
11700
11800
11900
12000
12100
12200
12300
12400
12500
12600
12700
12800
12900
13000
13100
13200
13300
13400
13500
13600
13700
13800
13900
14000
14100
14200
14300
62
1,0003
231,1928
21,421
1,0004
233,3388
21,5009
1,0004
235,4933
21,5892
1,0005
237,657
21,6866
1,0006
239,8309
21,7937
1,0006
242,0161
21,9113
1,0007
244,2136
22,0403
1,0008
246,4245
22,1814
1,0009
248,6503
22,3355
1,001
250,8921
22,5035
1,0012
253,1514
22,6863
1,0013
255,4299
22,8851
1,0015
257,729
23,1006
1,0016
260,0506
23,3341
1,0018
262,3965
23,5866
1,002
264,7686
23,8593
1,0023
267,169
24,1532
1,0025
269,6
24,4696
1,0028
272,0637
24,8097
1,0031
274,5628
25,1748
1,0034
277,0996
25,5661
1,0038
279,6769
25,9849
1,0041
282,2975
26,4326
1,0046
284,9644
26,9104
1,005
287,6807
27,4198
1,0055
290,4495
27,9621
1,006
293,2742
28,5386
1,0066
296,1584
29,1508
1,0072
299,1056
29,8
1,0079
302,1197
30,4875
1,0086
305,2044
31,2147
1,0093
308,364
31,983
1,0102
311,6025
32,7936
229,9841
230,1766
230,3681
230,5588
230,7486
230,9378
231,1264
231,3146
231,5024
231,69
231,8775
232,0651
232,2527
232,4407
232,6291
232,8182
233,0079
233,1986
233,3903
233,5833
233,7777
233,9737
234,1714
234,3712
234,5732
234,7775
234,9844
235,1942
235,407
235,623
235,8426
236,0659
236,2931
A.1 Argon
14400
14500
14600
14700
14800
14900
15000
15100
15200
15300
15400
15500
15600
15700
15800
15900
16000
16100
16200
16300
16400
16500
16600
16700
16800
16900
17000
17100
17200
17300
17400
17500
17600
63
1,0111
314,9242
33,6479
1,012
318,3335
34,5469
1,013
321,8351
35,4921
1,0141
325,4335
36,4844
1,0153
329,1336
37,5249
1,0165
332,9401
38,6148
1,0178
336,8582
39,7549
1,0192
340,8928
40,946
1,0207
345,0491
42,189
1,0223
349,3324
43,4844
1,024
353,7478
44,833
1,0258
358,3007
46,235
1,0277
362,9966
47,6908
1,0298
367,8407
49,2005
1,0319
372,8385
50,7643
1,0342
377,9953
52,3818
1,0366
383,3166
54,053
1,0391
388,8077
55,7772
1,0418
394,4738
57,5538
1,0446
400,3202
59,3821
1,0476
406,3519
61,261
1,0508
412,574
63,1893
1,0541
418,9914
65,1655
1,0576
425,6087
67,188
1,0612
432,4305
69,2551
1,0651
439,4611
71,3645
1,0692
446,7047
73,5142
1,0734
454,1652
75,7015
1,0779
461,8462
77,9238
1,0826
469,751
80,1782
1,0875
477,8828
82,4616
1,0926
486,2442
84,7706
1,098
494,8376
87,1018
236,5246
236,7606
237,0012
237,2468
237,4977
237,754
238,0161
238,2842
238,5585
238,8394
239,127
239,4217
239,7237
240,0332
240,3505
240,6759
241,0095
241,3516
241,7025
242,0622
242,4311
242,8094
243,1971
243,5946
244,0018
244,4191
244,8464
245,284
245,7318
246,1901
246,6588
247,1379
247,6276
A.2 Argon 1+
17700
17800
17900
18000
18100
18200
18300
18400
18500
18600
18700
18800
18900
19000
19100
19200
19300
19400
19500
19600
19700
19800
19900
20000
20100
A.2
64
1,1036
1,1095
1,1156
1,122
1,1287
1,1357
1,143
1,1506
1,1585
1,1668
1,1753
1,1842
1,1935
1,2031
1,2132
1,2235
1,2343
1,2455
1,2571
1,2691
1,2816
1,2945
1,3079
1,3217
1,336
503,6652
512,7284
522,0286
531,5666
541,3429
551,3574
561,6096
572,0987
582,8231
593,781
604,9701
616,3876
628,03
639,8937
651,9742
664,267
676,7668
689,468
702,3645
715,4498
728,717
742,159
755,768
769,5361
783,4552
89,4513
91,8155
94,1902
96,5712
98,9542
101,3347
103,7082
106,07
108,4154
110,7396
113,0379
115,3053
117,5371
119,7286
121,8751
123,9719
126,0146
127,9987
129,92
131,7745
133,5583
135,2678
136,8995
138,4501
139,9169
248,1277
248,6383
249,1593
249,6907
250,2323
250,7841
251,3458
251,9174
252,4987
253,0894
253,6894
254,2983
254,9159
255,542
256,1761
256,818
257,4674
258,1238
258,7868
259,4561
260,1313
260,8119
261,4975
262,1876
262,8819
Argon 1+
T (K)
9900
10000
10100
Q
5,6243
210,7302
20,8604
242,4209
5,6277
212,8162
20,859
242,6305
5,631
214,902
20,8577
242,8381
Table A.2: Thermodynamic properties of Argon 1+
A.2 Argon 1+
10200
10300
10400
10500
10600
10700
10800
10900
11000
11100
11200
11300
11400
11500
11600
11700
11800
11900
12000
12100
12200
12300
12400
12500
12600
12700
12800
12900
13000
13100
13200
65
5,6343
216,9877
20,8564
243,0436
5,6375
219,0733
20,8552
243,247
5,6407
221,1588
20,854
243,4485
5,6438
223,2441
20,8529
243,6481
5,6468
225,3294
20,8518
243,8457
5,6498
227,4145
20,8507
244,0415
5,6527
229,4995
20,8497
244,2355
5,6556
231,5844
20,8487
244,4276
5,6585
233,6692
20,8478
244,618
5,6613
235,754
20,8469
244,8067
5,664
237,8386
20,8461
244,9937
5,6667
239,9232
20,8453
245,179
5,6694
242,0077
20,8445
245,3626
5,672
244,0921
20,8438
245,5447
5,6746
246,1764
20,8432
245,7251
5,6772
248,2607
20,8426
245,904
5,6797
250,345
20,8421
246,0814
5,6821
252,4292
20,8416
246,2573
5,6846
254,5133
20,8412
246,4317
5,687
256,5974
20,8409
246,6047
5,6893
258,6815
20,8406
246,7762
5,6916
260,7655
20,8404
246,9463
5,6939
262,8495
20,8402
247,1151
5,6962
264,9336
20,8402
247,2825
5,6984
267,0176
20,8402
247,4485
5,7006
269,1016
20,8403
247,6133
5,7028
271,1856
20,8405
247,7767
5,7049
273,2697
20,8408
247,9389
5,707
275,3538
20,8413
248,0998
5,7091
277,438
20,8418
248,2596
5,7111
279,5222
20,8424
248,418
A.2 Argon 1+
13300
13400
13500
13600
13700
13800
13900
14000
14100
14200
14300
14400
14500
14600
14700
14800
14900
15000
15100
15200
15300
15400
15500
15600
15700
15800
15900
16000
16100
16200
16300
66
5,7131
281,6065
20,8432
248,5754
5,7151
283,6908
20,8441
248,7315
5,7171
285,7753
20,8451
248,8865
5,719
287,8598
20,8463
249,0403
5,7209
289,9445
20,8476
249,193
5,7228
292,0294
20,8491
249,3447
5,7246
294,1144
20,8508
249,4952
5,7265
296,1995
20,8527
249,6447
5,7283
298,2849
20,8547
249,7931
5,7301
300,3705
20,857
249,9405
5,7318
302,4563
20,8595
250,0869
5,7336
304,5424
20,8622
250,2322
5,7353
306,6288
20,8652
250,3766
5,737
308,7155
20,8684
250,52
5,7387
310,8025
20,8719
250,6625
5,7404
312,8898
20,8757
250,804
5,742
314,9776
20,8797
250,9446
5,7436
317,0658
20,8841
251,0843
5,7453
319,1544
20,8889
251,2231
5,7469
321,2436
20,8939
251,361
5,7484
323,3332
20,8994
251,498
5,75
325,4235
20,9052
251,6342
5,7515
327,5143
20,9114
251,7695
5,7531
329,6058
20,9181
251,904
5,7546
331,6979
20,9252
252,0377
5,7561
333,7908
20,9328
252,1706
5,7575
335,8845
20,9408
252,3027
5,759
337,979
20,9494
252,434
5,7605
340,0744
20,9585
252,5645
5,7619
342,1707
20,9682
252,6943
5,7633
344,2681
20,9785
252,8234
A.2 Argon 1+
16400
16500
16600
16700
16800
16900
17000
17100
17200
17300
17400
17500
17600
17700
17800
17900
18000
18100
18200
18300
18400
18500
18600
18700
18800
18900
19000
19100
19200
19300
19400
67
5,7647
346,3665
20,9894
252,9517
5,7662
348,466
21,0009
253,0794
5,7675
350,5667
21,0131
253,2063
5,7689
352,6686
21,0259
253,3325
5,7703
354,7719
21,0395
253,4581
5,7717
356,8765
21,0539
253,583
5,773
358,9827
21,0691
253,7073
5,7744
361,0904
21,085
253,8309
5,7757
363,1997
21,1018
253,9539
5,777
365,3108
21,1196
254,0763
5,7783
367,4236
21,1382
254,198
5,7797
369,5384
21,1578
254,3192
5,781
371,6552
21,1784
254,4399
5,7823
373,7742
21,2
254,5599
5,7836
375,8953
21,2227
254,6794
5,7849
378,0187
21,2465
254,7984
5,7862
380,1446
21,2715
254,9168
5,7874
382,2731
21,2976
255,0347
5,7887
384,4042
21,325
255,1521
5,79
386,5381
21,3537
255,2691
5,7913
388,675
21,3837
255,3855
5,7926
390,8149
21,4151
255,5015
5,7938
392,958
21,4479
255,617
5,7951
395,1045
21,4822
255,7321
5,7964
397,2545
21,5179
255,8468
5,7977
399,4082
21,5553
255,961
5,7989
401,5656
21,5943
256,0749
5,8002
403,7271
21,6349
256,1884
5,8015
405,8927
21,6773
256,3014
5,8028
408,0626
21,7214
256,4142
5,8041
410,237
21,7674
256,5265
A.3 Argon 2+
19500
19600
19700
19800
19900
20000
20100
A.3
68
5,8054
5,8067
5,808
5,8093
5,8106
5,812
5,8133
412,4161
414,6001
416,7892
418,9835
421,1834
423,389
425,6004
21,8152
21,865
21,9168
21,9707
22,0267
22,0849
22,1453
256,6386
256,7503
256,8617
256,9728
257,0836
257,1942
257,3045
Argon 2+
T (K)
9900
10000
10100
10200
10300
10400
10500
10600
10700
10800
10900
11000
11100
11200
11300
11400
11500
11600
11700
11800
Q
9,0089
223,7067
23,1608
247,6487
9,0286
226,0226
23,1561
247,8814
9,0483
228,338
23,151
248,1118
9,0679
230,6528
23,1456
248,3399
9,0874
232,9671
23,1399
248,5656
9,1067
235,2807
23,1338
248,7892
9,126
237,5938
23,1275
249,0105
9,1453
239,9062
23,1209
249,2297
9,1644
242,218
23,1141
249,4468
9,1834
244,5291
23,107
249,6618
9,2023
246,8394
23,0998
249,8747
9,2211
249,149
23,0923
250,0856
9,2399
251,4578
23,0846
250,2946
9,2585
253,7659
23,0767
250,5016
9,2771
256,0732
23,0686
250,7067
9,2956
258,3796
23,0604
250,9099
9,314
260,6853
23,0521
251,1113
9,3322
262,99
23,0436
251,3108
9,3504
265,294
23,0349
251,5086
9,3685
267,597
23,0262
251,7046
A.3 Argon 2+
11900
12000
12100
12200
12300
12400
12500
12600
12700
12800
12900
13000
13100
13200
13300
13400
13500
13600
13700
13800
13900
14000
14100
14200
14300
14400
14500
14600
14700
14800
14900
69
9,3866
269,8992
23,0173
251,8989
9,4045
272,2005
23,0084
252,0914
9,4223
274,5009
22,9993
252,2823
9,4401
276,8003
22,9902
252,4716
9,4577
279,0989
22,981
252,6592
9,4753
281,3965
22,9717
252,8453
9,4928
283,6932
22,9624
253,0298
9,5102
285,989
22,953
253,2127
9,5275
288,2839
22,9436
253,3941
9,5447
290,5777
22,9342
253,574
9,5618
292,8707
22,9247
253,7525
9,5789
295,1627
22,9152
253,9294
9,5958
297,4537
22,9057
254,105
9,6127
299,7438
22,8961
254,2792
9,6295
302,0329
22,8866
254,4519
9,6462
304,3211
22,8771
254,6233
9,6628
306,6084
22,8676
254,7934
9,6793
308,8947
22,8581
254,9621
9,6958
311,18
22,8486
255,1295
9,7122
313,4644
22,8392
255,2957
9,7284
315,7478
22,8298
255,4605
9,7446
318,0303
22,8204
255,6242
9,7608
320,3119
22,8111
255,7866
9,7768
322,5926
22,8019
255,9477
9,7928
324,8723
22,7926
256,1077
9,8086
327,1511
22,7835
256,2665
9,8244
329,429
22,7744
256,4242
9,8401
331,706
22,7654
256,5806
9,8558
333,9821
22,7565
256,736
9,8713
336,2573
22,7476
256,8903
9,8868
338,5316
22,7388
257,0434
A.3 Argon 2+
15000
15100
15200
15300
15400
15500
15600
15700
15800
15900
16000
16100
16200
16300
16400
16500
16600
16700
16800
16900
17000
17100
17200
17300
17400
17500
17600
17700
17800
17900
18000
70
9,9022
340,8051
22,7302
257,1955
9,9175
343,0776
22,7216
257,3465
9,9327
345,3494
22,7131
257,4964
9,9479
347,6203
22,7047
257,6454
9,963
349,8903
22,6964
257,7932
9,978
352,1596
22,6883
257,9401
9,9929
354,428
22,6802
258,086
10,0078
356,6956
22,6723
258,2309
10,0226
358,9624
22,6646
258,3748
10,0373
361,2285
22,6569
258,5178
10,0519
363,4938
22,6494
258,6598
10,0665
365,7584
22,642
258,8009
10,081
368,0222
22,6348
258,9411
10,0954
370,2854
22,6277
259,0804
10,1097
372,5478
22,6208
259,2187
10,124
374,8095
22,6141
259,3562
10,1382
377,0706
22,6075
259,4928
10,1523
379,331
22,601
259,6286
10,1664
381,5908
22,5948
259,7635
10,1804
383,85
22,5887
259,8976
10,1943
386,1086
22,5829
260,0308
10,2082
388,3666
22,5772
260,1633
10,222
390,624
22,5717
260,2949
10,2357
392,8809
22,5664
260,4257
10,2493
395,1373
22,5613
260,5558
10,2629
397,3932
22,5564
260,6851
10,2765
399,6486
22,5517
260,8136
10,2899
401,9035
22,5473
260,9413
10,3033
404,1581
22,5431
261,0684
10,3166
406,4122
22,5391
261,1946
10,3299
408,6659
22,5353
261,3202
A.4 Argon 3+
18100
18200
18300
18400
18500
18600
18700
18800
18900
19000
19100
19200
19300
19400
19500
19600
19700
19800
19900
20000
20100
A.4
71
10,3431
10,3562
10,3693
10,3823
10,3953
10,4082
10,421
10,4338
10,4465
10,4592
10,4718
10,4843
10,4968
10,5093
10,5216
10,534
10,5462
10,5584
10,5706
10,5827
10,5948
410,9192
413,1722
415,4249
417,6773
419,9295
422,1814
424,4331
426,6846
428,9359
431,1871
433,4382
435,6893
437,9403
440,1913
442,4423
444,6933
446,9444
449,1957
451,4471
453,6987
455,9505
22,5318
22,5285
22,5255
22,5227
22,5201
22,5179
22,5159
22,5142
22,5127
22,5116
22,5107
22,5101
22,5099
22,5099
22,5102
22,5109
22,5119
22,5132
22,5148
22,5168
22,5191
261,445
261,5692
261,6926
261,8154
261,9374
262,0588
262,1796
262,2996
262,4191
262,5379
262,656
262,7736
262,8905
263,0068
263,1226
263,2377
263,3523
263,4663
263,5797
263,6926
263,8049
Argon 3+
T (K)
9900
10000
10100
10200
10300
10400
Q
4,4985
235,2116
29,5695
243,0367
4,5149
238,1718
29,6331
243,3342
4,5314
241,1381
29,6929
243,6293
4,5482
244,1102
29,7488
243,9221
4,5652
247,0877
29,801
244,2126
4,5823
250,0703
29,8496
244,5008
A.4 Argon 3+
10500
10600
10700
10800
10900
11000
11100
11200
11300
11400
11500
11600
11700
11800
11900
12000
12100
12200
12300
12400
12500
12600
12700
12800
12900
13000
13100
13200
13300
13400
13500
72
4,5997
253,0575
29,8945
244,7867
4,6173
256,0491
29,9359
245,0702
4,635
259,0446
29,9738
245,3515
4,6529
262,0437
30,0083
245,6305
4,671
265,0461
30,0396
245,9072
4,6893
268,0515
30,0676
246,1817
4,7078
271,0595
30,0924
246,4539
4,7264
274,0699
30,1142
246,7239
4,7452
277,0823
30,133
246,9917
4,7641
280,0964
30,1488
247,2572
4,7832
283,112
30,1619
247,5206
4,8024
286,1287
30,1722
247,7818
4,8218
289,1463
30,1798
248,0408
4,8414
292,1646
30,1848
248,2977
4,8611
295,1832
30,1874
248,5524
4,8809
298,2019
30,1875
248,805
4,9008
301,2206
30,1852
249,0556
4,9209
304,2389
30,1807
249,304
4,9411
307,2567
30,174
249,5503
4,9614
310,2736
30,1652
249,7946
4,9819
313,2896
30,1544
250,0369
5,0024
316,3044
30,1415
250,2771
5,0231
319,3179
30,1269
250,5153
5,0439
322,3298
30,1103
250,7515
5,0648
325,3399
30,0921
250,9858
5,0857
328,3481
30,0722
251,2181
5,1068
331,3543
30,0507
251,4484
5,128
334,3582
30,0276
251,6769
5,1493
337,3598
30,0031
251,9034
5,1707
340,3588
29,9772
252,1281
5,1921
343,3551
29,9499
252,3508
A.4 Argon 3+
13600
13700
13800
13900
14000
14100
14200
14300
14400
14500
14600
14700
14800
14900
15000
15100
15200
15300
15400
15500
15600
15700
15800
15900
16000
16100
16200
16300
16400
16500
16600
73
5,2136
346,3487
29,9214
252,5718
5,2353
349,3394
29,8916
252,7909
5,257
352,327
29,8607
253,0081
5,2787
355,3115
29,8287
253,2236
5,3006
358,2927
29,7956
253,4373
5,3225
361,2706
29,7616
253,6493
5,3445
364,245
29,7266
253,8595
5,3666
367,2159
29,6907
254,068
5,3887
370,1831
29,6541
254,2748
5,4108
373,1466
29,6166
254,4798
5,4331
376,1064
29,5784
254,6833
5,4554
379,0623
29,5395
254,885
5,4777
382,0143
29,4999
255,0852
5,5001
384,9623
29,4598
255,2837
5,5226
387,9062
29,4191
255,4806
5,5451
390,8461
29,3779
255,676
5,5676
393,7818
29,3362
255,8697
5,5902
396,7133
29,2941
256,062
5,6128
399,6406
29,2516
256,2527
5,6354
402,5636
29,2087
256,4419
5,6581
405,4823
29,1655
256,6296
5,6809
408,3967
29,122
256,8158
5,7036
411,3067
29,0783
257,0005
5,7264
414,2123
29,0343
257,1839
5,7492
417,1136
28,9901
257,3658
5,7721
420,0104
28,9457
257,5462
5,795
422,9027
28,9012
257,7253
5,8178
425,7906
28,8566
257,9031
5,8408
428,674
28,812
258,0794
5,8637
431,553
28,7672
258,2544
5,8867
434,4275
28,7224
258,4281
A.4 Argon 3+
16700
16800
16900
17000
17100
17200
17300
17400
17500
17600
17700
17800
17900
18000
18100
18200
18300
18400
18500
18600
18700
18800
18900
19000
19100
19200
19300
19400
19500
19600
19700
74
5,9096
437,2975
28,6776
258,6005
5,9326
440,163
28,6329
258,7716
5,9556
443,0241
28,5881
258,9414
5,9786
445,8806
28,5434
259,1099
6,0016
448,7327
28,4988
259,2772
6,0247
451,5804
28,4543
259,4432
6,0477
454,4236
28,4099
259,608
6,0708
457,2624
28,3656
259,7717
6,0938
460,0967
28,3215
259,9341
6,1169
462,9267
28,2776
260,0953
6,1399
465,7522
28,2338
260,2554
6,163
468,5734
28,1902
260,4144
6,1861
471,3903
28,1469
260,5722
6,2091
474,2028
28,1038
260,7289
6,2322
477,0111
28,0609
260,8844
6,2552
479,815
28,0183
261,0389
6,2783
482,6147
27,9759
261,1923
6,3013
485,4102
27,9338
261,3447
6,3244
488,2015
27,892
261,496
6,3474
490,9886
27,8506
261,6462
6,3704
493,7716
27,8094
261,7954
6,3935
496,5505
27,7686
261,9437
6,4165
499,3253
27,7281
262,0909
6,4395
502,0961
27,6879
262,2371
6,4624
504,8629
27,6481
262,3823
6,4854
507,6258
27,6086
262,5266
6,5084
510,3847
27,5696
262,6699
6,5313
513,1397
27,5309
262,8123
6,5542
515,8909
27,4925
262,9537
6,5771
518,6382
27,4546
263,0943
6,6
521,3818
27,4171
263,2339
A.5 Argon 4+
19800
19900
20000
20100
A.5
75
6,6229
6,6458
6,6686
6,6914
524,1216
526,8578
529,5903
532,3192
27,3799
27,3432
27,3069
27,271
263,3726
263,5105
263,6474
263,7835
Argon 4+
T (K)
9900
10000
10100
10200
10300
10400
10500
10600
10700
10800
10900
11000
11100
11200
11300
11400
11500
11600
11700
11800
11900
12000
12100
Q
7,8795
232,1873
23,2118
247,3916
7,905
234,5085
23,2113
247,6249
7,9302
236,8296
23,2105
247,8559
7,9552
239,1505
23,2092
248,0845
7,9801
241,4714
23,2075
248,311
8,0048
243,792
23,2055
248,5352
8,0293
246,1125
23,2032
248,7572
8,0536
248,4327
23,2006
248,9772
8,0777
250,7526
23,1976
249,195
8,1017
253,0722
23,1944
249,4108
8,1255
255,3914
23,1909
249,6245
8,1491
257,7104
23,1872
249,8363
8,1725
260,0289
23,1832
250,0461
8,1958
262,347
23,179
250,254
8,219
264,6647
23,1747
250,4601
8,2419
266,9819
23,1701
250,6642
8,2648
269,2987
23,1653
250,8666
8,2874
271,615
23,1604
251,0671
8,3099
273,9308
23,1554
251,2659
8,3323
276,246
23,1502
251,4629
8,3545
278,5608
23,1448
251,6583
8,3766
280,875
23,1394
251,8519
8,3985
283,1887
23,1338
252,0439
A.5 Argon 4+
12200
12300
12400
12500
12600
12700
12800
12900
13000
13100
13200
13300
13400
13500
13600
13700
13800
13900
14000
14100
14200
14300
14400
14500
14600
14700
14800
14900
15000
15100
15200
76
8,4203
285,5018
23,1282
252,2343
8,4419
287,8143
23,1225
252,4231
8,4634
290,1263
23,1167
252,6103
8,4848
292,4376
23,1108
252,796
8,506
294,7484
23,1049
252,9801
8,5271
297,0586
23,099
253,1627
8,5481
299,3682
23,093
253,3439
8,5689
301,6772
23,087
253,5235
8,5896
303,9856
23,081
253,7018
8,6102
306,2934
23,0749
253,8786
8,6306
308,6006
23,0689
254,0541
8,651
310,9072
23,0629
254,2282
8,6712
313,2132
23,0569
254,4009
8,6913
315,5186
23,0509
254,5723
8,7112
317,8234
23,045
254,7424
8,7311
320,1276
23,0391
254,9112
8,7508
322,4312
23,0332
255,0788
8,7704
324,7342
23,0274
255,245
8,7899
327,0367
23,0217
255,4101
8,8092
329,3385
23,016
255,5739
8,8285
331,6399
23,0104
255,7366
8,8477
333,9406
23,0048
255,898
8,8667
336,2408
22,9993
256,0583
8,8856
338,5405
22,994
256,2175
8,9045
340,8396
22,9887
256,3755
8,9232
343,1382
22,9835
256,5324
8,9418
345,4363
22,9784
256,6882
8,9603
347,7339
22,9735
256,8429
8,9787
350,031
22,9686
256,9966
8,997
352,3276
22,9638
257,1492
9,0152
354,6238
22,9592
257,3007
A.5 Argon 4+
15300
15400
15500
15600
15700
15800
15900
16000
16100
16200
16300
16400
16500
16600
16700
16800
16900
17000
17100
17200
17300
17400
17500
17600
17700
17800
17900
18000
18100
18200
18300
77
9,0333
356,9195
22,9547
257,4513
9,0513
359,2147
22,9503
257,6008
9,0692
361,5096
22,9461
257,7493
9,087
363,804
22,942
257,8969
9,1047
366,0979
22,938
258,0435
9,1223
368,3916
22,9342
258,1891
9,1398
370,6848
22,9305
258,3338
9,1573
372,9777
22,927
258,4775
9,1746
375,2702
22,9236
258,6204
9,1918
377,5624
22,9203
258,7623
9,209
379,8543
22,9173
258,9033
9,2261
382,1458
22,9144
259,0435
9,243
384,4371
22,9116
259,1828
9,2599
386,7282
22,9091
259,3212
9,2767
389,019
22,9067
259,4588
9,2934
391,3095
22,9044
259,5955
9,3101
393,5998
22,9024
259,7315
9,3266
395,89
22,9005
259,8666
9,3431
398,18
22,8988
260,0009
9,3595
400,4698
22,8973
260,1344
9,3758
402,7594
22,8959
260,2671
9,392
405,0489
22,8948
260,3991
9,4081
407,3384
22,8938
260,5303
9,4242
409,6277
22,893
260,6607
9,4402
411,917
22,8924
260,7904
9,4561
414,2062
22,892
260,9194
9,4719
416,4954
22,8918
261,0477
9,4877
418,7846
22,8918
261,1752
9,5033
421,0738
22,892
261,302
9,519
423,363
22,8924
261,4282
9,5345
425,6523
22,893
261,5536
A.6 Argon 5+
18400
18500
18600
18700
18800
18900
19000
19100
19200
19300
19400
19500
19600
19700
19800
19900
20000
20100
A.6
78
9,55
9,5653
9,5807
9,5959
9,6111
9,6262
9,6413
9,6562
9,6712
9,686
9,7008
9,7155
9,7302
9,7448
9,7593
9,7738
9,7882
9,8025
427,9416
430,231
432,5205
434,8102
437,1
439,39
441,6802
443,9705
446,2611
448,552
450,8431
453,1346
455,4263
457,7184
460,0108
462,3036
464,5968
466,8904
22,8938
22,8947
22,8959
22,8973
22,8989
22,9007
22,9027
22,9049
22,9073
22,9099
22,9128
22,9158
22,919
22,9225
22,9262
22,93
22,9341
22,9384
261,6784
261,8024
261,9259
262,0486
262,1708
262,2922
262,4131
262,5333
262,6529
262,7719
262,8904
263,0082
263,1254
263,242
263,3581
263,4736
263,5886
263,703
Argon 5+
T (K)
9900
10000
10100
10200
10300
10400
10500
10600
10700
Q
4,9024
221,4169
20,9946
242,3581
4,9117
223,5161
20,9906
242,5691
4,9209
225,615
20,9868
242,7779
4,9299
227,7135
20,9831
242,9847
4,9388
229,8116
20,9796
243,1894
4,9475
231,9094
20,9761
243,3921
4,9561
234,0069
20,9729
243,5928
4,9645
236,104
20,9698
243,7916
4,9728
238,2008
20,9668
243,9884
A.6 Argon 5+
10800
10900
11000
11100
11200
11300
11400
11500
11600
11700
11800
11900
12000
12100
12200
12300
12400
12500
12600
12700
12800
12900
13000
13100
13200
13300
13400
13500
13600
13700
13800
79
4,981
240,2974
20,964
244,1835
4,9891
242,3936
20,9613
244,3767
4,997
244,4896
20,9587
244,5681
5,0048
246,5854
20,9563
244,7578
5,0125
248,6809
20,954
244,9457
5,0201
250,7762
20,9518
245,1319
5,0275
252,8712
20,9498
245,3165
5,0349
254,9661
20,948
245,4995
5,0421
257,0608
20,9462
245,6809
5,0493
259,1554
20,9446
245,8606
5,0563
261,2498
20,9432
246,0389
5,0632
263,344
20,9419
246,2156
5,07
265,4382
20,9407
246,3909
5,0768
267,5322
20,9397
246,5646
5,0834
269,6261
20,9388
246,737
5,0899
271,7199
20,9381
246,9079
5,0964
273,8137
20,9376
247,0775
5,1027
275,9075
20,9372
247,2456
5,109
278,0012
20,9369
247,4125
5,1152
280,0948
20,9368
247,578
5,1213
282,1885
20,9369
247,7422
5,1273
284,2822
20,9371
247,9051
5,1333
286,376
20,9376
248,0668
5,1391
288,4698
20,9381
248,2272
5,1449
290,5636
20,9389
248,3865
5,1506
292,6575
20,9398
248,5445
5,1563
294,7516
20,941
248,7014
5,1618
296,8457
20,9423
248,8571
5,1673
298,94
20,9438
249,0116
5,1727
301,0345
20,9455
249,1651
5,1781
303,1291
20,9473
249,3174
A.6 Argon 5+
13900
14000
14100
14200
14300
14400
14500
14600
14700
14800
14900
15000
15100
15200
15300
15400
15500
15600
15700
15800
15900
16000
16100
16200
16300
16400
16500
16600
16700
16800
16900
80
5,1834
305,224
20,9494
249,4686
5,1886
307,319
20,9517
249,6188
5,1938
309,4143
20,9542
249,768
5,1989
311,5099
20,9569
249,9161
5,2039
313,6057
20,9598
250,0631
5,2089
315,7018
20,9629
250,2092
5,2138
317,7983
20,9663
250,3543
5,2187
319,8951
20,9699
250,4984
5,2235
321,9923
20,9737
250,6416
5,2282
324,0898
20,9777
250,7838
5,2329
326,1878
20,982
250,925
5,2376
328,2863
20,9865
251,0654
5,2422
330,3851
20,9913
251,2049
5,2467
332,4845
20,9963
251,3434
5,2512
334,5844
21,0015
251,4811
5,2556
336,6848
21,007
251,618
5,26
338,7858
21,0128
251,754
5,2644
340,8874
21,0188
251,8891
5,2687
342,9896
21,0251
252,0234
5,2729
345,0924
21,0317
252,157
5,2771
347,1959
21,0385
252,2897
5,2813
349,3002
21,0456
252,4216
5,2854
351,4051
21,053
252,5527
5,2895
353,5108
21,0607
252,6831
5,2936
355,6172
21,0686
252,8128
5,2976
357,7245
21,0769
252,9416
5,3015
359,8326
21,0854
253,0698
5,3055
361,9416
21,0942
253,1972
5,3094
364,0515
21,1033
253,3239
5,3132
366,1623
21,1128
253,45
5,317
368,274
21,1225
253,5753
A.6 Argon 5+
17000
17100
17200
17300
17400
17500
17600
17700
17800
17900
18000
18100
18200
18300
18400
18500
18600
18700
18800
18900
19000
19100
19200
19300
19400
19500
19600
19700
19800
19900
20000
81
5,3208
370,3868
21,1325
253,6999
5,3246
372,5005
21,1428
253,8239
5,3283
374,6154
21,1535
253,9472
5,332
376,7313
21,1644
254,0699
5,3356
378,8483
21,1757
254,1919
5,3393
380,9664
21,1873
254,3133
5,3429
383,0857
21,1992
254,434
5,3464
385,2062
21,2114
254,5542
5,35
387,328
21,2239
254,6737
5,3535
389,451
21,2368
254,7927
5,3569
391,5754
21,25
254,911
5,3604
393,7011
21,2635
255,0288
5,3638
395,8281
21,2774
255,146
5,3672
397,9566
21,2916
255,2626
5,3706
400,0864
21,3061
255,3787
5,3739
402,2178
21,321
255,4942
5,3773
404,3506
21,3361
255,6092
5,3806
406,485
21,3517
255,7236
5,3838
408,621
21,3675
255,8375
5,3871
410,7585
21,3837
255,9509
5,3903
412,8977
21,4003
256,0638
5,3936
415,0386
21,4172
256,1762
5,3967
417,1812
21,4344
256,2881
5,3999
419,3255
21,4519
256,3995
5,4031
421,4716
21,4699
256,5104
5,4062
423,6195
21,4881
256,6208
5,4093
425,7692
21,5067
256,7308
5,4124
427,9208
21,5256
256,8403
5,4155
430,0744
21,5449
256,9493
5,4186
432,2298
21,5646
257,0579
5,4216
434,3873
21,5845
257,166
A.7 Argon 6+
20100
A.7
82
5,4247
436,5467
21,6048
257,2737
Argon 6+
T (K)
9900
10000
10100
10200
10300
10400
10500
10600
10700
10800
10900
11000
11100
11200
11300
11400
11500
11600
11700
11800
11900
12000
12100
12200
12300
12400
Q
1,000
205,7848
20,7875
227,5613
1,000
207,8636
20,7877
227,7703
1,000
209,9424
20,7879
227,9771
1,000
212,0212
20,7881
228,1819
1,000
214,1
20,7884
228,3847
1,000
216,1788
20,7887
228,5856
1,000
218,2577
20,789
228,7845
1,000
220,3367
20,7894
228,9816
1,000
222,4156
20,7898
229,1768
1,000
224,4946
20,7903
229,3702
1,000
226,5737
20,7908
229,5618
1,000
228,6528
20,7914
229,7517
1,000
230,732
20,7921
229,9399
1,000
232,8112
20,7928
230,1263
1,000
234,8905
20,7935
230,3112
1,000
236,9699
20,7944
230,4944
1,000
239,0494
20,7953
230,676
1,000
241,129
20,7963
230,856
1,000
243,2087
20,7974
231,0346
1,000
245,2885
20,7986
231,2116
1,000
247,3684
20,7999
231,3871
1,000
249,4485
20,8014
231,5611
1,000
251,5287
20,8029
231,7338
1,000
253,609
20,8046
231,905
1,000
255,6896
20,8064
232,0748
1,000
257,7703
20,8083
232,2433
A.7 Argon 6+
12500
12600
12700
12800
12900
13000
13100
13200
13300
13400
13500
13600
13700
13800
13900
14000
14100
14200
14300
14400
14500
14600
14700
14800
14900
15000
15100
15200
15300
15400
15500
83
1,000
259,8513
20,8104
232,4105
1,000
261,9324
20,8126
232,5763
1,000
264,0138
20,815
232,7408
1,000
266,0954
20,8176
232,9041
1,000
268,1773
20,8204
233,0661
1,000
270,2595
20,8233
233,2269
1,000
272,342
20,8265
233,3865
1,000
274,4248
20,8298
233,5449
1,000
276,5079
20,8334
233,7021
1,000
278,5915
20,8372
233,8582
1,000
280,6754
20,8412
234,0131
1,000
282,7597
20,8455
234,1669
1,000
284,8445
20,8501
234,3197
1,000
286,9298
20,8549
234,4713
1,000
289,0155
20,86
234,6219
1,000
291,1018
20,8654
234,7715
1,000
293,1886
20,8711
234,92
1,000
295,276
20,8771
235,0675
1,000
297,364
20,8834
235,214
1,000
299,4527
20,89
235,3596
1,000
301,542
20,897
235,5042
1,000
303,6321
20,9044
235,6478
1,000
305,7229
20,9121
235,7906
1,000
307,8145
20,9202
235,9324
1,000
309,907
20,9287
236,0733
1,000
312,0003
20,9376
236,2133
1,000
314,0945
20,9469
236,3524
1,000
316,1897
20,9566
236,4907
1,000
318,2858
20,9668
236,6282
1,000
320,383
20,9774
236,7648
1,000
322,4813
20,9884
236,9006
A.7 Argon 6+
15600
15700
15800
15900
16000
16100
16200
16300
16400
16500
16600
16700
16800
16900
17000
17100
17200
17300
17400
17500
17600
17700
17800
17900
18000
18100
18200
18300
18400
18500
18600
84
1,000
324,5807
21
237,0356
1,000
326,6813
21,012
237,1699
1,000
328,7831
21,0245
237,3033
1,000
330,8862
21,0375
237,436
1,000
332,9907
21,051
237,5679
1,000
335,0965
21,0651
237,6991
1,000
337,2037
21,0797
237,8296
1,000
339,3124
21,0948
237,9594
1,000
341,4227
21,1105
238,0885
1,000
343,5345
21,1267
238,2168
1,000
345,648
21,1436
238,3445
1,001
347,7633
21,161
238,4716
1,001
349,8803
21,179
238,598
1,001
351,9991
21,1977
238,7237
1,001
354,1198
21,2169
238,8488
1,001
356,2425
21,2368
238,9733
1,001
358,3672
21,2574
239,0972
1,001
360,494
21,2785
239,2205
1,001
362,6229
21,3004
239,3432
1,001
364,7541
21,3229
239,4653
1,001
366,8875
21,3461
239,5869
1,001
369,0233
21,3699
239,7079
1,001
371,1615
21,3945
239,8284
1,001
373,3022
21,4198
239,9483
1,001
375,4455
21,4457
240,0677
1,001
377,5914
21,4724
240,1866
1,001
379,74
21,4999
240,305
1,001
381,8914
21,528
240,4229
1,001
384,0457
21,5569
240,5403
1,001
386,2028
21,5865
240,6572
1,001
388,363
21,6169
240,7736
A.7 Argon 6+
18700
18800
18900
19000
19100
19200
19300
19400
19500
19600
19700
19800
19900
20000
20100
85
1,001
1,001
1,002
1,002
1,002
1,002
1,002
1,002
1,002
1,002
1,002
1,002
1,002
1,002
1,003
390,5262
392,6926
394,8623
397,0352
399,2115
401,3913
403,5747
405,7616
407,9523
410,1468
412,3451
414,5474
416,7537
418,9641
421,1787
21,6481
21,68
21,7127
21,7462
21,7805
21,8155
21,8514
21,888
21,9255
21,9638
22,0028
22,0427
22,0834
22,125
22,1673
240,8896
241,0052
241,1203
241,2349
241,3492
241,463
241,5764
241,6894
241,8021
241,9143
242,0262
242,1377
242,2489
242,3597
242,4701
THERMODYNAMIC PROPERTIES FOR THE SEPERATE SPECIES FOR OXYGEN
86
Appendix B
seperate species for oxygen
This appendix contains the thermodynamic properties calculated for the seperate species
of oxygen.
B.1
Oxygen
T (K)
9900
10000
10100
10200
10300
10400
10500
10600
10700
10800
10900
11000
Q
9,4054
217,0817
23,2091
235,9099
9,4185
219,4033
23,2235
236,1432
9,4316
221,7264
23,2383
236,3744
9,4447
224,051
23,2536
236,6034
9,4578
226,3772
23,2696
236,8303
9,471
228,705
23,2863
237,0552
9,4842
231,0345
23,3039
237,2782
9,4975
233,3658
23,3224
237,4991
9,5107
235,699
23,3421
237,7182
9,524
238,0342
23,3629
237,9355
9,5373
240,3716
23,3851
238,1509
9,5507
242,7113
23,4088
238,3646
Table B.1: Thermodynamic properties of Oxygen
B.1 Oxygen
11100
11200
11300
11400
11500
11600
11700
11800
11900
12000
12100
12200
12300
12400
12500
12600
12700
12800
12900
13000
13100
13200
13300
13400
13500
13600
13700
13800
13900
14000
14100
14200
14300
87
9,564
245,0534
23,4341
9,5774
247,3982
23,4611
9,5908
249,7457
23,4901
9,6042
252,0963
23,5211
9,6177
254,45
23,5543
9,6312
256,8072
23,5898
9,6447
259,168
23,6278
9,6583
261,5328
23,6686
9,6718
263,9019
23,7121
9,6854
266,2754
23,7587
9,6991
268,6537
23,8085
9,7128
271,0372
23,8616
9,7265
273,4261
23,9182
9,7402
275,8209
23,9786
9,754
278,222
24,0428
9,7678
280,6296
24,1112
9,7817
283,0444
24,1838
9,7956
285,4665
24,2608
9,8096
287,8967
24,3425
9,8237
290,3352
24,429
9,8377
292,7826
24,5206
9,8519
295,2395
24,6174
9,8661
297,7063
24,7195
9,8804
300,1836
24,8273
9,8948
302,672
24,9409
9,9092
305,172
25,0605
9,9237
307,6843
25,1863
9,9384
310,2095
25,3185
9,9531
312,7482
25,4572
9,9679
315,3011
25,6027
9,9828
317,869
25,7552
9,9978
320,4524
25,9148
10,013
323,0522
26,0817
238,5765
238,7868
238,9955
239,2026
239,4081
239,6122
239,8149
240,0161
240,2161
240,4147
240,612
240,8082
241,0032
241,1972
241,39
241,5819
241,7727
241,9627
242,1518
242,3401
242,5277
242,7145
242,9007
243,0863
243,2713
243,4558
243,6398
243,8235
244,0068
244,1898
244,3725
244,5551
244,7376
B.1 Oxygen
14400
14500
14600
14700
14800
14900
15000
15100
15200
15300
15400
15500
15600
15700
15800
15900
16000
16100
16200
16300
16400
16500
16600
16700
16800
16900
17000
17100
17200
17300
17400
17500
17600
88
10,0282
325,669
26,2561
10,0436
328,3036
26,4382
10,0591
330,9569
26,6281
10,0748
333,6295
26,8261
10,0906
336,3224
27,0322
10,1066
339,0362
27,2468
10,1227
341,772
27,4698
10,139
344,5305
27,7015
10,1555
347,3126
27,942
10,1722
350,1192
28,1914
10,1891
352,9512
28,45
10,2061
355,8095
28,7177
10,2234
358,695
28,9948
10,2409
361,6088
29,2813
10,2587
364,5516
29,5774
10,2766
367,5246
29,8831
10,2949
370,5286
30,1986
10,3134
373,5646
30,5239
10,3321
376,6337
30,8591
10,3511
379,7368
31,2043
10,3705
382,8749
31,5594
10,3901
386,049
31,9246
10,41
389,2601
32,2999
10,4303
392,5093
32,6853
10,4508
395,7975
33,0808
10,4718
399,1258
33,4864
10,493
402,4952
33,9022
10,5147
405,9066
34,328
10,5367
409,3611
34,7638
10,5591
412,8597
35,2096
10,5819
416,4033
35,6654
10,6051
419,9931
36,131
10,6287
423,6299
36,6064
244,9199
245,1022
245,2846
245,467
245,6496
245,8323
246,0153
246,1986
246,3823
246,5663
246,7508
246,9358
247,1214
247,3075
247,4944
247,682
247,8703
248,0595
248,2495
248,4405
248,6324
248,8253
249,0194
249,2145
249,4108
249,6083
249,8071
250,0072
250,2086
250,4115
250,6157
250,8214
251,0286
B.2 Oxygen 1+
17700
17800
17900
18000
18100
18200
18300
18400
18500
18600
18700
18800
18900
19000
19100
19200
19300
19400
19500
19600
19700
19800
19900
20000
20100
B.2
89
10,6528
10,6773
10,7023
10,7277
10,7537
10,7801
10,8071
10,8345
10,8625
10,8911
10,9202
10,9499
10,9802
11,0111
11,0426
11,0748
11,1076
11,141
11,1752
11,21
11,2455
11,2818
11,3187
11,3565
11,395
427,3147
431,0485
434,8322
438,6668
442,5532
446,4923
450,485
454,5322
458,6347
462,7933
467,0088
471,2821
475,6139
480,0049
484,4559
488,9674
493,5402
498,1748
502,8719
507,632
512,4555
517,3431
522,295
527,3118
532,3938
37,0915
37,5861
38,0902
38,6036
39,1261
39,6576
40,1978
40,7467
41,3041
41,8695
42,443
43,0241
43,6128
44,2085
44,8112
45,4205
46,0361
46,6576
47,2848
47,9173
48,5548
49,1968
49,8431
50,4931
51,1467
251,2374
251,4478
251,6597
251,8734
252,0887
252,3057
252,5245
252,745
252,9674
253,1916
253,4176
253,6455
253,8753
254,107
254,3407
254,5763
254,8138
255,0533
255,2948
255,5383
255,7838
256,0312
256,2807
256,5322
256,7856
Oxygen 1+
T (K)
9900
10000
10100
Q
4,2197
223,1327
27,6321
229,8567
4,2287
225,9021
27,7551
230,1351
4,238
228,6836
27,8755
230,4118
Table B.2: Thermodynamic properties of Oxygen 1+
B.2 Oxygen 1+
10200
10300
10400
10500
10600
10700
10800
10900
11000
11100
11200
11300
11400
11500
11600
11700
11800
11900
12000
12100
12200
12300
12400
12500
12600
12700
12800
12900
13000
13100
13200
90
4,2475
231,4771
27,9934
230,6871
4,2571
234,2822
28,1087
230,9607
4,2669
237,0987
28,2213
231,2329
4,277
239,9264
28,3313
231,5034
4,2872
242,7649
28,4385
231,7725
4,2975
245,614
28,5429
232,04
4,3081
248,4734
28,6445
232,306
4,3189
251,3428
28,7433
232,5705
4,3298
254,2219
28,8392
232,8334
4,3409
257,1105
28,9322
233,0948
4,3521
260,0083
29,0224
233,3547
4,3636
262,9149
29,1096
233,6131
4,3752
265,8301
29,194
233,8699
4,3869
268,7536
29,2755
234,1253
4,3989
271,6851
29,3541
234,3791
4,411
274,6243
29,4298
234,6314
4,4232
277,571
29,5026
234,8821
4,4357
280,5248
29,5726
235,1314
4,4482
283,4854
29,6397
235,3792
4,461
286,4526
29,704
235,6254
4,4738
289,4261
29,7656
235,8701
4,4869
292,4056
29,8243
236,1134
4,5
295,3909
29,8803
236,3551
4,5134
298,3816
29,9335
236,5953
4,5268
301,3775
29,9841
236,834
4,5404
304,3783
30,0321
237,0712
4,5542
307,3838
30,0774
237,307
4,5681
310,3937
30,1201
237,5412
4,5821
313,4078
30,1603
237,774
4,5962
316,4257
30,198
238,0052
4,6105
319,4473
30,2332
238,235
B.2 Oxygen 1+
13300
13400
13500
13600
13700
13800
13900
14000
14100
14200
14300
14400
14500
14600
14700
14800
14900
15000
15100
15200
15300
15400
15500
15600
15700
15800
15900
16000
16100
16200
16300
91
4,6249
322,4723
30,2661
238,4633
4,6394
325,5004
30,2965
238,6901
4,6541
328,5315
30,3246
238,9155
4,6689
331,5653
30,3504
239,1394
4,6838
334,6015
30,374
239,3618
4,6988
337,64
30,3954
239,5828
4,7139
340,6805
30,4147
239,8023
4,7292
343,7229
30,4318
240,0204
4,7445
346,7668
30,4469
240,2371
4,76
349,8122
30,46
240,4523
4,7755
352,8588
30,4712
240,6661
4,7912
355,9064
30,4804
240,8785
4,807
358,9548
30,4878
241,0894
4,8229
362,0038
30,4933
241,299
4,8388
365,0534
30,4971
241,5071
4,8549
368,1032
30,4992
241,7139
4,8711
371,1532
30,4996
241,9193
4,8873
374,2031
30,4984
242,1233
4,9037
377,2528
30,4957
242,3259
4,9201
380,3022
30,4913
242,5272
4,9366
383,351
30,4856
242,7272
4,9533
386,3992
30,4784
242,9257
4,9699
389,4466
30,4697
243,123
4,9867
392,4931
30,4598
243,3189
5,0036
395,5386
30,4486
243,5135
5,0205
398,5828
30,4361
243,7068
5,0375
401,6257
30,4223
243,8988
5,0546
404,6672
30,4075
244,0895
5,0717
407,7072
30,3915
244,2789
5,089
410,7455
30,3744
244,467
5,1063
413,782
30,3562
244,6539
B.2 Oxygen 1+
16400
16500
16600
16700
16800
16900
17000
17100
17200
17300
17400
17500
17600
17700
17800
17900
18000
18100
18200
18300
18400
18500
18600
18700
18800
18900
19000
19100
19200
19300
19400
92
5,1236
416,8167
30,3371
244,8395
5,1411
419,8494
30,317
245,0238
5,1585
422,8801
30,2959
245,2069
5,1761
425,9086
30,274
245,3888
5,1937
428,9348
30,2513
245,5695
5,2114
431,9588
30,2277
245,749
5,2291
434,9804
30,2033
245,9272
5,2469
437,9994
30,1782
246,1043
5,2648
441,016
30,1525
246,2802
5,2827
444,0299
30,126
246,4549
5,3006
447,0412
30,0989
246,6285
5,3186
450,0497
30,0712
246,8009
5,3366
453,0554
30,0429
246,9722
5,3547
456,0582
30,0141
247,1423
5,3729
459,0582
29,9847
247,3113
5,3911
462,0551
29,9549
247,4792
5,4093
465,0491
29,9246
247,646
5,4276
468,0401
29,8939
247,8117
5,4459
471,0279
29,8629
247,9763
5,4642
474,0126
29,8314
248,1399
5,4826
476,9942
29,7996
248,3023
5,5011
479,9725
29,7675
248,4638
5,5195
482,9477
29,7351
248,6242
5,538
485,9195
29,7024
248,7835
5,5566
488,8881
29,6695
248,9418
5,5751
491,8534
29,6364
249,0991
5,5937
494,8154
29,6031
249,2555
5,6124
497,7741
29,5697
249,4108
5,631
500,7293
29,536
249,5651
5,6497
503,6813
29,5023
249,7184
5,6684
506,6298
29,4684
249,8708
B.3 Oxygen 2+
19500
19600
19700
19800
19900
20000
20100
B.3
93
5,6871
5,7059
5,7247
5,7435
5,7623
5,7812
5,8001
509,5749
512,5167
515,455
518,39
521,3215
524,2497
527,1744
29,4345
29,4005
29,3665
29,3324
29,2983
29,2643
29,2302
250,0222
250,1727
250,3222
250,4708
250,6185
250,7653
250,9112
Oxygen 2+
T (K)
9900
10000
10100
10200
10300
10400
10500
10600
10700
10800
10900
11000
11100
11200
11300
11400
11500
11600
11700
11800
Q
8,9988
215,4239
22,9123
235,3749
9,0094
217,7162
22,9334
235,6053
9,0201
220,0106
22,954
235,8336
9,0308
222,307
22,9741
236,0599
9,0416
224,6054
22,9937
236,2841
9,0524
226,9057
23,0129
236,5064
9,0632
229,208
23,0316
236,7267
9,074
231,5121
23,0499
236,9451
9,0849
233,8179
23,0678
237,1616
9,0958
236,1256
23,0853
237,3762
9,1067
238,435
23,1023
237,5891
9,1177
240,746
23,119
237,8002
9,1287
243,0588
23,1353
238,0094
9,1397
245,3731
23,1512
238,217
9,1507
247,689
23,1667
238,4229
9,1617
250,0064
23,1819
238,6271
9,1728
252,3254
23,1968
238,8296
9,1839
254,6458
23,2114
239,0305
9,195
256,9676
23,2256
239,2298
9,2061
259,2909
23,2395
239,4275
B.3 Oxygen 2+
11900
12000
12100
12200
12300
12400
12500
12600
12700
12800
12900
13000
13100
13200
13300
13400
13500
13600
13700
13800
13900
14000
14100
14200
14300
14400
14500
14600
14700
14800
14900
94
9,2173
261,6155
23,2532
239,6237
9,2285
263,9415
23,2665
239,8183
9,2397
266,2688
23,2796
240,0115
9,2509
268,5974
23,2924
240,2031
9,2621
270,9273
23,3049
240,3933
9,2733
273,2584
23,3172
240,5821
9,2846
275,5907
23,3293
240,7694
9,2959
277,9243
23,3411
240,9553
9,3071
280,259
23,3527
241,1399
9,3184
282,5948
23,3641
241,3231
9,3298
284,9318
23,3752
241,505
9,3411
287,2698
23,3862
241,6855
9,3524
289,609
23,397
241,8648
9,3638
291,9492
23,4076
242,0427
9,3751
294,2905
23,418
242,2194
9,3865
296,6328
23,4282
242,3949
9,3979
298,9761
23,4383
242,5691
9,4093
301,3205
23,4482
242,7421
9,4207
303,6658
23,4579
242,914
9,4321
306,012
23,4675
243,0846
9,4435
308,3593
23,477
243,2541
9,4549
310,7074
23,4863
243,4224
9,4664
313,0565
23,4955
243,5896
9,4778
315,4065
23,5045
243,7557
9,4893
317,7574
23,5135
243,9206
9,5007
320,1092
23,5223
244,0845
9,5122
322,4619
23,531
244,2473
9,5236
324,8154
23,5396
244,4091
9,5351
327,1698
23,5481
244,5698
9,5466
329,525
23,5565
244,7295
9,558
331,8811
23,5649
244,8881
B.3 Oxygen 2+
15000
15100
15200
15300
15400
15500
15600
15700
15800
15900
16000
16100
16200
16300
16400
16500
16600
16700
16800
16900
17000
17100
17200
17300
17400
17500
17600
17700
17800
17900
18000
95
9,5695
334,238
23,5731
245,0458
9,581
336,5957
23,5813
245,2025
9,5925
338,9542
23,5894
245,3581
9,604
341,3136
23,5974
245,5129
9,6155
343,6737
23,6053
245,6666
9,627
346,0346
23,6132
245,8194
9,6385
348,3963
23,621
245,9713
9,6499
350,7588
23,6287
246,1223
9,6614
353,1221
23,6364
246,2723
9,6729
355,4861
23,6441
246,4215
9,6844
357,8509
23,6517
246,5697
9,6959
360,2165
23,6593
246,7171
9,7074
362,5828
23,6668
246,8636
9,7189
364,9498
23,6743
247,0093
9,7304
367,3176
23,6817
247,1541
9,7419
369,6862
23,6892
247,2981
9,7534
372,0554
23,6965
247,4413
9,7649
374,4255
23,7039
247,5836
9,7764
376,7962
23,7113
247,7251
9,7879
379,1677
23,7186
247,8659
9,7994
381,5399
23,7259
248,0058
9,8109
383,9129
23,7332
248,145
9,8224
386,2866
23,7405
248,2834
9,8339
388,661
23,7478
248,4211
9,8453
391,0362
23,7551
248,558
9,8568
393,412
23,7624
248,6941
9,8683
395,7886
23,7697
248,8295
9,8798
398,166
23,7769
248,9642
9,8912
400,544
23,7842
249,0982
9,9027
402,9228
23,7915
249,2315
9,9142
405,3023
23,7988
249,364
B.4 Oxygen 3+
18100
18200
18300
18400
18500
18600
18700
18800
18900
19000
19100
19200
19300
19400
19500
19600
19700
19800
19900
20000
20100
B.4
96
9,9256
9,9371
9,9485
9,96
9,9714
9,9829
9,9943
10,0058
10,0172
10,0286
10,0401
10,0515
10,0629
10,0743
10,0857
10,0971
10,1085
10,1199
10,1313
10,1427
10,1541
407,6826
410,0636
412,4453
414,8277
417,2109
419,5948
421,9795
424,3649
426,7511
429,138
431,5257
433,9141
436,3033
438,6932
441,084
443,4755
445,8677
448,2608
450,6546
453,0492
455,4446
23,8062
23,8135
23,8208
23,8282
23,8356
23,843
23,8504
23,8579
23,8654
23,8729
23,8805
23,888
23,8957
23,9033
23,911
23,9187
23,9265
23,9343
23,9422
23,9501
23,958
249,4959
249,6271
249,7576
249,8874
250,0166
250,1451
250,273
250,4002
250,5268
250,6527
250,7781
250,9028
251,0269
251,1504
251,2733
251,3957
251,5174
251,6386
251,7592
251,8792
251,9987
Oxygen 3+
T (K)
9900
10000
10100
10200
10300
10400
Q
5,7822
208,857
20,8481
231,0341
5,7844
210,9421
20,8529
231,2436
5,7865
213,0276
20,8579
231,4512
5,7886
215,1137
20,8633
231,6567
5,7906
217,2003
20,869
231,8602
5,7926
219,2875
20,8751
232,0619
B.4 Oxygen 3+
10500
10600
10700
10800
10900
11000
11100
11200
11300
11400
11500
11600
11700
11800
11900
12000
12100
12200
12300
12400
12500
12600
12700
12800
12900
13000
13100
13200
13300
13400
13500
97
5,7946
221,3753
20,8815
232,2617
5,7966
223,4638
20,8882
232,4597
5,7985
225,553
20,8954
232,6558
5,8004
227,6429
20,9028
232,8502
5,8023
229,7336
20,9107
233,0429
5,8041
231,825
20,919
233,2339
5,806
233,9174
20,9276
233,4233
5,8077
236,0106
20,9367
233,611
5,8095
238,1047
20,9462
233,7972
5,8113
240,1998
20,9561
233,9818
5,813
242,296
20,9664
234,1648
5,8147
244,3931
20,9771
234,3464
5,8164
246,4914
20,9883
234,5265
5,8181
248,5908
21
234,7052
5,8197
250,6914
21,0121
234,8825
5,8214
252,7932
21,0246
235,0583
5,823
254,8963
21,0376
235,2329
5,8246
257,0008
21,0511
235,4061
5,8262
259,1066
21,065
235,578
5,8278
261,2138
21,0794
235,7486
5,8294
263,3225
21,0943
235,918
5,8309
265,4327
21,1097
236,0861
5,8325
267,5444
21,1255
236,2531
5,834
269,6578
21,1418
236,4188
5,8356
271,7728
21,1587
236,5834
5,8371
273,8895
21,176
236,7469
5,8386
276,008
21,1938
236,9092
5,8401
278,1283
21,212
237,0704
5,8416
280,2504
21,2308
237,2306
5,8431
282,3745
21,2501
237,3897
5,8446
284,5005
21,2699
237,5478
B.4 Oxygen 3+
13600
13700
13800
13900
14000
14100
14200
14300
14400
14500
14600
14700
14800
14900
15000
15100
15200
15300
15400
15500
15600
15700
15800
15900
16000
16100
16200
16300
16400
16500
16600
98
5,8461
286,6285
21,2901
237,7048
5,8476
288,7585
21,3109
237,8609
5,8491
290,8907
21,3321
238,0159
5,8506
293,0249
21,3538
238,17
5,8521
295,1614
21,376
238,3232
5,8536
297,3002
21,3987
238,4754
5,8551
299,4412
21,4219
238,6267
5,8566
301,5846
21,4456
238,7771
5,8581
303,7303
21,4698
238,9267
5,8596
305,8785
21,4944
239,0753
5,8611
308,0292
21,5195
239,2232
5,8626
310,1825
21,5451
239,3701
5,8641
312,3383
21,5711
239,5163
5,8656
314,4967
21,5976
239,6616
5,8671
316,6578
21,6246
239,8062
5,8687
318,8216
21,652
239,95
5,8702
320,9882
21,6799
240,093
5,8717
323,1576
21,7083
240,2352
5,8733
325,3299
21,737
240,3768
5,8749
327,5051
21,7662
240,5175
5,8764
329,6832
21,7959
240,6576
5,878
331,8642
21,826
240,797
5,8796
334,0484
21,8565
240,9357
5,8812
336,2356
21,8874
241,0736
5,8828
338,4259
21,9187
241,211
5,8844
340,6193
21,9505
241,3476
5,8861
342,816
21,9826
241,4837
5,8877
345,0159
22,0152
241,619
5,8894
347,219
22,0481
241,7538
5,891
349,4255
22,0814
241,8879
5,8927
351,6353
22,1151
242,0214
B.4 Oxygen 3+
16700
16800
16900
17000
17100
17200
17300
17400
17500
17600
17700
17800
17900
18000
18100
18200
18300
18400
18500
18600
18700
18800
18900
19000
19100
19200
19300
19400
19500
19600
19700
99
5,8944
353,8485
22,1492
242,1544
5,8961
356,0652
22,1836
242,2867
5,8979
358,2853
22,2184
242,4185
5,8996
360,5089
22,2536
242,5496
5,9014
362,736
22,2891
242,6803
5,9031
364,9667
22,3249
242,8103
5,9049
367,201
22,3611
242,9399
5,9068
369,4389
22,3976
243,0688
5,9086
371,6805
22,4344
243,1973
5,9104
373,9258
22,4715
243,3252
5,9123
376,1748
22,5089
243,4527
5,9142
378,4276
22,5467
243,5796
5,9161
380,6842
22,5847
243,706
5,918
382,9445
22,623
243,8319
5,9199
385,2088
22,6616
243,9574
5,9219
387,4769
22,7004
244,0823
5,9239
389,7489
22,7395
244,2068
5,9259
392,0248
22,7789
244,3309
5,9279
394,3047
22,8185
244,4544
5,93
396,5885
22,8584
244,5775
5,932
398,8763
22,8985
244,7002
5,9341
401,1682
22,9388
244,8225
5,9362
403,4641
22,9794
244,9443
5,9383
405,7641
23,0201
245,0656
5,9405
408,0681
23,0611
245,1866
5,9427
410,3763
23,1023
245,3071
5,9449
412,6886
23,1437
245,4272
5,9471
415,0051
23,1852
245,5469
5,9493
417,3257
23,227
245,6662
5,9516
419,6505
23,2689
245,7852
5,9539
421,9794
23,311
245,9037
B.5 Oxygen 4+
19800
19900
20000
20100
B.5
100
5,9562
5,9586
5,9609
5,9633
424,3127
426,6501
428,9918
431,3377
23,3532
23,3956
23,4381
23,4808
246,0218
246,1396
246,257
246,374
Oxygen 4+
T (K)
9900
10000
10100
10200
10300
10400
10500
10600
10700
10800
10900
11000
11100
11200
11300
11400
11500
11600
11700
11800
11900
12000
12100
Q
1,0001
205,8413
20,8552
216,1398
1,0001
207,9271
20,8624
216,3494
1,0001
210,0138
20,8702
216,557
1,0001
212,1012
20,8786
216,7627
1,0001
214,1895
20,8876
216,9664
1,0001
216,2787
20,8973
217,1683
1,0001
218,369
20,9076
217,3683
1,0001
220,4603
20,9187
217,5665
1,0001
222,5527
20,9305
217,763
1,0002
224,6464
20,9431
217,9578
1,0002
226,7414
20,9565
218,1509
1,0002
228,8378
20,9708
218,3423
1,0002
230,9356
20,9859
218,5322
1,0002
233,035
21,0019
218,7205
1,0003
235,136
21,0189
218,9072
1,0003
237,2388
21,0368
219,0925
1,0003
239,3434
21,0557
219,2763
1,0003
241,4499
21,0756
219,4587
1,0004
243,5585
21,0966
219,6397
1,0004
245,6693
21,1186
219,8193
1,0004
247,7823
21,1417
219,9976
1,0005
249,8977
21,166
220,1746
1,0005
252,0155
21,1914
220,3504
B.5 Oxygen 4+
12200
12300
12400
12500
12600
12700
12800
12900
13000
13100
13200
13300
13400
13500
13600
13700
13800
13900
14000
14100
14200
14300
14400
14500
14600
14700
14800
14900
15000
15100
15200
101
1,0006
254,136
21,2181
220,5249
1,0006
256,2592
21,2459
220,6982
1,0006
258,3852
21,2749
220,8704
1,0007
260,5142
21,3052
221,0414
1,0008
262,6463
21,3368
221,2113
1,0008
264,7816
21,3697
221,3801
1,0009
266,9203
21,4039
221,5478
1,0009
269,0624
21,4395
221,7145
1,001
271,2082
21,4764
221,8802
1,0011
273,3578
21,5147
222,045
1,0012
275,5112
21,5544
222,2087
1,0012
277,6687
21,5955
222,3715
1,0013
279,8304
21,6381
222,5335
1,0014
281,9964
21,6821
222,6945
1,0015
284,1669
21,7276
222,8547
1,0016
286,3419
21,7745
223,014
1,0017
288,5218
21,823
223,1726
1,0018
290,7066
21,8729
223,3303
1,0019
292,8964
21,9244
223,4873
1,002
295,0915
21,9774
223,6435
1,0022
297,292
22,0319
223,799
1,0023
299,4979
22,0879
223,9538
1,0024
301,7096
22,1455
224,108
1,0026
303,9271
22,2046
224,2614
1,0027
306,1506
22,2652
224,4142
1,0029
308,3802
22,3274
224,5664
1,003
310,6161
22,3912
224,718
1,0032
312,8585
22,4565
224,869
1,0034
315,1075
22,5234
225,0195
1,0036
317,3632
22,5918
225,1693
1,0037
319,6259
22,6618
225,3187
B.5 Oxygen 4+
15300
15400
15500
15600
15700
15800
15900
16000
16100
16200
16300
16400
16500
16600
16700
16800
16900
17000
17100
17200
17300
17400
17500
17600
17700
17800
17900
18000
18100
18200
18300
102
1,0039
321,8956
22,7333
225,4675
1,0041
324,1726
22,8063
225,6159
1,0044
326,4569
22,8809
225,7637
1,0046
328,7488
22,957
225,9111
1,0048
331,0484
23,0346
226,0581
1,005
333,3558
23,1137
226,2046
1,0053
335,6711
23,1943
226,3506
1,0055
337,9947
23,2764
226,4963
1,0058
340,3265
23,36
226,6416
1,0061
342,6667
23,445
226,7865
1,0063
345,0155
23,5315
226,931
1,0066
347,373
23,6194
227,0752
1,0069
349,7394
23,7087
227,2191
1,0072
352,1148
23,7995
227,3626
1,0075
354,4994
23,8916
227,5058
1,0079
356,8932
23,9851
227,6487
1,0082
359,2964
24,0799
227,7914
1,0085
361,7092
24,176
227,9337
1,0089
364,1317
24,2735
228,0758
1,0093
366,564
24,3723
228,2176
1,0096
369,0062
24,4723
228,3592
1,01
371,4585
24,5735
228,5005
1,0104
373,9209
24,676
228,6417
1,0108
376,3937
24,7797
228,7826
1,0113
378,8769
24,8845
228,9232
1,0117
381,3706
24,9905
229,0637
1,0121
383,875
25,0976
229,204
1,0126
386,3902
25,2058
229,3442
1,0131
388,9162
25,315
229,4841
1,0135
391,4532
25,4253
229,6239
1,014
394,0013
25,5367
229,7635
B.6 Oxygen 5+
18400
18500
18600
18700
18800
18900
19000
19100
19200
19300
19400
19500
19600
19700
19800
19900
20000
20100
B.6
103
1,0145
1,015
1,0156
1,0161
1,0167
1,0172
1,0178
1,0184
1,019
1,0196
1,0202
1,0209
1,0215
1,0222
1,0229
1,0236
1,0243
1,025
396,5606
399,1312
401,7131
404,3065
406,9114
409,528
412,1563
414,7964
417,4483
420,1122
422,7881
425,4762
428,1763
430,8887
433,6133
436,3502
439,0996
441,8613
25,649
25,7622
25,8764
25,9915
26,1074
26,2242
26,3418
26,4601
26,5792
26,6991
26,8196
26,9407
27,0625
27,1848
27,3078
27,4312
27,5551
27,6795
229,903
230,0423
230,1815
230,3206
230,4595
230,5983
230,737
230,8756
231,0141
231,1524
231,2907
231,4289
231,5671
231,7051
231,843
231,9809
232,1187
232,2565
Oxygen 5+
T (K)
9900
10000
10100
10200
10300
10400
10500
10600
10700
Q
2
205,7868
20,7901
221,897
2
207,8659
20,7906
222,1059
2
209,945
20,7912
222,3128
2
212,0241
20,7918
222,5177
2
214,1033
20,7924
222,7205
2
216,1826
20,7932
222,9214
2
218,262
20,794
223,1204
2
220,3414
20,7948
223,3175
2
222,4209
20,7958
223,5128
B.6 Oxygen 5+
10800
10900
11000
11100
11200
11300
11400
11500
11600
11700
11800
11900
12000
12100
12200
12300
12400
12500
12600
12700
12800
12900
13000
13100
13200
13300
13400
13500
13600
13700
13800
104
2
224,5006
20,7968
223,7062
2
226,5803
20,7979
223,8979
2
228,6601
20,7991
224,0878
2
230,7401
20,8003
224,2761
2
232,8202
20,8017
224,4626
2
234,9005
20,8032
224,6475
2
236,9809
20,8048
224,8308
2
239,0614
20,8065
225,0125
2
241,1422
20,8084
225,1927
2
243,2231
20,8104
225,3713
2
245,3043
20,8125
225,5484
2,0001
247,3856
20,8147
225,7241
2,0001
249,4672
20,8171
225,8983
2,0001
251,549
20,8196
226,071
2,0001
253,6311
20,8223
226,2424
2,0001
255,7135
20,8252
226,4124
2,0001
257,7962
20,8282
226,581
2,0001
259,8792
20,8315
226,7483
2,0001
261,9625
20,8348
226,9143
2,0001
264,0461
20,8384
227,0791
2,0001
266,1302
20,8422
227,2425
2,0001
268,2146
20,8462
227,4047
2,0001
270,2994
20,8504
227,5657
2,0001
272,3847
20,8548
227,7255
2,0002
274,4704
20,8594
227,8841
2,0002
276,5566
20,8642
228,0416
2,0002
278,6432
20,8693
228,1979
2,0002
280,7304
20,8746
228,3531
2,0002
282,8182
20,8802
228,5071
2,0002
284,9065
20,886
228,6601
2,0003
286,9954
20,8921
228,812
B.6 Oxygen 5+
13900
14000
14100
14200
14300
14400
14500
14600
14700
14800
14900
15000
15100
15200
15300
15400
15500
15600
15700
15800
15900
16000
16100
16200
16300
16400
16500
16600
16700
16800
16900
105
2,0003
289,0849
20,8984
228,9629
2,0003
291,1751
20,905
229,1127
2,0003
293,2659
20,9118
229,2616
2,0003
295,3574
20,919
229,4094
2,0004
297,4497
20,9264
229,5562
2,0004
299,5427
20,9341
229,7021
2,0004
301,6365
20,9422
229,847
2,0004
303,7312
20,9505
229,9909
2,0005
305,8266
20,9591
230,134
2,0005
307,923
20,968
230,2761
2,0005
310,0203
20,9773
230,4173
2,0006
312,1185
20,9868
230,5577
2,0006
314,2176
20,9967
230,6971
2,0006
316,3178
21,0069
230,8358
2,0007
318,419
21,0175
230,9736
2,0007
320,5213
21,0284
231,1105
2,0008
322,6247
21,0396
231,2467
2,0008
324,7293
21,0511
231,382
2,0008
326,835
21,0631
231,5165
2,0009
328,9419
21,0753
231,6503
2,0009
331,05
21,0879
231,7833
2,001
333,1595
21,1009
231,9156
2,0011
335,2702
21,1142
232,0471
2,0011
337,3823
21,1279
232,1779
2,0012
339,4958
21,142
232,3079
2,0012
341,6107
21,1564
232,4373
2,0013
343,7271
21,1712
232,5659
2,0014
345,845
21,1864
232,6939
2,0014
347,9644
21,202
232,8212
2,0015
350,0854
21,2179
232,9478
2,0016
352,208
21,2342
233,0738
B.6 Oxygen 5+
17000
17100
17200
17300
17400
17500
17600
17700
17800
17900
18000
18100
18200
18300
18400
18500
18600
18700
18800
18900
19000
19100
19200
19300
19400
19500
19600
19700
19800
19900
20000
106
2,0017
354,3323
21,2509
233,1991
2,0018
356,4582
21,2679
233,3238
2,0018
358,5859
21,2854
233,4479
2,0019
360,7153
21,3032
233,5713
2,002
362,8465
21,3214
233,6942
2,0021
364,9796
21,34
233,8164
2,0022
367,1145
21,359
233,938
2,0023
369,2514
21,3783
234,0591
2,0024
371,3902
21,398
234,1796
2,0025
373,531
21,4182
234,2995
2,0026
375,6738
21,4387
234,4189
2,0027
377,8188
21,4596
234,5378
2,0029
379,9658
21,4808
234,656
2,003
382,1149
21,5025
234,7738
2,0031
384,2663
21,5245
234,8911
2,0032
386,4199
21,547
235,0078
2,0034
388,5757
21,5698
235,124
2,0035
390,7338
21,5929
235,2397
2,0037
392,8943
21,6165
235,3549
2,0038
395,0571
21,6404
235,4697
2,004
397,2224
21,6647
235,5839
2,0041
399,3901
21,6894
235,6977
2,0043
401,5603
21,7144
235,8111
2,0044
403,733
21,7398
235,9239
2,0046
405,9082
21,7656
236,0363
2,0048
408,0861
21,7917
236,1483
2,0049
410,2666
21,8182
236,2598
2,0051
412,4498
21,8451
236,3709
2,0053
414,6356
21,8723
236,4816
2,0055
416,8242
21,8998
236,5919
2,0057
419,0156
21,9277
236,7017
B.7 Oxygen 6+
20100
B.7
107
2,0059
421,2098
21,956
236,8112
Oxygen 6+
T (K)
9900
10000
10100
10200
10300
10400
10500
10600
10700
10800
10900
11000
11100
11200
11300
11400
11500
11600
11700
11800
11900
12000
12100
12200
12300
12400
Q
1
205,7841
20,7863
216,1335
1
207,8628
20,7863
216,3424
1
209,9414
20,7863
216,5492
1
212,02
20,7863
216,754
1
214,0986
20,7863
216,9568
1
216,1773
20,7863
217,1577
1
218,2559
20,7863
217,3566
1
220,3345
20,7863
217,5536
1
222,4131
20,7863
217,7488
1
224,4918
20,7863
217,9422
1
226,5704
20,7863
218,1337
1
228,649
20,7863
218,3236
1
230,7277
20,7863
218,5117
1
232,8063
20,7863
218,6981
1
234,8849
20,7863
218,8829
1
236,9635
20,7863
219,066
1
239,0422
20,7863
219,2475
1
241,1208
20,7863
219,4275
1
243,1994
20,7863
219,6059
1
245,278
20,7863
219,7828
1
247,3567
20,7863
219,9583
1
249,4353
20,7863
220,1322
1
251,5139
20,7863
220,3047
1
253,5926
20,7863
220,4758
1
255,6712
20,7863
220,6455
1
257,7498
20,7863
220,8138
B.7 Oxygen 6+
12500
12600
12700
12800
12900
13000
13100
13200
13300
13400
13500
13600
13700
13800
13900
14000
14100
14200
14300
14400
14500
14600
14700
14800
14900
15000
15100
15200
15300
15400
15500
108
1
259,8284
20,7863
220,9807
1
261,9071
20,7863
221,1464
1
263,9857
20,7863
221,3107
1
266,0643
20,7863
221,4737
1
268,1429
20,7863
221,6355
1
270,2216
20,7863
221,796
1
272,3002
20,7863
221,9553
1
274,3788
20,7863
222,1133
1
276,4575
20,7863
222,2702
1
278,5361
20,7863
222,4259
1
280,6147
20,7863
222,5805
1
282,6933
20,7863
222,7339
1
284,772
20,7863
222,8862
1
286,8506
20,7863
223,0373
1
288,9292
20,7863
223,1874
1
291,0078
20,7863
223,3364
1
293,0865
20,7863
223,4844
1
295,1651
20,7863
223,6313
1
297,2437
20,7863
223,7771
1
299,3224
20,7863
223,922
1
301,401
20,7863
224,0658
1
303,4796
20,7863
224,2087
1
305,5582
20,7863
224,3506
1
307,6369
20,7863
224,4915
1
309,7155
20,7863
224,6315
1
311,7941
20,7863
224,7705
1
313,8728
20,7863
224,9086
1
315,9514
20,7863
225,0458
1
318,03
20,7863
225,1822
1
320,1086
20,7863
225,3176
1
322,1873
20,7863
225,4521
B.7 Oxygen 6+
15600
15700
15800
15900
16000
16100
16200
16300
16400
16500
16600
16700
16800
16900
17000
17100
17200
17300
17400
17500
17600
17700
17800
17900
18000
18100
18200
18300
18400
18500
18600
109
1
324,2659
20,7863
225,5858
1
326,3445
20,7863
225,7186
1
328,4231
20,7863
225,8506
1
330,5018
20,7863
225,9817
1
332,5804
20,7863
226,112
1
334,659
20,7863
226,2416
1
336,7377
20,7863
226,3703
1
338,8163
20,7863
226,4982
1
340,8949
20,7863
226,6253
1
342,9735
20,7863
226,7517
1
345,0522
20,7863
226,8773
1
347,1308
20,7863
227,0021
1
349,2094
20,7863
227,1262
1
351,288
20,7863
227,2496
1
353,3667
20,7863
227,3722
1
355,4453
20,7863
227,4941
1
357,5239
20,7863
227,6153
1
359,6026
20,7863
227,7358
1
361,6812
20,7863
227,8556
1
363,7598
20,7863
227,9747
1
365,8384
20,7863
228,0932
1
367,9171
20,7863
228,211
1
369,9957
20,7863
228,3281
1
372,0743
20,7863
228,4445
1
374,153
20,7863
228,5603
1
376,2316
20,7863
228,6755
1
378,3102
20,7863
228,79
1
380,3888
20,7863
228,9039
1
382,4675
20,7863
229,0172
1
384,5461
20,7863
229,1298
1
386,6247
20,7863
229,2419
B.7 Oxygen 6+
18700
18800
18900
19000
19100
19200
19300
19400
19500
19600
19700
19800
19900
20000
20100
110
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
388,7033
390,782
392,8606
394,9392
397,0179
399,0965
401,1751
403,2537
405,3324
407,411
409,4896
411,5682
413,6469
415,7255
417,8041
20,7863
20,7863
20,7863
20,7863
20,7863
20,7863
20,7863
20,7863
20,7863
20,7863
20,7863
20,7863
20,7863
20,7863
20,7863
229,3533
229,4642
229,5745
229,6842
229,7933
229,9018
230,0098
230,1172
230,2241
230,3304
230,4362
230,5415
230,6462
230,7504
230,854
THERMODYNAMIC PROPERTIES FOR THE SEPERATE SPECIES FOR HYDROGEN 111
Appendix C
seperate species for hydrogen
This appendix contains the thermodynamic properties calculated for hydrogen.
C.1
Hydrogen
T (K)
9900
10000
10100
10200
10300
10400
10500
10600
10700
10800
10900
11000
11100
Q
2,0003
205,9693
21,0695
187,3376
2,0003
208,0782
21,1097
187,5495
2,0004
210,1914
21,1545
187,7598
2,0005
212,3093
21,2045
187,9685
2,0005
214,4325
21,26
188,1756
2,0006
216,5615
21,3216
188,3813
2,0007
218,697
21,3897
188,5856
2,0008
220,8397
21,4648
188,7887
2,0009
222,9902
21,5476
188,9907
2,0011
225,1495
21,6386
189,1915
2,0012
227,3182
21,7383
189,3914
2,0014
229,4975
21,8475
189,5904
2,0015
231,6881
21,9668
189,7887
Table C.1: Thermodynamic properties of Hydrogen
C.1 Hydrogen
11200
11300
11400
11500
11600
11700
11800
11900
12000
12100
12200
12300
12400
12500
12600
12700
12800
12900
13000
13100
13200
13300
13400
13500
13600
13700
13800
13900
14000
14100
14200
14300
14400
112
2,0017
233,8912
22,0969
189,9863
2,002
236,1078
22,2384
190,1833
2,0022
238,3393
22,3921
190,3799
2,0025
240,5867
22,5587
190,5762
2,0028
242,8515
22,7391
190,7723
2,0031
245,135
22,9339
190,9683
2,0034
247,4388
23,1441
191,1644
2,0038
249,7644
23,3705
191,3606
2,0043
252,1134
23,6138
191,5572
2,0047
254,4877
23,8751
191,7542
2,0052
256,8891
24,1551
191,9519
2,0058
259,3194
24,4547
192,1503
2,0064
261,7807
24,775
192,3496
2,0071
264,2751
25,1166
192,5499
2,0078
266,8048
25,4807
192,7515
2,0086
269,372
25,8681
192,9544
2,0094
271,9792
26,2796
193,1589
2,0103
274,6288
26,7164
193,3651
2,0113
277,3233
27,1791
193,5732
2,0123
280,0655
27,6689
193,7833
2,0135
282,858
28,1864
193,9956
2,0147
285,7037
28,7327
194,2104
2,016
288,6056
29,3086
194,4278
2,0174
291,5665
29,9149
194,6479
2,0189
294,5896
30,5524
194,871
2,0205
297,678
31,2219
195,0973
2,0223
300,8351
31,9241
195,3269
2,0241
304,064
32,6598
195,56
2,0261
307,3682
33,4295
195,7969
2,0282
310,751
34,234
196,0376
2,0304
314,2161
35,0737
196,2825
2,0328
317,767
35,9491
196,5317
2,0353
321,4072
36,8607
196,7854
C.1 Hydrogen
14500
14600
14700
14800
14900
15000
15100
15200
15300
15400
15500
15600
15700
15800
15900
16000
16100
16200
16300
16400
16500
16600
16700
16800
16900
17000
17100
17200
17300
17400
17500
17600
17700
113
2,0380
325,1403
37,8088
197,0437
2,0409
328,9701
38,7938
197,3069
2,0439
332,9003
39,8157
197,5752
2,0471
336,9345
40,8749
197,8487
2,0505
341,0765
41,9713
198,1276
2,0541
345,33
43,1049
198,4121
2,0578
349,6987
44,2754
198,7024
2,0618
354,1863
45,4828
198,9986
2,0661
358,7965
46,7267
199,3009
2,0705
363,5329
48,0065
199,6095
2,0752
368,399
49,3218
199,9244
2,0801
373,3984
50,6719
200,2459
2,0853
378,5345
52,0559
200,5741
2,0907
383,8107
53,473
200,9091
2,0964
389,2302
54,9222
201,251
2,1024
394,7961
56,4022
201,6
2,1087
400,5116
57,9119
201,9561
2,1153
406,3795
59,4498
202,3194
2,1222
412,4025
61,0144
202,6901
2,1295
418,5832
62,6042
203,0681
2,1370
424,9241
64,2172
203,4535
2,1450
431,4273
65,8517
203,8465
2,1532
438,0951
67,5057
204,2469
2,1619
444,9291
69,1771
204,6549
2,1709
451,931
70,8636
205,0705
2,1803
459,1022
72,563
205,4936
2,1901
466,4439
74,2729
205,9242
2,2003
473,9571
75,9908
206,3622
2,2109
481,6423
77,714
206,8078
2,2220
489,5
79,4401
207,2606
2,2335
497,5303
81,1661
207,7208
2,2454
505,7331
82,8895
208,1882
2,2579
514,108
84,6073
208,6627
C.1 Hydrogen
17800
17900
18000
18100
18200
18300
18400
18500
18600
18700
18800
18900
19000
19100
19200
19300
19400
19500
19600
19700
19800
19900
20000
20100
114
2,2708
2,2842
2,2981
2,3125
2,3275
2,3430
2,3590
2,3757
2,3929
2,4107
2,4291
2,4481
2,4678
2,4881
2,5090
2,5307
2,5530
2,5760
2,5997
2,6242
2,6493
2,6753
2,7020
2,7294
522,6543
531,371
540,2568
549,3102
558,5293
567,912
577,4558
587,158
597,0156
607,0255
617,1839
627,4872
637,9312
648,5117
659,2242
670,0639
681,026
692,1051
703,2961
714,5934
725,9915
737,4844
749,0665
760,7316
86,3167
88,0149
89,6989
91,3657
93,0126
94,6366
96,2349
97,8046
99,343
100,8474
102,315
103,7434
105,1302
106,4728
107,7692
109,0171
110,2146
111,3597
112,4508
113,4863
114,4648
115,3849
116,2457
117,046
209,1442
209,6325
210,1276
210,6291
211,1371
211,6512
212,1713
212,6971
213,2285
213,7653
214,307
214,8536
215,4048
215,9602
216,5196
217,0827
217,6492
218,2188
218,7912
219,3662
219,9433
220,5223
221,1028
221,6846
TABLES FOR THE CALCULATION OF THE MACH NUMBER
115
Appendix D
Tables for the calculation of the
Mach number
D.1
Table of net power and Cooling water temperature
I=300,A=12.5
I=300,A=22.5
I=400,A=12.5
I=400,A=22.5
net power
Twater
net power
Twater
net power
Twater
net power
Twater
38343,3697
31,8
39173,627
28,6
60182,645
35,7
62481,7451
35,7
38343,3697
31,8
39474,2031
28,6
60182,645
35,7
63119,4696
35,7
38343,3697
31,8
39474,2031
28,6
59325,4185
35,6
62162,8828
35,7
38343,3697
31,8
38753,3844
28,6
59990,3247
35,6
62800,6073
35,7
36590,3689
31,7
38753,3844
28,6
59103,7831
35,6
64129,0456
35,7
37786,7635
31,8
38069,6601
28,6
59108,5704
35,6
63166,1862
35,7
37868,5512
31,8
38677,415
28,6
58987,9631
35,5
63915,0769
35,7
37868,5512
31,8
39625,4448
28,6
59538,5668
35,5
63273,1706
35,7
37733,4293
31,8
39247,3404
28,6
58987,9631
35,5
63273,1706
35,7
37843,0043
31,8
38764,8702
28,6
59758,8083
35,5
61724,052
35,8
37843,0043
31,8
39216,5046
28,6
60428,0816
35,5
62585,5028
35,8
37654,0647
31,8
38980,0492
28,6
59873,9931
35,5
62585,5028
35,8
37591,3994
31,9
38603,6872
28,6
60649,717
35,5
62554,5781
35,7
37591,3994
31,9
38980,0492
28,6
59548,3243
35,5
61912,6718
35,7
38335,4293
31,9
39079,3231
28,7
58544,6923
35,5
62661,5625
35,7
38335,4293
31,9
38319,6294
28,7
59548,3243
35,5
62126,6406
35,7
37844,247
31,9
39003,3537
28,7
59548,3243
35,5
62982,5156
35,7
37844,247
31,9
38547,5375
28,7
60363,8103
35,5
61912,6718
35,7
38471,3689
32
38547,5375
28,7
59694,7223
35,5
61399,4153
35,7
38471,3689
32
38547,5375
28,7
59694,7223
35,5
61582,7781
35,7
38471,3689
32
39812,9589
28,6
59694,7223
35,5
62441,4411
35,7
Table D.1: Net power (W) and Temperature of cooling
water (°C) for different currents and amounts of argon
D.1 Table of net power and Cooling water temperature
116
38471,3689
38471,3689
37042,4597
37042,4597
37552,6393
38381,973
37867,6116
37867,6116
38553,4268
37867,6116
37778,0066
37778,0066
37347,642
38139,642
38139,642
37509,8543
37509,8543
36770,0521
36770,0521
36770,0521
37015,1889
37240,6427
37240,6427
38300,4316
38300,4316
36656,9481
32
32
31,9
31,9
31,9
32
32
32
32
32
32
32
31,9
31,9
31,9
31,9
31,9
31,9
31,9
31,9
31,9
31,9
31,9
31,8
31,8
31,9
39365,5063
39812,9589
39290,9309
39224,719
39821,3225
39448,4453
39448,4453
39514,6572
40036,6852
39173,6553
38800,7781
38800,7781
39737,8999
39210,2319
38835,6123
40325,6863
39952,8091
40623,988
40251,1109
38880,6249
38435,2632
38435,2632
39305,0502
39748,321
39157,2933
39392,0506
28,6
28,6
28,6
28,6
28,6
28,6
28,6
28,6
28,6
28,7
28,7
28,7
28,8
28,8
28,8
28,8
28,8
28,8
28,8
28,8
28,8
28,8
28,8
28,8
28,8
28,8
60363,8103
60634,2333
59971,418
59971,418
60965,641
60163,145
59602,0869
60611,9916
59714,2985
59478,6923
59478,6923
60259,295
59915,7068
60613,2363
61282,3243
60501,7217
59331,2512
60109,4145
58997,7527
59664,7498
60015,3567
59342,0869
60015,3567
59454,2985
58867,4497
59425,023
35,5
35,3
35,3
35,3
35,3
35,4
35,4
35,4
35,4
35,3
35,3
35,3
35,3
35,2
35,2
35,2
35,1
35,1
35,1
35,1
35,2
35,2
35,2
35,2
35
35
62441,4411
61797,4439
62688,5041
63541,5913
62408,6836
61331,8701
62301,0023
61331,8701
61331,8701
62798,5962
62798,5962
63338,7454
62582,5366
62526,7792
63499,0477
62310,7196
63391,0179
62310,7196
61570,6896
62542,9581
61786,7493
62754,2789
63400,367
62538,9162
62115,2648
63192,0783
35,7
35,7
35,6
35,6
35,7
35,7
35,7
35,7
35,7
35,7
35,7
35,7
35,7
35,7
35,7
35,7
35,7
35,7
35,6
35,6
35,6
35,5
35,5
35,5
35,5
35,5
117
37010,8261
37338,6139
37859,248
37338,6139
37701,947
37701,947
36516,1608
36871,9785
36626,9785
37064,3251
37501,6717
36626,9785
36991,7964
36869,5553
36869,5553
37935,1912
37935,1912
37608,4035
37608,4035
37197,3431
37638,1745
37197,3431
37902,6734
37373,6757
37373,6757
36559,9504
31,8
31,7
31,7
31,7
31,7
31,7
31,7
31,6
31,5
31,5
31,5
31,5
31,5
31,5
31,5
31,3
31,3
31,3
31,3
31,3
31,3
31,3
31,3
31,3
31,3
31,3
39909,1999
39244,2937
38881,2636
39328,7162
39328,7162
38806,6882
39346,6882
39346,6882
39719,5654
39719,5654
38402,8101
38854,4445
38402,8101
39080,2617
39124,1408
39497,018
38676,6882
39049,5654
39946,398
39575,2632
40391,7597
39797,9441
38834,9295
39204,3218
40097,2913
39656,1114
28,8
28,8
28,9
28,9
28,9
28,9
29
29
29
29
29,1
29,1
29,1
29,1
29,1
29,1
29,1
29,1
29,1
29,1
29,1
29,1
29,1
29,1
29,1
29,1
59425,023
58867,4497
58755,935
59425,023
58755,935
59982,5963
60381,5963
59824,023
59154,935
60158,567
59600,9937
59647,7068
60318,8857
60326,6729
59543,6309
60438,5361
59543,6309
59425,7229
60323,4159
59537,9345
59836,9495
60624,8703
59611,8293
60287,19
60271,433
60271,433
35
35
35
35
35
35
34,9
34,9
34,9
34,9
34,9
34,9
34,9
34,8
34,8
34,8
34,8
34,8
34,8
34,8
34,8
34,8
34,8
34,8
34,7
34,7
62115,2648
62653,6715
62274,7337
62925,0036
62057,977
62925,0036
62274,7337
61755,8543
61217,4476
61863,5357
61863,5357
62401,9424
62452,2306
61696,0218
61696,0218
62560,2605
61804,0516
62257,9011
62257,9011
63504,0775
63504,0775
62742,9899
62801,5351
61803,8686
61803,8686
61153,5987
35,5
35,5
35,5
35,5
35,5
35,5
35,5
35,4
35,4
35,4
35,4
35,4
35,4
35,4
35,4
35,4
35,4
35,4
35,4
35,4
35,4
35,4
35,4
35,3
35,3
35,3
118
36559,9504
35743,2509
35743,2509
36322,7376
36322,7376
36322,7376
37598,3124
31,3
31,2
31,2
31,2
31,2
31,2
31,1
40023,7613
39870,4286
40311,6085
39796,8986
40605,7284
39943,9586
39870,3236
29,1
29,1
29,1
29,1
29,1
29,1
29,2
59029,1162
58597,1472
59380,1893
59380,1893
58597,1472
59225,7523
59788,5529
34,7
34,6
34,6
34,6
34,6
34,6
34,6
62020,6253
62020,6253
61625,2319
60755,4175
61733,9587
61785,2335
61785,2335
35,3
35,3
35,3
35,3
35,3
35,5
35,5
119
D.2 Table of calculated Mach numbers
D.2
Table of calculated Mach numbers
Table D.2: The calculated Mach number for different
experiment conditions
M
M
M
M
300A,12.5slm 300A,22.5slm 400A,12.5slm 400A,22.5slm
0,644125454
0,791729541
0,816498325
0,924554147
0,644125454
0,797804418
0,816498325
0,933990677
0,644125454
0,797804418
0,804866395
0,919835882
0,644125454
0,78323611
0,81388716
0,929272411
0,614674839
0,78323611
0,801859474
0,948929563
0,634775096
0,769417509
0,801924423
0,934681951
0,636149038
0,781700709
0,800286225
0,945763428
0,636149038
0,80086113
0,807756233
0,93626502
0,633879142
0,793219346
0,800286225
0,93626502
0,635719878
0,783468247
0,810744236
0,913345005
0,635719878
0,79259613
0,819824228
0,92609209
0,632545906
0,787817182
0,812306942
0,92609209
0,631495434
0,780210613
0,822831142
0,925631871
0,631495434
0,787817182
0,807888612
0,916133463
0,643994343
0,78982748
0,794272396
0,927214939
0,643994343
0,774473403
0,807888612
0,919299599
0,635743004
0,788292072
0,807888612
0,931964143
0,635743004
0,779079626
0,818952263
0,916133463
0,64628027
0,779079626
0,809874785
0,90853871
0,64628027
0,779079626
0,809874785
0,911251963
0,64628027
0,804650937
0,809874785
0,923957761
0,64628027
0,795607571
0,818952263
0,923957761
0,64628027
0,804650937
0,822617125
0,914428414
0,622273832
0,794100344
0,813624792
0,927610974
0,622273832
0,79276215
0,813624792
0,94023423
0,630844305
0,804819971
0,827113292
0,923473043
0,644778509
0,797283833
0,816227889
0,90753923
0,636137755
0,797283833
0,808616065
0,921879662
0,636137755
0,798622027
0,822317349
0,90753923
120
0,64765876
0,636137755
0,634632482
0,634632482
0,627400569
0,640705325
0,640705325
0,630125563
0,630125563
0,617697675
0,617697675
0,617697675
0,621815712
0,625603095
0,625603095
0,643404142
0,643404142
0,615797648
0,621740221
0,627244468
0,635990504
0,627244468
0,633348033
0,633348033
0,61342823
0,619403354
0,615285482
0,622632335
0,629979187
0,615285482
0,621413947
0,619360456
0,619360456
0,63725724
0,63725724
0,80917262
0,791734017
0,784197841
0,784197841
0,803141858
0,792477171
0,784905742
0,815021596
0,807485383
0,821050565
0,813514354
0,785815491
0,776814295
0,776814295
0,794393541
0,803352478
0,79140723
0,796151905
0,806603998
0,793165593
0,785832275
0,794875775
0,794875775
0,784325026
0,79524293
0,79524293
0,802779218
0,802779218
0,776169869
0,785297978
0,776169869
0,789862032
0,790748885
0,798285209
0,781705296
121
0,810138429
0,806940044
0,806940044
0,817530384
0,812868965
0,822330287
0,831407699
0,820817386
0,804935863
0,815493057
0,800411352
0,809460375
0,814218948
0,805084802
0,814218948
0,806607159
0,798641638
0,806206111
0,806206111
0,798641638
0,797128742
0,806206111
0,797128742
0,813770584
0,819181762
0,811617306
0,80253996
0,81615598
0,808591525
0,809225269
0,818330983
0,818434664
0,807811358
0,81995228
0,807811358
0,90753923
0,929242653
0,929242653
0,937235342
0,926045578
0,925220525
0,939607365
0,922023451
0,938008828
0,922023451
0,911070509
0,925457309
0,914267576
0,928581625
0,938141859
0,925394881
0,919126067
0,935059789
0,919126067
0,927092927
0,921485745
0,931107857
0,918278373
0,931107857
0,921485745
0,913805246
0,905838408
0,915398615
0,915398615
0,923365452
0,92410957
0,912919901
0,912919901
0,925708095
0,914518425
0,631767671
0,631767671
0,624862441
0,632267782
0,624862441
0,636710987
0,627824578
0,627824578
0,614155151
0,614155151
0,600433637
0,600433637
0,610168154
0,610168154
0,610168154
0,789241621
0,807367754
0,799866645
0,816369083
0,804367311
0,784903555
0,792369445
0,8104175
0,80150069
0,808931365
0,805832315
0,814749124
0,80434618
0,820693664
0,80731845
122
0,806211734
0,818390478
0,807734077
0,811790728
0,822480223
0,808736586
0,817899011
0,817683277
0,817683277
0,800829162
0,794966868
0,805590124
0,805590124
0,794966868
0,803494932
0,921234064
0,921234064
0,939673814
0,939673814
0,928411953
0,92927825
0,914513129
0,914513129
0,904891071
0,917720482
0,917720482
0,911869838
0,898999176
0,91347867
0,914242559
PROGRAMS FOR MATLAB
123
Appendix E
Programs for matlab
E.1
Program for calculation of Partition function,Enthalpy,
frozen specific heat and Entropy
color
function[Q,H,Cpf,S]=calculateqhc
T=[9900:100:20100];
type atom=’h’;
[geg1,geg2]=xlsread(’H.xls’);% puts the numerical values in geg1 and the strings in geg2
ifstrcmp(type atom,’ar’)==1
M=40;
elseifstrcmp(type atom,’o’)==1
M=16;
elseifstrcmp(type atom,’h’)==1
M=1;
end
Q=zeros(length(T),1);
Qp=zeros(length(T),1);
Qpp=zeros(length(T),1);
H=zeros(length(T),1); %enthalpy
Cpf=zeros(length(T),1);%frozen thermal capacity at constant pressure
S=zeros(length(T),1);%entropy
c=1.438786;
R=8.31451;
E.1 Program for calculation of Partition function,Enthalpy, frozen specific heat and Entropy124
limit=1000;%the amount of iterations wanted
J=zeros(1,limit);
Level=zeros(1,limit);
geg3=zeros(length(geg1(:,1)),1);
iflength(geg1(1,:))==1 % if the J ’s are written in fraction they are read as string, and
geg1 will have 1 column,if J is integer geg1 will only have 2 columns
fori=1:length(geg1(:,1))
ifstrcmp(geg2(i,3),’ 1/2 ’)==1 %compare string to string
geg3(i,1)=1/2;
elseifstrcmp(geg2(i,3),’ 3/2 ’)==1
geg3(i,1)=3/2;
geg3(i,1)=5/2;
geg3(i,1)=7/2;
geg3(i,1)=9/2;
geg3(i,1)=11/2;
geg3(i,1)=13/2;
geg3(i,1)=15/2;
geg3(i,1)=17/2;
geg3(i,1)=19/2;
geg3(i,1)=21/2;
geg3(i,1)=23/2;
geg3(i,1)=25/2;
geg3(i,1)=27/2;
geg3(i,1)=29/2;
geg3(i,1)=31/2;
geg3(i,1)=33/2;
geg3(i,1)=35/2;
geg3(i,1)=37/2;
geg3(i,1)=39/2;
geg3(i,1)=41/2;
elseifstrcmp(geg2(i,3),’ ’)==1
geg3(i,1)=0;
end
end
fori=1:limit
ifi<=length(geg1(:,1))
ifisnan(geg3(i,1))==1 % is the value is not a number then we put the value to 0
geg3(i,1)=0;
end
J(1,i)=geg3(i,1);
elseifi>length(geg1(:,1))
J(1,i)=0;
end
end
forj=1:limit
ifj<=length(geg1(:,1))%the levels are written in the 4th column
ifisnan(geg1(j,1))==1
geg1(j,1)=0;
end
Level(1,j)=geg1(j,1);
elseifj>length(geg1(:,1))
Level(1,j)=0;
end
end
else% here J’s are integer and read as numbers, geg1 will only have 2 columns.
fori=1:limit
ifi<=length(geg1(:,1))
ifisnan(geg1(i,1))==1 % is the value is not a number then we put the value to 0
geg1(i,1)=0;
end
J(1,i)=geg1(i,1);
elseifi>length(geg1(:,1))
J(1,i)=0;
end
end
forj=1:limit
ifj<=length(geg1(:,2))
ifisnan(geg1(j,2))==1
geg1(j,2)=0;
end
Level(1,j)=geg1(j,2);
elseifj>length(geg1(:,2))
Level(1,j)=0;
end
end
end
forl=1:length(T)
fork=1:limit
ifk==1 | Level(1,k)∼=0 %because the NAN’s were also made 0.
Q(l)=Q(l)+(2*J(1,k)+1)*exp(-c*Level(1,k)/T(l));%formula given bij P. Krenek
Qp(l)=Qp(l)+(2*J(1,k)+1)*(c*Level(1,k)/T(l))*exp(-c*Level(1,k)/T(l));
Qpp(l)=Qpp(l)+(2*J(1,k)+1)*(c*Level(1,k)/T(l))ˆ2*exp(-c*Level(1,k)/T(l));
end
end
H(l)=R*T(l)*(2.5+Qp(l)/Q(l))/1000;
Cpf(l)=R*(2.5+(Qpp(l)/Q(l))-(Qp(l)/Q(l))ˆ2);
S(l)=R*(2.5*log(T(l))+1.5*log(M)-1.16487+log(Q(l))+(Qp(l)/Q(l)));
end
H;
E.2 Program for calculation of integrals
127
Cpf;
E.2
Program for calculation of integrals
%function [F,mflux]=calculation mass power flux
%values of current and argon flow
I=300;
F ar=22.5;
%reading in the data
load(’C:\Documents and Settings\Adinda\Mijn documenten\school\Adinda\thesis\programmatanj
%initializing the parameters
Arp=(0:10:100);%percentage of argon
temp=(500:100:49500);%temperature range in which the thermodynamic properties
were calculated
m1=zeros(11,95,15);%matrix to hold the data
enthalpy1=zeros(11,95);
rho1=zeros(11,95);
speedofsounde1=zeros(11,95);
temp1=zeros(11,95);
m2=zeros(11,79,15);%matrix to hold the data
enthalpy2=zeros(11,79);
rho2=zeros(11,79);
speedofsounde2=zeros(11,79);
temp2=zeros(11,79);
%reading in the thermodynamic properties
%T<20000K
fori=1:10
m1(i,:,:)=load(strcat(’C:\Documents and Settings\Adinda\Mijn documenten\school\Adinda\thesis
1),’.dat’));
enthalpy1(i,:)=m1(i,:,3).*10ˆ6;%put MJ/kg to J/kg
rho1(i,:)=m1(i,:,9).*(10ˆ(-3));% g/m3 to kg/m3
speedofsounde1(i,:)=m1(i,:,15);%m/s
temp1=m1(i,:,1);
end
m1(11,:,:)=load(strcat(’C:\Documents and Settings\Adinda\Mijn documenten\school\Adinda\thes
128
enthalpy1(11,:)=m1(11,:,3).*10ˆ6;%put MJ/kg to J/kg
rho1(11,:)=m1(11,:,9).*(10ˆ(-3));% g/m3 to kg/m3
speedofsounde1(11,:)=m1(11,:,15);%m/s
temp1=m1(11,:,1);
%T>20000K
fori=1:10
m2(i,:,:)=load(strcat(’C:\Documents and Settings\Adinda\Mijn documenten\school\Adinda\thesis
1),’A.dat’));
enthalpy2(i,:)=m2(i,:,3).*10ˆ6;%put MJ/kg to J/kg
rho2(i,:)=m2(i,:,9).*(10ˆ(-3));% g/m3 to kg/m3
speedofsounde2(i,:)=m2(i,:,15);%m/s
temp2=m2(i,:,1);
end
m2(11,:,:)=load(strcat(’C:\Documents and Settings\Adinda\Mijn documenten\school\Adinda\thes
enthalpy2(11,:)=m2(11,:,3).*10ˆ6;%put MJ/kg to J/kg
rho2(11,:)=m2(11,:,9).*(10ˆ(-3));% g/m3 to kg/m3
speedofsounde2(11,:)=m2(11,:,15);%m/s
temp2=m2(11,:,1);
par=eval(strcat(’T’,int2str(I),’Ar’,int2str(F ar+0.5),’z2’));
par1=eval(strcat(’Arp’,int2str(I),’Ar’,int2str(F ar+0.5)));
r=zeros(length(par(:,1)),1);
radius=zeros(1,length(par(:,1)));
T=zeros(1,length(par(:,1)));
Ar=zeros(1,length(par1(:,1)));
fori=1:length(par(:,1))
radius(1,i)=par(i,1)*10ˆ(-3);% mm to m
r(i,1)=par(i,1);
T(1,i)=par(i,2);
Ar(1,i)=par1(i,2);
end
iflength(radius(1,:))>35;
forj=36:length(radius(1,:))
radius(1,j)=NaN;
T(1,j)=NaN;
Ar(1,j)=NaN;
end
129
end
l = find(∼isnan(radius));
radius = radius(1,l);
i = find(∼isnan(T));
T = T(1,i);
k = find(∼isnan(Ar));
Ar = Ar(1,k);
%interpolation
h int1=interp2(temp1,Arp,enthalpy1,T,Ar);
rho int1=interp2(temp1,Arp,rho1,T,Ar);
speedofsounde int1=interp2(temp1,Arp,speedofsounde1,T,Ar);
h int2=interp2(temp2,Arp,enthalpy2,T,Ar);
rho int2=interp2(temp2,Arp,rho2,T,Ar);
speedofsounde int2=interp2(temp2,Arp,speedofsounde2,T,Ar);
%integration
int1=0;
int2=0;
fori=1:34
int1=int1+2*pi*(radius(1,i+1)-radius(1,i))*(rho int1(i)*(speedofsounde int1(i))*radius(1,i)+radius(
int2=int2+2*pi*(radius(1,i+1)-radius(1,i))*(radius(1,i)*rho int1(i)*(speedofsounde int1(i))
*h int1(i)+radius(1,i+1)*rho int1(i+1)*(speedofsounde int1(i+1))*h int1(i+1))/2;
end
%plotting the enthalpy and the density of the plasma
figure
subplot(2,2,1)
plot(radius,h int1,’r’,radius,h int2,’g’)
xlabel(’radius [m]’)
ylabel(’interpolated enthalpy [J/kg]’)
subplot(2,2,2)
plot(T,h int1,’r’,T,h int2,’g’)
xlabel(’Temperature [K]’)
ylabel(’interpolated enthalpy [J/kg]’)
subplot(2,2,3)
plot(radius,rho int2)
xlabel(’radius [m]’)
ylabel(’interpolated density [kg/m3]’)
subplot(2,2,4)
plot(T,rho int2)
xlabel(’Temperature [K]’)
ylabel(’interpolated density [kg/m3]’)
130
BIBLIOGRAPHY
131
Bibliography
[1] AS CR M. Hrabovsky, Insitute of plasma physics. Dc arc thermal plasmas-generation,
diagnostics and applications. In Proceedings of the 2nd International Workshop on
Cold Atmospheric Pressure Plasmas: Sources and Applications (CAPPSA 2005),
2005.
[2] M. Hrabovsky. Electric arcs in generators of thermal plasma. In Proceedings of 11th
Symposium on Physics of Switching Arc., 1994.
[3] M Konrad M Hlina T. Kavka G. van Oost E. Beeckman J. Verstraeten J. Ledecky
E. Balabanove M. Hrabovsky, V Kopecky. Gasification of bio mass in water-stabilized
dc arc plasma. In Proceedings of 17th International Symposium on Plasma Chemistry,
2005.
[4] J. Pieters M. Tendler J. Verstraeten Department of applied physics Ghent University
Insitute of plasma physics G. van Oost, M. Hrabovsky. Novel project on total plasma
reduction of waste. In Problems of Atomic Science and Technology, 2005.
[5] FAUCHAIS Pierre BOULOS Maher I. Thermal plasmas: fundamentals and applications vol 1. BERTRAMS PRINT ON DE, 1994.
[6] G. Van Oost. Plasmafysica: Deel A Hogetemperatuursfysica. Ugent Universiteit, 2005.
[7] L.A Kennedy A.Fridman. Plasma Physics and Engineering. Taylos Francis, 2004.
[8] R.P.W Scott. Gas chromatography. http://www.chromatography-online.org/GC/
Introduction/rs1.html, WWW.
[9] A Galassi M Piselli M Sciascia R. Benocci, P Esena. Study of the thermal plasma
etching at atmospheric pressure on silica rods. Journal of Physics D: Applied Physics,
37(8):1206–1213, April 2004.
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[10] Université de Sherbrooke Department of chemical engineering Maher I. Boulos, Plasma
technology research centre. Diagnostics of thermal plasmas. Frontiers in Low Temperature Plasma Diagnostics III, pages 7–8, February 1999.
[11] E. Siores MF. Elchinger C.A Destefani, A.B Murphy. Enthalpy probe diagnostics
of an atmospheric pressure argon microwave induced plasma. IEEE transactions on
plasma science, 30(4):1587–1591, 2002.
[12] M. Hrabovsky. Generation of thermal plasmas in liquid-stabilized and hybrid dc-arc
torches. Pure and Applied Chemistry, 74(3):429–434, July 2001.
[13] V. Sember T Kavka O Chumack M Konrad M. Hrabovsky, V Kopecky. Properties of hybrid water/gas dc arcplasma torch. IEEE Transactions on Plasma Science,
34(4):1566– 1575, August 2006.
[14] V Kopecky V. Sember M. Hrabovsky, M Konrad. Properties of water stabilized plasma
torches. Solonenko, O.P. (ed.): Thermal Plasma Torches and Technologies, 1:240–255,
1999.
[15] B Alexandrovich Ntishchenko R Piejak, V Godyak. Surface temperature and thermal
balance of probes immersed in high-density plasma. Plasma Sources Sci. Technol.,
7(4):590–598, August 1998.
[16] C. Katsonis B. Pateyron. Proprietes thermodynamiques et coefficients de transport.
Plasma Sources Sci. Technol., 7(4):590–598, August 1998.
[17] M.Hrabovsky P. Krenek. H20-ar plasma property functions for modeling of hybrid
water-gas plasma torch. Plasma Sources Sci. Technol., 7(4):590–598, August 2007.
[18] Tetyana Kavka. Study of thermal plasma jets, generated by DC arc plasma torches
used in plasma spraying applications. PhD thesis, Charles University, Prague, 2006.
[19] Wikipedia. Wikipedia, the free encyclopedia. http://en.wikipedia.org/, WWW.
[20] NIST. Nist data base. http://physics.nist.gov, WWW.
LIST OF FIGURES
133
List of Figures
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
2.1
2.2
2.3
2.4
2.5
potential distribution along the arc . . . . . . . . . . . . . . . . . . . . . .
voltage (Volt) and current (Ampere) of the arc in a channel 1.smaller diameter; 2. larger diameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
: Scheme of the Gas stabilized torch . . . . . . . . . . . . . . . . . . . . . .
: comparison of power versus mass flowrate between gas and water- stabilized torches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Scheme of hybrid torch . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
illustration of mass balance for Argon . . . . . . . . . . . . . . . . . . . . .
Composition of gas containing H vs temperature . . . . . . . . . . . . . . .
composition of Argon gas for temperature range 10000K to 50000K . . . .
5
6
9
11
12
15
17
22
24
25
26
26
2.9
2.10
2.11
2.12
2.13
: Scheme of the reactor system . . . . . . . . . . . . . . . . . . . . . . . . .
: Input and output for the reactor system . . . . . . . . . . . . . . . . . .
Detailed schematic of measuring points in the system . . . . . . . . . . . .
Composition of the syngas in Molar fraction in relation to the Temperature
: Enthalpy flux (right) and density(left) vs the radius for the water stabilized
torch and the hybrid torch measured at the nozzle . . . . . . . . . . . . . .
Schematic of the enthalpy probe system . . . . . . . . . . . . . . . . . . . .
Schematic of tare and sample tests for enthalpy probe . . . . . . . . . . . .
: Temperature range for different diagnostic measures (left); enthalpy probe
in plasma (right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
schematic of a thermocouple . . . . . . . . . . . . . . . . . . . . . . . . . .
: Laminar flow and turbulent flow velocity profiles in a tube . . . . . . . .
: schematic of the quadrupole mass spectrometer . . . . . . . . . . . . . .
: schematic of the inner workings of the mass spectrometer . . . . . . . . .
: Schematic of the gas chromatrograph . . . . . . . . . . . . . . . . . . . .
3.1
The current-voltage levels for several argon inputs . . . . . . . . . . . . . .
39
2.6
2.7
2.8
28
29
30
30
31
34
35
36
37
LIST OF FIGURES
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
3.14
3.15
3.16
3.17
3.18
3.19
3.20
3.21
3.22
The arc power (above) and the net power(below) vs the argon inpute for
several currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Loss total enthalpy and the total power of the arc (J) vs the current for
Ar=12.5 slm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ar=17.5 slm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ar=22.5 slm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Efficiency of the water-stabilized part of the arc . . . . . . . . . . . . . . .
Efficiency of the arc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Losses to the stabilizing water vs the amount of argon for different currents
molar fraction of argon for different currents and argon . . . . . . . . . . .
Temperature profile for different currents and amounts of argon input . . .
Thermodynamic properties of oxygen vs temperature . . . . . . . . . . . .
Thermodynamic properties of Hydrogen vs temperature . . . . . . . . . . .
Thermodynamic properties of argon vs temperature . . . . . . . . . . . . .
Composition of pure steam for temperatures up to 10000K . . . . . . . . .
Composition for pure steam for temperatures from 10000K up to 50000K .
Composition for 50% Argon for temperatures up to 20000K . . . . . . . . .
Composition for 50% Argon for temperatures from 10000K up to 50000K .
Enthalpy (left) and Density vs the temperature for I=300A and AR=22.5
slm for interp1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Enthalphy and Density profiles for I=300A and Ar=22.5 slm . . . . . . . .
Mach number vs current for different amounts of argon . . . . . . . . . . .
Equilibrium speed of sound for different amounts of argon . . . . . . . . .
Velocity (m/s] profile for different experiment conditions . . . . . . . . . .
134
39
39
40
40
41
42
42
43
44
46
46
47
49
49
50
50
51
52
53
54
55
LIST OF TABLES
135
List of Tables
3.1
3.2
3.3
3.4
3.5
3.6
3.7
A.1
A.1
A.1
A.2
A.2
A.2
A.2
A.3
A.3
A.3
A.4
A.4
A.4
A.4
A.5
A.5
A.5
Calculated intergrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table with calculated Mach numbers . . . . . . . . . . . . . . . . . . . . .
Power and Mass flux for the hybrid torch . . . . . . . . . . . . . . . . . . .
Comparison of characteristics for the water-stabilized and hybrid torch . .
Remaining percentage of argon provided by dr Kavka . . . . . . . . . . . .
Remaining percentage of argon and net power calculated using the measured
values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
mass fraction of Argon present in the hybrid torch jet: row 1: measured
values, row 2: calculated with 3.5, row 3: calculated with 3.6 . . . . . . . .
51
52
54
56
58
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
properties
properties
properties
properties
properties
properties
properties
properties
properties
properties
properties
properties
properties
properties
properties
properties
properties
of
of
of
of
of
of
of
of
of
of
of
of
of
of
of
of
of
Argon
Argon
Argon
Argon
Argon
Argon
Argon
Argon
Argon
Argon
Argon
Argon
Argon
Argon
Argon
Argon
Argon
. .
. .
. .
1+
1+
1+
1+
2+
2+
2+
3+
3+
3+
3+
4+
4+
4+
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59
59
LIST OF TABLES
136
A.6
A.6
A.6
A.6
A.7
A.7
A.7
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
properties
properties
properties
properties
properties
properties
properties
of
of
of
of
of
of
of
Argon
Argon
Argon
Argon
Argon
Argon
Argon
5+
5+
5+
5+
6+
6+
6+
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78
79
80
81
82
83
84
B.1
B.1
B.1
B.2
B.2
B.2
B.2
B.3
B.3
B.3
B.4
B.4
B.4
B.4
B.5
B.5
B.5
B.6
B.6
B.6
B.6
B.7
B.7
B.7
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
Thermodynamic
properties
properties
properties
properties
properties
properties
properties
properties
properties
properties
properties
properties
properties
properties
properties
properties
properties
properties
properties
properties
properties
properties
properties
properties
of
of
of
of
of
of
of
of
of
of
of
of
of
of
of
of
of
of
of
of
of
of
of
of
Oxygen . . .
Oxygen . . .
Oxygen . . .
Oxygen 1+
Oxygen 1+
Oxygen 1+
Oxygen 1+
Oxygen 2+
Oxygen 2+
Oxygen 2+
Oxygen 3+
Oxygen 3+
Oxygen 3+
Oxygen 3+
Oxygen 4+
Oxygen 4+
Oxygen 4+
Oxygen 5+
Oxygen 5+
Oxygen 5+
Oxygen 5+
Oxygen 6+
Oxygen 6+
Oxygen 6+
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86
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C.1 Thermodynamic properties of Hydrogen . . . . . . . . . . . . . . . . . . . 111
LIST OF TABLES
137
D.1 Net power and Temperature of cooling water . . . . . . . . . . . . . . . . . 116
D.2 The calculated Mach number for different experiment conditions . . . . . . 120

Measurement and calculation of thermodynamic properties of the

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