Measurement and calculation of thermodynamic properties of the
Transkript
Measurement and calculation of thermodynamic properties of the
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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 2 4 5 8 13 14 14 16 . . . . . . . . . 23 23 26 27 28 31 31 33 35 36 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . for argon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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+ . . . . . . . . . . . . . . . . . . species . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . for oxygen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 38 43 45 48 56 59 . . . . . . . 61 61 64 68 71 75 78 82 . . . . . . . 86 86 89 93 96 100 103 107 C Thermodynamic properties for the seperate species for hydrogen 111 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 1.3 How plasma is made : The plasma torch 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 1.3 How plasma is made : The plasma torch 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 1.3 How plasma is made : The plasma torch 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 How plasma is made : The plasma torch 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. 1.3 How plasma is made : The plasma torch 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 1.3 How plasma is made : The plasma torch 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 1.3 How plasma is made : The plasma torch 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 1.3 How plasma is made : The plasma torch 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) 1.4 Thermodynamic properties of plasma 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 1.4 Thermodynamic properties of plasma 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 1.4 Thermodynamic properties of plasma 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 2πrρchdr + (λ + Cw (TB − Twater )) 2πrρcdr 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. 1.4 Thermodynamic properties of plasma 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. 1.4 Thermodynamic properties of plasma 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 1.4 Thermodynamic properties of plasma 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 1.4 Thermodynamic properties of plasma 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) 1.4 Thermodynamic properties of plasma 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− 1.4 Thermodynamic properties of plasma 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. 2.2 Diagnostics for thermal 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 Diagnostics for thermal plasmas: 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. 2.2 Diagnostics for thermal plasmas: 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 2.2 Diagnostics for thermal plasmas: 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 Diagnostics for thermal plasmas: 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 2.2 Diagnostics for thermal plasmas: 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 2.2 Diagnostics for thermal plasmas: 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 2.2 Diagnostics for thermal plasmas: 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. 2.2 Diagnostics for thermal plasmas: 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= 2.2 Diagnostics for thermal plasmas: 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 2.2 Diagnostics for thermal plasmas: 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 3.1 Measured results 40 Figure 3.4: Loss total enthalpy and the total power of the arc (J) vs the current for Ar=17.5 slm Figure 3.5: Loss total enthalpy and the total power of the arc (J) vs the current for Ar=22.5 slm 3.1 Measured results 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. 3.1 Measured results 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 Calculation of the thermodynamic properties of the separate components 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. 3.2 Calculation of the thermodynamic properties of the separate components 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. 3.3 Calculation of the thermodynamic properties of the plasma Figure 3.11: Thermodynamic properties of oxygen vs temperature Figure 3.12: Thermodynamic properties of Hydrogen vs temperature 46 3.3 Calculation of the thermodynamic properties of the plasma 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- 3.4 Program for the Calculation of the Mass flux and the Energy flux 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 3.4 Program for the Calculation of the Mass flux and the Energy flux 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 3.4 Program for the Calculation of the Mass flux and the Energy flux 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 3.4 Program for the Calculation of the Mass flux and the Energy flux 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) 2πrρchdr + (λ + Cw (TB − Twater )) 2πrρcdr 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 3.4 Program for the Calculation of the Mass flux and the Energy flux 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. 3.4 Program for the Calculation of the Mass flux and the Energy flux 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 3.4 Program for the Calculation of the Mass flux and the Energy flux 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. 3.5 Calculation of the amount of Argon present in the plasma jet 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) 3.5 Calculation of the amount of Argon present in the plasma jet 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 Table A.1: Thermodynamic properties of Argon Continued on next page 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 Table A.1: Thermodynamic properties of Argon Continued on next page 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 H (MJ/kg) Cpf (kJ/kgK) S (MJ/kg) 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+ Continued on next page 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 Table A.2: Thermodynamic properties of Argon 1+ Continued on next page 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 Table A.2: Thermodynamic properties of Argon 1+ Continued on next page 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 Table A.2: Thermodynamic properties of Argon 1+ Continued on next page 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 H (MJ/kg) Cpf (kJ/kgK) S (MJ/kg) 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 Table A.3: Thermodynamic properties of Argon 2+ Continued on next page 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 Table A.3: Thermodynamic properties of Argon 2+ Continued on next page 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 Table A.3: Thermodynamic properties of Argon 2+ Continued on next page 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 H (MJ/kg) Cpf (kJ/kgK) S (MJ/kg) 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 Table A.4: Thermodynamic properties of Argon 3+ Continued on next page 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 Table A.4: Thermodynamic properties of Argon 3+ Continued on next page 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 Table A.4: Thermodynamic properties of Argon 3+ Continued on next page 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 Table A.4: Thermodynamic properties of Argon 3+ Continued on next page 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 H (MJ/kg) Cpf (kJ/kgK) S (MJ/kg) 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 Table A.5: Thermodynamic properties of Argon 4+ Continued on next page 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 Table A.5: Thermodynamic properties of Argon 4+ Continued on next page 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 Table A.5: Thermodynamic properties of Argon 4+ Continued on next page 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 H (MJ/kg) Cpf (kJ/kgK) S (MJ/kg) 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 Table A.6: Thermodynamic properties of Argon 5+ Continued on next page 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 Table A.6: Thermodynamic properties of Argon 5+ Continued on next page 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 Table A.6: Thermodynamic properties of Argon 5+ Continued on next page 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 Table A.6: Thermodynamic properties of Argon 5+ Continued on next page 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 H (MJ/kg) Cpf (kJ/kgK) S (MJ/kg) 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 Table A.7: Thermodynamic properties of Argon 6+ Continued on next page 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 Table A.7: Thermodynamic properties of Argon 6+ Continued on next page 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 Table A.7: Thermodynamic properties of Argon 6+ Continued on next page 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 Thermodynamic properties for the 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 H (MJ/kg) Cpf (kJ/kgK) S (MJ/kg) 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 Continued on next page 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 Table B.1: Thermodynamic properties of Oxygen Continued on next page 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 Table B.1: Thermodynamic properties of Oxygen Continued on next page 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 H (MJ/kg) Cpf (kJ/kgK) S (MJ/kg) 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+ Continued on next page 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 Table B.2: Thermodynamic properties of Oxygen 1+ Continued on next page 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 Table B.2: Thermodynamic properties of Oxygen 1+ Continued on next page 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 Table B.2: Thermodynamic properties of Oxygen 1+ Continued on next page 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 H (MJ/kg) Cpf (kJ/kgK) S (MJ/kg) 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 Table B.3: Thermodynamic properties of Oxygen 2+ Continued on next page 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 Table B.3: Thermodynamic properties of Oxygen 2+ Continued on next page 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 Table B.3: Thermodynamic properties of Oxygen 2+ Continued on next page 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 H (MJ/kg) Cpf (kJ/kgK) S (MJ/kg) 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 Table B.4: Thermodynamic properties of Oxygen 3+ Continued on next page 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 Table B.4: Thermodynamic properties of Oxygen 3+ Continued on next page 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 Table B.4: Thermodynamic properties of Oxygen 3+ Continued on next page 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 Table B.4: Thermodynamic properties of Oxygen 3+ Continued on next page 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 H (MJ/kg) Cpf (kJ/kgK) S (MJ/kg) 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 Table B.5: Thermodynamic properties of Oxygen 4+ Continued on next page 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 Table B.5: Thermodynamic properties of Oxygen 4+ Continued on next page 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 Table B.5: Thermodynamic properties of Oxygen 4+ Continued on next page 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 H (MJ/kg) Cpf (kJ/kgK) S (MJ/kg) 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 Table B.6: Thermodynamic properties of Oxygen 5+ Continued on next page 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 Table B.6: Thermodynamic properties of Oxygen 5+ Continued on next page 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 Table B.6: Thermodynamic properties of Oxygen 5+ Continued on next page 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 Table B.6: Thermodynamic properties of Oxygen 5+ Continued on next page 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 H (MJ/kg) Cpf (kJ/kgK) S (MJ/kg) 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 Table B.7: Thermodynamic properties of Oxygen 6+ Continued on next page 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 Table B.7: Thermodynamic properties of Oxygen 6+ Continued on next page 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 Table B.7: Thermodynamic properties of Oxygen 6+ Continued on next page 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 Thermodynamic properties for the 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 H (MJ/kg) Cpf (kJ/kgK) S (MJ/kg) 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 Continued on next page 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 Table C.1: Thermodynamic properties of Hydrogen Continued on next page 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 Table C.1: Thermodynamic properties of Hydrogen Continued on next page 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 D.1 Table of net power and Cooling water temperature 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 D.1 Table of net power and Cooling water temperature 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 D.1 Table of net power and Cooling water temperature 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 D.2 Table of calculated Mach numbers 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 D.2 Table of calculated Mach numbers 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; elseifstrcmp(geg2(i,3),’ 5/2 ’)==1 geg3(i,1)=5/2; elseifstrcmp(geg2(i,3),’ 7/2 ’)==1 geg3(i,1)=7/2; elseifstrcmp(geg2(i,3),’ 9/2 ’)==1 geg3(i,1)=9/2; elseifstrcmp(geg2(i,3),’ 11/2 ’)==1 geg3(i,1)=11/2; elseifstrcmp(geg2(i,3),’ 13/2 ’)==1 geg3(i,1)=13/2; elseifstrcmp(geg2(i,3),’ 15/2 ’)==1 geg3(i,1)=15/2; elseifstrcmp(geg2(i,3),’ 17/2 ’)==1 geg3(i,1)=17/2; elseifstrcmp(geg2(i,3),’ 19/2 ’)==1 geg3(i,1)=19/2; elseifstrcmp(geg2(i,3),’ 21/2 ’)==1 geg3(i,1)=21/2; elseifstrcmp(geg2(i,3),’ 23/2 ’)==1 geg3(i,1)=23/2; elseifstrcmp(geg2(i,3),’ 25/2 ’)==1 geg3(i,1)=25/2; elseifstrcmp(geg2(i,3),’ 27/2 ’)==1 geg3(i,1)=27/2; elseifstrcmp(geg2(i,3),’ 29/2 ’)==1 E.1 Program for calculation of Partition function,Enthalpy, frozen specific heat and Entropy125 geg3(i,1)=29/2; elseifstrcmp(geg2(i,3),’ 31/2 ’)==1 geg3(i,1)=31/2; elseifstrcmp(geg2(i,3),’ 33/2 ’)==1 geg3(i,1)=33/2; elseifstrcmp(geg2(i,3),’ 35/2 ’)==1 geg3(i,1)=35/2; elseifstrcmp(geg2(i,3),’ 37/2 ’)==1 geg3(i,1)=37/2; elseifstrcmp(geg2(i,3),’ 39/2 ’)==1 geg3(i,1)=39/2; elseifstrcmp(geg2(i,3),’ 41/2 ’)==1 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 E.1 Program for calculation of Partition function,Enthalpy, frozen specific heat and Entropy126 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 E.2 Program for calculation of integrals 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 E.2 Program for calculation of integrals 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]’) E.2 Program for calculation of integrals 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. BIBLIOGRAPHY 132 [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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Loss total enthalpy and the total power of the arc (J) vs the current for Ar=17.5 slm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Loss total enthalpy and the total power of the arc (J) vs the current for 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+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 C.1 Thermodynamic properties of Hydrogen . . . . . . . . . . . . . . . . . . . 111 C.1 Thermodynamic properties of Hydrogen . . . . . . . . . . . . . . . . . . . 112 C.1 Thermodynamic properties of Hydrogen . . . . . . . . . . . . . . . . . . . 113 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