Calculation of thermodynamic properties and

Download PDF
2 downloads 0 Views 3MB Size Report
Comment
Oct 10, 2017 - The thermodynamic properties and transport coefficients of C5F10O-CO2 gas mixtures, which are .... The following neutral and charged species are main spe- ... the mass density q, enthalpy h and specific heat cp can be.
Calculation of thermodynamic properties and transport coefficients of C5F10O-CO2 thermal plasmas Xingwen Li, Xiaoxue Guo, Anthony B. Murphy, Hu Zhao, Jian Wu, and Ze Guo

Citation: Journal of Applied Physics 122, 143302 (2017); doi: 10.1063/1.5006635 View online: http://dx.doi.org/10.1063/1.5006635 View Table of Contents: http://aip.scitation.org/toc/jap/122/14 Published by the American Institute of Physics

JOURNAL OF APPLIED PHYSICS 122, 143302 (2017)

Calculation of thermodynamic properties and transport coefficients of C5F10O-CO2 thermal plasmas Xingwen Li,1,a) Xiaoxue Guo,1 Anthony B. Murphy,2 Hu Zhao,3 Jian Wu,1 and Ze Guo1 1

State Key Laboratory of Electrical Insulation and Power Equipment, Xi’an Jiaotong University, No. 28 Xianning West Road, Xi’an, Shaanxi Province 710049, China 2 CSIRO Manufacturing, P.O. Box 218, Lindfield, New South Wales 2070, Australia 3 School of Automation, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, China

(Received 8 May 2017; accepted 26 September 2017; published online 10 October 2017) The thermodynamic properties and transport coefficients of C5F10O-CO2 gas mixtures, which are being considered as substitutes for SF6 in circuit breaker applications, are calculated for the temperature range from 300 K to 30 000 K and the pressure range from 0.05 MPa to 1.6 MPa. Special attention is paid on investigating the evolution of thermophysical properties of C5F10OCO2 mixtures with different mixing ratios and with different pressures; both the mixing ratio and pressure significantly affect the properties. This is explained mainly in terms of the changes in the temperatures at which the dissociation and ionization reactions take place. Comparisons of different thermophysical properties of C5F10O-CO2 mixtures with those of SF6 are also carried out. It is found that most of the thermophysical properties of the C5F10O-CO2 mixtures, such as thermal conductivity, viscosity, and electrical conductivity, become closer to those of SF6 as the C5F10O concentration increases. The composition and thermophysical properties of pure C5F10O in the temperature range from 300 K to 2000 K based on the decomposition pathway are also given. The calculation results provide a basis for further study of the insulation and arc-quenching capability of C5F10O-CO2 gas mixtures as substitutes for SF6. Published by AIP Publishing. https://doi.org/10.1063/1.5006635

I. INTRODUCTION

Pure SF6 has been widely used in medium- and highvoltage electrical equipment for several decades. In recent years, the environmental impact, in particular, that related to the high global warming potential (GWP), of SF6 has caused extensive concerns. It is necessary to find technically- and economically-viable alternatives to SF6. A large amount of efforts have been expended in the search for potential SF6 substitutes. Previous research has mainly focused on the use of pure gases and gas mixtures, such as CO2,1,2 N2,1,2 CF3I,3–5 SF6/N2,6–8 SF6/CO2,9 c-C4F8/ N2,10 CF3I/CO2,5 and CF3I/N2.4,5,10 Recently, attention was drawn to some new alternatives, such as the family of fluoroketones (CnF2nO, mainly C5F10O and C6F12O). These compounds have some advantages over pure SF6. First, the dielectric strengths of C5F10O and C6F12O are about 2 and 2.5 times that of pure SF6, respectively.11 Second, C5F10O and C6F12O both have a global warming potential of 1, which is much lower than SF6. However, at standard atmospheric pressure, the liquefaction temperatures of C5F10O and C6F12O are about 24  C and 49  C,11 respectively, which are much higher than that of SF6. For this reason, they cannot be used in pure form as an insulating or interrupting medium. It is expected that this problem can be solved by adding a certain amount of a buffer gas with a relatively low liquefaction temperature. C5F10O, C6F12O, and their mixtures with air and CO2 have been closely examined internationally. McLinden a)

Email: [email protected]

0021-8979/2017/122(14)/143302/11/$30.00

et al.12 reported the comprehensive thermodynamic property measurements of 1,1,1,2,2,4,5,5,5-nonafluoro-4-(trifluoromethyl)-3-pentanone (with the empirical formula C6F12O). Preve et al.13 gave an overview of the main properties, such as toxicity, stability, and dielectric properties, of the possible alternatives to SF6, including families of fluoroketones. The studies show that some of the most interesting candidates could be used as a dielectric medium. The dielectric performance of C5F10O and its mixtures with air was analyzed by Simka and Ranjan.14 The results indicated that the dielectric strength of C5F10O and its mixtures was comparable to that of SF6. Mantilla et al.11 presented the insulation performance of gas mixtures composed of fluoroketones (C5F10O, C6F12O) with technical air or CO2. The studies mentioned above are focused on the dielectric properties of the new potential SF6 substitutes. However, knowledge of the thermophysical properties of CnF2nO and its mixtures is the basis for understanding the thermal plasma behavior and applying the new potential SF6 substitutes to the high-voltage electrical apparatus. The present paper addresses the thermophysical properties of C5F10O and its mixtures with CO2 in conditions relevant to the arcing period and post-arc period in high-voltage circuit breakers, which normally corresponds to the temperature range from 30 000 K down to 300 K and pressures above atmospheric. In this paper, the composition of C5F10O-CO2 mixtures for the temperature range from 300 K to 30 000 K and the pressure range from 0.05 MPa to 1.6 MPa is calculated under the assumption of the local thermodynamic equilibrium (LTE). The assumption of LTE means that the chemical

122, 143302-1

Published by AIP Publishing.

143302-2

Li et al.

equilibrium composition is obtained. This corresponds to that during arcing and the post-arc period of circuit breaker operation, but not to the composition during the initial decomposition of C5F10O. Using the composition data, the mass density, enthalpy, and specific heat of C5F10O-CO2 mixtures are then obtained based on the definitions of these thermodynamic properties. The electrical conductivity, thermal conductivity, and viscosity of C5F10O-CO2 mixtures are then calculated using the Chapman–Enskog method of solution of the Boltzmann equation. The influence of mixing ratios and gas pressure on the thermodynamic properties and transport coefficients is analyzed in detail. In addition, this paper also compares the thermophysical properties of C5F10O-CO2 mixtures to those of pure SF6. Finally, the decomposition of pure C5F10O in the temperature range from 300 K to 2000 K is calculated using the mass action law, and the associated thermophysical properties are also obtained. II. PLASMA COMPOSITION AND COLLISION INTEGRALS A. Plasma composition

The first stage in the determination of the thermophysical properties of a thermal plasma is the calculation of the composition. Calculations were performed assuming local thermodynamic equilibrium in the temperature range from 300 K to 30 000 K, for pressures between 0.05 MPa and 1.6 MPa; these conditions are appropriate to the arcing period and the postarc period in high-voltage circuit breakers.

J. Appl. Phys. 122, 143302 (2017)

The following neutral and charged species are main species that have to be taken into consideration within the relevant temperature range: C2F6, C2F4, C2F2, CF2O, C3O2, CO2, O2, CO, CF, CF2, CF3, CF4, C5, C4, C3, C2, C, F, O, Cþ, Fþ, Oþ, C2þ, F2þ, O2þ, and e–.The plasma composition is determined using the minimization of Gibbs free energy, the conservation of pressure and the requirement of electrical neutrality.15,16 The data needed for the calculation of internal partition functions and the standard enthalpy of formation were obtained from Moore17,18 and the NIST–JANAF Thermochemical Tables.19 Figure 1 shows the composition of a plasma formed from 90% CO2 and10% C5F10O at 0.8 MPa. The mixing ratio refers to the initial ratio of mass fractions of gases. It can be concluded that C5F10O is not reformed in the post-arc period when the temperature decreases down to room temperature. In 90% CO2 and 10% C5F10O mixtures, CF2O, CO2, CO, and CF4 are formed with the decreasing temperature, while C2F6, C3O2, CO, CF4, and C5 are formed in 10% CO2 and 90% C5F10O mixtures. Above 5000 K, C5F10O molecules decompose into small molecules, CO2, O2, CO, CF, and C2, and atoms, C, F, and O. As the temperature rises further, significant ionization occurs from about 6700 K. Carbon atoms are first ionized, followed by oxygen atoms and then fluorine atoms; this is a consequence of their different first ionization potentials (11.28 eV for C, 13.64 eV for O, and 17.45 eV for F). B. Collision integrals

Another prerequisite for the calculation of the transport coefficients is the values of the collision integrals between

FIG. 1. Composition of the C5F10O-CO2 plasma as a function of temperature at 0.4 MPa; (a) 90% CO2 and 10% C5F10O (300 K–5000 K), (b) 90% CO2 and 10% C5F10O (5000 K–30 000 K), (c) 10% CO2 and 90% C5F10O (300 K–5000 K), and (d) 10% CO2 and 90% C5F10O (5000 K–30 000 K).

143302-3

Li et al.

J. Appl. Phys. 122, 143302 (2017)

different species, which are averages over a Maxwellian distribution of the collision cross-section for each pair of species. The collision integral for an interaction between species i and j is defined as follows:20 ðl;sÞ Xij

¼

2pkTij lij

!12 1 ð1 ð

2

ec c2sþ3  ð1  cosl vÞbdbdc; (1)

0 0

where subscripts i and j represent species i and j, v, and b are, respectively, the deflection angle and the impact parameter, the reduced relative speed c is given by  1=2 c ¼ lij =2kB T g;

(2)

where g is the relative speed of the species i and j, and the reduced mass lij is defined as lij ¼ mi mj =ðmi þ mj Þ:

FIG. 3. Enthalpy of the plasma formed from 90% CO2 and 10% C5F10O as a function of temperature for different pressures.

(3)

The required collision integrals for the interactions between different species present were calculated using the methods given by Murphy21 and Zhang et al.,22 with the C–C collision integral replaced by the values given by Stallcop et al.23 III. THERMODYNAMIC PROPERTIES

Once the composition and partition functions are known, the mass density q, enthalpy h and specific heat cp can be easily obtained.20 A. Influence of gas pressure

The mass density of the plasma formed from 90% CO2 and 10% C5F10O at different pressures is shown in Fig. 2. As expected, the mass density increases with gas pressure and decreases with temperature. Increasing the temperature decreases the total number density as per the ideal gas law, and also leads to dissociation and ionization reactions, both of which decrease the mass density. Increasing the pressure

FIG. 2. Mass density of the plasma formed from 90% CO2 and 10% C5F10O as a function of temperature for different pressures.

increases the number density of the species present, and also delays the dissociation and ionization reactions, both of which increase the mass density at a given temperature. Figures 3 and 4 illustrate the change of enthalpy and specific heat at constant pressure of the 10%C5F10O90%CO2 mixture at different pressures. The peaks in the specific heat below 5000 K, and at about 7000 K, 15 000 K, and 30 000 K are, respectively, associated with the dissociation of CO2 and O2 to CO and O, dissociation of CO to C and O, the first ionization of the atomic species and the second ionization of the ions. Unlike pure CO2, 10%C5F10O-90%CO2 mixtures have another characteristic peak around 2200 K, corresponding to the rapid dissociation of CF2O. As the gas pressure increases, the peaks of the specific heat associated with the decomposition and ionization processes shift to higher temperatures, accompanied by a decrease in amplitude. The enthalpy is the integral of the specific heat with respect to temperature, so the peaks in the specific heat are reflected in rapid increases in the enthalpy.

FIG. 4. Specific heat at constant pressure of the plasma formed from 90% CO2 and 10% C5F10O as a function of temperature for different pressures.

143302-4

Li et al.

J. Appl. Phys. 122, 143302 (2017)

FIG. 5. Mass density of CO2-C5F10O plasmas with different mixing ratios as a function of temperature at 0.8 MPa.

FIG. 7. Specific heat at constant pressure of CO2-C5F10O plasmas with different mixing ratios as a function of temperature at 0.8 MPa.

B. Influence of mixing ratios

mixtures below 8400 K, while above 8400 K it has the opposite effect. These trends are related to the mass density changes. For pure CO2, the specific heat shows characteristic peaks around 8200 K and 17 700 K. These maxima correspond to, respectively, the dissociation of CO, and the ionization of C and O. For pure C5F10O, the first peak values are shifted from 8200 K to 7800 K. This is partly because the decrease in CO partial pressure shifts its dissociation reaction to a lower temperature (as indicated by the Le Chatelier’s principle), and partly because the dissociation of CF and C2, which are important species when the C5F10O fraction is large, occur at a lower temperature than that of CO. Similarly, the second peak is shifted from 17 700 K to 19 500 K due to the reduction of the partial pressure of O atoms and the increased partial pressure of F atoms, which ionize at a higher temperature, as shown in Fig. 1.

As shown in Fig. 5, the mixing ratio does not greatly affect the mass density of CO2-C5F10O plasmas. This can be explained that the molecules will eventually decompose into atoms (C, F, O) and ions (Cþ, Fþ, Oþ, C2þ, F2þ, and O2þ) with similar atomic masses. However, since the atomic mass of F is higher than those of C and O, the mass density of the plasma increases with increasing C5F10O concentration. Figures 6 and 7, respectively, present the enthalpy and specific heat at constant pressure at 0.8 MPa for different C5F10O-CO2 mixing ratios. The CO2 content affects the number and position of peaks of specific heat. For example, when the percentage of CO2 reaches 90%, the peaks resulting from C5 and CF4 at about 1200 and 3000 K disappear, and the temperatures of the specific heat peaks corresponding to CF2 and CF are shifted from 3400 K to 2800 and 4000 K to 3400 K, respectively. Unlike the pure C5F10O plasma, only three peaks are observed in a pure CO2 plasma, because the peaks associated with CF2O, CF4, CF2, and CF in C5F10O vanish. It can be also observed that increasing the fraction of C5F10O increases the enthalpy of C5F10O-CO2

IV. TRANSPORT PROPERTIES

The transport properties are calculated using the Chapman–Enskog solution of Boltzmann equation, assuming that the particle distribution function is a first-order perturbation to the Maxwellian distribution; the perturbation is then expressed in series of Sonine polynomials, finally leading to a system of linear equation that can be suitably solved to obtain different transport properties. In this work, for C5F10O-CO2 mixtures the computation has been carried out using the expressions reported by Murphy et al.15,21 A. Influence of gas pressure

The electrical conductivity of C5F10O-CO2 mixtures at different gas pressures is shown in Fig. 8. The electrical conductivity is larger for lower pressures for temperatures up to about 11 000 K, and increases with pressure at higher temperatures. This can be understood by noting that electrical conductivity is proportional, to a first approximation, to 1 P ð1;1Þ ne =ðT 2 j6¼e nj Xej Þ, where ne is the electron density, nj is ð1;1Þ

FIG. 6. Enthalpy of CO2-C5F10O plasmas with different mixing ratios as a function of temperature at 0.8 MPa.

the number density of species j, and Xej is a collision integral for interactions between electrons and species j.24 For a

143302-5

Li et al.

J. Appl. Phys. 122, 143302 (2017)

FIG. 8. Electrical conductivity of the plasma formed from 90% CO2 and 10% C5F10O as a function of temperature for different pressures. ð1;1Þ

ð1;1Þ

ð1;1Þ

given atomic species X, XeX2þ > XeXþ  XeX ; i.e., the collision integral increases with the degree of ionization, because of the strong Coulomb interaction between charged species. As pressure increases, the first ionization of atoms is delayed. Thus, the increase in electron density with pressure is slower than that of the total density. At lower temperatures, this is the dominant effect, resulting in a reduction in electrical conductivity as the pressure increases. However, at higher temperatures, for which first ionization is essentially complete, the delay in second and subsequent ionizations means that the average collision integral is smaller, so electrical conductivity increases with pressure. The thermal conductivity at different pressures is shown in Fig. 9. Thermal conductivity is the sum of four main components: heavy-species translational, electron translational, internal, and reaction thermal conductivity.21 The peaks of thermal conductivity are associated with the reaction component, and correspond to the same decomposition and ionization processes associated with peaks in the specific heat. As the gas pressure increases, the peaks are shifted to higher temperatures, accompanied by a decrease in amplitude. At

FIG. 9. Thermal conductivity of the plasma formed from 90% CO2 and 10% C5F10O as a function of temperature for different pressures.

high temperatures, the electron translational component of the thermal conductivity dominates; this has a similar dependence on pressure to the electrical conductivity. The viscosity of a C5F10O-CO2 mixture in the pressure range from 0.05 to 1.6 MPa is shown in Fig. 10. Before ionization occurs, the viscosity is mainly determined by the collisions between neutral species, whose collision integrals gradually decrease with the increase of temperature. Together with the usual T1/2 dependence of viscosity of a neutral gas, this leads to the increase in viscosity with temperature. After ionization occurs, the viscosity increases with pressure at temperatures above 10 000 K. As noted above, the collision integrals for the Coulomb interactions between charged species are much larger than those between neutral species, and increase as the degree of ionization increases. The increase in pressure reduces the degree of ionization of the gas, so the collision integrals are decreased; like all transport coefficients, viscosity is inversely proportional to the collision integrals between the species present in the plasma. B. Influence of mixing ratios

The influence of the addition of C5F10O to CO2 on the electrical conductivity at a given pressure is presented in Fig. 11. It can be seen that the calculated electrical conductivity is only weakly dependent on the mixing ratio. At temperatures between about 15 000 K and 20 000 K, the electrical conductivity is slightly decreased when the C5F10O fraction is increased, because ionization of F occurs at higher temperatures than ionization of C and O, so the electron density is lower. At temperatures above 20 000 K, the electrical conductivity is almost independent of the mixing ratio. As noted in Fig. 1, the addition of C5F10O leads to a significant decrease in the Oþ concentration and a significant increase in that of Fþ, but does not substantially affect the Cþ concentration. The ionization energies of O and F atoms are higher than that of C atoms (and similarly those of Oþ and Fþ ions are higher than that of Cþ ions). As a result, the increase of the F concentration leads to a reduction in the number of

FIG. 10. Viscosity of the plasma formed from 90% CO2 and 10% C5F10O as a function of temperature for different pressures.

143302-6

Li et al.

FIG. 11. Electrical conductivity of CO2-C5F10O plasmas as a function of temperature for different mixing ratios at 0.8 MPa.

charged and multiply-charged species at a given temperature, while the decrease in the O concentration has an opposite effect; the effects almost cancel. The calculated thermal conductivity of C5F10O-CO2 mixtures is illustrated in Fig. 12. Generally, the thermal conductivity increases with temperature, but with peaks due to the reaction thermal conductivity associated with dissociation and ionization. Below 5000 K, the peaks resulting from C5 and CF4 disappear with increasing CO2 content, similar to the specific heat. The peaks of thermal conductivity resulting from the dissociation of CF2O, CF4, CF2, and CF in C5F10O mixtures are also weakened. For the 90%C5F10O-10%CO2 mixture, there are two peaks around 7800 K and 20 400 K. The first peak is attributed to the dissociation of C2, CF and CO, and the second peak to the ionization of F. When CO2 is added, the dissociation of CO is shifted to a higher temperature, as discussed in Sec. III B, and C2, CF, and F become less important species. Consequently, the first peak shifts to higher temperature and the second peak becomes smaller.

FIG. 12. Thermal conductivity of CO2-C5F10O plasmas as a function of temperature for different mixing ratios at 0.8 MPa.

J. Appl. Phys. 122, 143302 (2017)

FIG. 13. Viscosity of CO2-C5F10O plasmas as a function of temperature for different mixing ratios at 0.8 MPa.

It can be observed from Fig. 13 that the addition of C5F10O leads to a decrease in viscosity in the temperature range from 5000 K to 14 000 K and an increase from 15 000 K. This behavior can be explained by the increased magnitude of neutral–neutral collision integrals for the species formed by the dissociation of C5F10O. As noted in Sec. III A, the viscosity of a thermal plasma is inversely related to the collision integrals, and before ionization, the viscosity is determined by neutral–neutral collisions. However, after ionization occurs, charged–charged interactions dominate. The density of charged species decreases with increasing C5F10O concentration due to the relatively-high ionization energy of F, resulting in a decrease in the effect of Coulomb interactions, and an increased viscosity above 15 000 K. V. DISCUSSION A. Comparisons of the thermophysical properties of C5F10O-CO2 mixtures and pure SF6 above 5000 K

Comparisons of the thermophysical properties of C5F10O-CO2 mixtures and pure SF6 are presented in this

FIG. 14. Comparison of mass density of CO2-C5F10O mixtures and pure SF6 at 0.1 MPa.

143302-7

Li et al.

FIG. 15. Comparison of enthalpy of CO2-C5F10O mixtures and pure SF6 at 0.1 MPa.

section. The mass density is illustrated in Fig. 14. It can be seen that the mass density of pure SF6 is higher than that of the C5F10O-CO2 mixtures at temperatures above 7500 K because the atomic mass of S is higher than those of C and O. The evolution of enthalpy is also related to the mass density changes, that is to say, a higher mass density leads to lower enthalpy, as shown in Fig. 15. The problem we are most concerned about is the plasma behavior in the arcing and post-arc periods, in particular, whether the new mixture has insulation and arc-quenching capabilities comparable to SF6. The electrical conductivity has a great impact on the plasma behavior. For the switching arc, it is advantageous, to avoid severe contact ablation in the stable arcing period, that the plasma has a relatively high electrical conductivity.25 However, it is helpful that the electrical conductivity drops to a very low level in a short period of time during the recovery period of the medium, so that post-arc breakdown can be avoided and the breaking capacity of the circuit breaker is improved. The electrical conductivity of C5F10O-CO2 mixtures is slightly higher than that of

FIG. 16. Comparison of electrical conductivity of CO2-C5F10O mixtures and pure SF6 at 0.1 MPa.

J. Appl. Phys. 122, 143302 (2017)

SF6 in the temperature range from 10 000 K to 25 000 K, and lower than that of SF6 below 10 000 K and above 25 000 K, as shown in Fig. 16. This suggests that the C5F10O-CO2 mixture has the desirable properties of high conductivity in the hightemperature arcing phase, and lower conductivity in the lowtemperature arc extinction phase. However, it is important to note that in the post-arc phase, deviations from LTE occur, and the rate of electron removal reactions becomes important. Thermal conductivity indicates the ability of arc to transfer the heat generated by the Joule heating in the core region of the arc to the outer arc region or even outside of the arc. In the arcing period, if the arc plasma can effectively transfer the energy generated by Joule heating to the periphery of the arc, this is helpful to extinguish the arc and improve the rate of recovery of dielectric strength of the medium. In Fig. 17, it can been seen that, unlike that of SF6,the thermal conductivity of C5F10O-CO2 mixtures has a peak at around 7900 K because of the dissociation of CO, C2, and CF, as shown in Fig. 1. This means thatC5F10O-CO2 mixtures have higher thermal conductivities than SF6 in the temperature range from 5000 K to 10 000 K. With the increase of concentration of C5F10O, the thermal conductivity of C5F10O-CO2 mixtures becomes closer to that of SF6. The viscosity mainly affects the radial distribution of the flow velocity of the arc plasma, which in turn affects the other arc characteristics and the energy transfer processes. As seen in Fig. 18, the viscosity of the 30%C5F10O-70%CO2 mixture has the same peak value as that of SF6. The peak value occurs at higher temperature for SF6, since S ionizes at higher temperatures than C and O. The broadly comparable viscosity values indicate that arcs in C5F10O-CO2 mixtures will have similar flow profiles to those in SF6. Since plasma behavior is very complex and may be influenced by many factors, it is not straightforward to predict or evaluate insulation and arc-quenching capability of a new promising substitute to SF6 based solely on its thermophysical properties. The calculation results do however provide the necessary data foundation for the further study of

FIG. 17. Comparison of thermal conductivity of CO2-C5F10O mixtures and pure SF6 at 0.1 MPa.

143302-8

Li et al.

J. Appl. Phys. 122, 143302 (2017)

B. Composition and thermophysical properties of pure C5F10O for the decomposition process

FIG. 18. Comparison of viscosity of CO2-C5F10O mixtures and pure SF6 at 0.1 MPa.

the behavior of plasmas using magnetohydrodynamics (MHD) arc models. As mentioned above, the liquefaction temperature of C5F10O at 0.1 MPa, is about 24  C, which does not satisfy the requirements for application in high-voltage electrical equipment. For indoor electrical equipment, the liquefaction temperature of the gaseous medium should not be higher than 5  C at the relevant filling pressure. To determine the applicable mixing ratio and filling pressure, we calculated the saturated vapor pressure of CO2-C5F10O mixtures at 5  C for different mixing ratios.23 As shown in Fig. 19, with increasing C5F10O fraction, the saturated vapor pressure of the gas mixture decreases rapidly. Meanwhile, the dielectric strength of CO2-C5F10O mixtures increases with the C5F10O fraction. For 30% C5F10O-70%CO2, the filling pressure of electrical equipment should be lower than 0.35 MPa, and its dielectric strength is about 0.57 times that of pure SF6. The calculated thermophysical properties of CO2-C5F10O mixtures, combined with their relative dielectric strength and saturated vapor pressure at a certain temperature, can be used to optimize the ratio of the gases for different applications.

FIG. 19. Saturated vapor pressure at 5  C and relative dielectric strength of CO2-C5F10O mixtures for different mixing ratios.26

The decomposition properties of the dielectric medium at temperatures from 300 to several thousand kelvin are also crucial to understanding the interruption process in mediumand high-voltage circuit breakers, because C5F10O is not reformed in the post-arc period, i.e., the decomposition process of C5F10O is irreversible. However, the decomposition products of C5F10O at a given pressure and temperature are still unknown. Fu et al.27 have investigated the decomposition pathway of C5F10O using the density functional theory (DFT). In the present work, the decomposition reaction mechanisms and products are determined using DFT and the NIST Chemical Kinetics Database.28 We took as many species as possible into consideration. The structural optimizations and vibrational frequency calculations were carried out with B3LYP/6–311 G(d,p), while energy calculations of the species used B2PLYPD3/def2TZVP. The internal partition function of C5F10O and its decomposition products were obtained from calculated vibrational frequencies. Since the chemical potentials li of C5F10O and some of its decomposition products at low temperatures are not yet available, the minimization of Gibbs free energy cannot be used to calculate the composition in this case. The partition function of the decomposition species Qi and the dissociation energy DEi have been obtained from DFT, so the Guldberg–Waage equation, combined with the conservation of elements and Dalton’s law, was instead chosen to calculate the composition of a pure C5F10O plasma,. In order to avoid errors arising from the accuracy of calculation of the free energy, the isomeric transformation process was ignored. 57 reactions and 39 species were taken into consideration for the temperature range from 300 K to 2000 K. Unfortunately, decomposition mechanisms of some species, such as CF ¼ CF2, C-CF2, and C ¼ CF2, are still unknown, resulting in errors at temperatures above 2000 K, around which CF2¼CF2 is dissociated into CF2. Thus, only results for temperature below 2000 K are shown here. Detailed information on all reactions is presented in the Appendix. The calculated composition of pure C5F10O at 0.1 MPa is shown in Fig. 20. It can be seen that C5F10O is significantly dissociated into smaller species around 1000 K. Intense decomposition reactions take place between 1000 and 1200 K. COCFCF3, COCF3, and CF3 are successively dissociated above 1200 K. The mole fractions of the species CF2¼CF2, COF, and CF3 are over 0.1 around 1200 K. Large mole fractions of CO and CF2 are formed above 1200 K. It can be predicted that at higher temperatures, CO and CF2 will become dominant in the plasma. COF-C-CF2 and CO-CF-CF2 are formed at a temperature above 1500 K and then dissociate into C-CF2 and CF from 1700 K. The predicted dissociation temperatures show good agreement with the NIST Chemical Kinetics Database. Using the composition shown in Fig. 1, it can be predicted that, based on the decomposition pathway, C3 and C2 are not expected to be formed, even at temperatures over 2000 K. However, to take all possible species formed from C, F, and O into consideration requires that the method of the minimization of Gibbs free energy to be used.

143302-9

Li et al.

J. Appl. Phys. 122, 143302 (2017)

FIG. 20. Composition of pure C5F10O plasma during decomposition as a function of temperature at 0.1 MPa.

FIG. 22. Enthalpy of pure C5F10O plasma during decomposition as a function of temperature at 0.1 MPa.

Discrepancies between results obtained with this method, and those obtained with the Guldberg–Waage equation as used in this section occur when the calculation is expanded to the temperatures from 2000 K to 5000 K. More effort is needed to investigate the decomposition pathway at those temperatures to obtain consistent method and results. The mass density, enthalpy, and specific heat were obtained using the calculated composition, and are shown in Figs. 21–23, respectively. Some parameters of C5F10O and its primary decomposition required in the calculation of collision integrals are not yet available. Even for the phenomenological potential, which is relatively simple, the required parameters of polarizability and effective electron number are still incomplete. Thus, to evaluate transport properties, we used linear fitting to obtain interaction potentials of reactants from products; for example, we obtained cross-section data for CF-CF2 molecules by adding those for CF and CF2. The electrical conductivity, thermal conductivity, and viscosity were obtained using the estimated collision integrals, and are shown in Figs. 24–26, respectively. The peaks of specific heat and

thermal conductivity correspond to the dissociation of C5F10O and its primary decomposition products. Accurate properties still have to be calculated, which will require a very significant effort. The mutual reactivity and reaction products of CO2-C5F10O mixtures are still under investigation. The results shown here are an initial step in determining the properties during the dissociation process of the new potential SF6 substitutes, C5F10O and its mixtures.

FIG. 21. Mass density of pure C5F10O plasma during decomposition as a function of temperature at 0.1 MPa.

VI. CONCLUSIONS

In this paper, calculations of the composition, thermodynamic properties, and transport coefficients of C5F10O-CO2 mixtures have been presented. The fluoroketone C5F10O is a strong candidate to replace SF6 in medium- and high-voltage circuit equipment, but because of its high liquefaction temperature, it has to be mixed with another gas such as CO2. The influence of the mixing ratio of the two gases and the gas pressure has been analyzed in detail. It was found that the pressure has a strong influence on all properties, especially in the high temperature range. This is largely due to the shift of dissociation and ionization reactions to higher

FIG. 23. Specific heat of pure C5F10O plasma during decomposition as a function of temperature at 0.1 MPa.

143302-10

Li et al.

FIG. 24. Electrical conductivity of pure C5F10O plasma during decomposition as a function of temperature at 0.1 MPa.

FIG. 25. Thermal conductivity of pure C5F10O plasma during decomposition as a function of temperature at 0.1 MPa.

J. Appl. Phys. 122, 143302 (2017)

temperature when the pressure is increased. Increasing the C5F10O fraction in the C5F10O-CO2 mixture also significantly affects the thermophysical properties, except for the electrical conductivity, for which the change is only small. As for the influence of pressure, the main reason for the changes is the different temperatures of the main dissociation and ionization reactions, However, the changes are more complicated in the case of the mixing ratio, since not only does changing the C5F10O fraction shift the temperature at which a particular reaction occurs, but it also changes the dominant reactions, from CO dissociation and C and O ionization at low fractions, to CF and C2 dissociation and F ionization at high fractions. The thermophysical properties of C5F10O-CO2 mixtures have also been compared those of pure SF6. With increasing C5F10O concentration, some of the properties, such as thermal conductivity and viscosity, of the C5F10O-CO2 mixtures become close to those of SF6. The main exceptions are the mass density and enthalpy; the latter is lower than that of SF6 because of the lower atomic masses of the constituent elements, and the enthalpy of the C5F10O-CO2 mixtures is higher due to the lower density and the different decomposition and ionization processes. The composition and thermophysical properties of pure C5F10O for the decomposition process from 300 K to 2000 K have also been analyzed. More effort is needed to understand the decomposition products, and their properties, in order to improve the accuracy and extend the data to include temperatures between 2000 and 5000 K. To our knowledge, our study provides the first data for the thermophysical properties of C5F10O-CO2 mixtures in the high temperature range relevant to arcing in high-voltage circuit breakers. The data are essential for computational modelling, which will provide an assessment of the insulation and arc-quenching capabilities of these new SF6 substitutes in circuit breakers. ACKNOWLEDGMENTS

The work was supported by the National Natural Science Foundation of China (51577143 and 51607143). APPENDIX: REACTIONS AND THEIR DISSOCIATION ENERGY IN A C5F10O PLASMA FOR TEMPERATURES BETWEEN 300 AND 1500 K.

FIG. 26. Viscosity of pure C5F10O plasma during decomposition as a function of temperature at 0.1 MPa.

1 2 3 4 5 6 7 8 9 10 11

Reactions

DEi (eV)

C5-PKF ! F3C-CF-CO-CF3 þ CF3 C5-PKF ! F3C-CF-CF3 þ CO-CF3 C5-PKF ! F3C-CF(CO)-CF3 þ CF3 F3C-CF-CO-CF3 ! CF-CO-CF3 þ CF3 F3C-CF-CO-CF3 ! CO-CF3 þ CF-CF3 F3C-CF-CF3 ! CF-CF3 þ CF3 F3C-CF-CF3 ! F3C-CF-CF3 þ F F3C-CF-CF3 ! F3C-CF2-CF2 F3C-CF(CO)-CF3 ! CO-CF-CF3 þ CF3 F3C-CF(CO)-CF3 ! F3C-C(COF)-CF3 F3C-CF(CO)-CF3 ! F3C-CF(COF)-CF2

2.96 2.64 2.95 3.78 3.16 3.49 5.77 0.49 1.39 0.63 0.18

143302-11

Li et al.

J. Appl. Phys. 122, 143302 (2017) 1

(Continued.)

12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57

Reactions

DEi (eV)

F3C-CF(CO)-CF3 ! F3C-CF-CF3 þ CO CF-CO-CF3 ! C-COF-CF3 CF-CO-CF3 ! CF2-CO-CF2 CF-CO-CF3 ! CO-CF3 þ CF F3C-CF-CF3 ! C-CF3 þ CF3 F3C-CF-CF3 ! F3C-CF ¼ CF2 F3C-CF2-CF2 ! CF2-CF3 þ CF2 F3C-CF2-CF2 ! CF2 ¼ CF2 þ CF3 CO-CF-CF3 ! COF-CF-CF2 F3C-C(COF)-CF3 ! F3C-C-CF3 þ COF F3C-CF ¼ CF2 ! CF-CF3 þ CF2 F3C-CF(COF)-CF2 ! F3C-CF ¼ CF2 þ COF F3C-CF(COF)-CF2 ! COF-CF-CF3 þ CF2 F3C-CF(COF)-CF2 ! COF-CF ¼ CF2 þ CF3 C-COF-CF3 ! C-COF þ CF3 C-COF-CF3 ! CF- CF3 þ CO CF2-CO-CF2 ! CF2 þ CO ¼ CF2 CF2-CO-CF2 ! COF-CF ¼ CF2 F3C-CF ¼ CF2 ! CF3-C ¼ CF2 þ F F3C-CF ¼ CF2 ! CF3 þ CF ¼ CF2 COF-CF-CF2 ! CF-CF2 þ COF COF-CF-CF2 ! CF2 þ CF-COF COF-CF-CF3 ! CF-CF3 þ COF C-COF ! C þ COF C-COF ! FCCO CF-CF3 ! CF þ CF3 CF-CF3 ! CF2 ¼ CF2 CO ¼ CF2 ! CF-COF CO ¼ CF2 ! CF2 þ CO COF-CF ¼ CF2 ! CO-CF-CF2 þ F COF-CF ¼ CF2 ! COF þ CF-CF2 COF-CF ¼ CF2 ! COF-C ¼ CF2 þ F CF3-C ¼ CF2 ! C ¼ CF2 þ CF3 FCCO ! CF þ CO CF2 ¼ CF2 ! C ¼ CF2 þ C CF-COF ! CF þ COF CO-CF-CF2 ! CF-CF2 þ CO COF-C ¼ CF2 ! C-CF2 þ COF F3C-CF ¼ CF2 ! CF2 ¼ CF2 þ CF2 CO-CF3 ! CF3 þ CO CF3-CF2 ! CF3 þ CF2 CF2 ¼ CF2 ! CF2 þ CF2 CF3 ! CF2 þ F COF ! F þ CO CF2 ! CF þ F CF ! F þ C

0.22 2.40 0.51 2.18 3.20 2.84 2.01 1.40 0.42 4.53 4.27 0.88 1.65 4.13 5.28 1.88 0.14 3.34 5.07 4.35 4.44 4.59 3.50 5.38 1.53 2.79 1.61 1.12 0.01 1.65 1.11 1.74 3.83 0.92 5.40 2.55 1.11 3.92 2.66 0.09 2.17 2.79 3.71 1.65 5.32 7.64

S. Meijer, J. Smit, and A. Girodet, “Comparison of the breakdown strength of N2, CO2, and SF6 using the extended up-and-down method,” in 8th International Conference on Properties and Applications of Dielectric Materials (2006), pp. 653–656. 2 K. Juhre and E. Kynast, “High pressure N2, N2/CO2 and CO2 gas insulation in comparison to SF6 in GIS applications,” in 14th International Symposium on High Voltage Engineering (ISH) (2005). 3 M. Kimura and Y. Nakamura, J. Phys. D: Appl. Phys. 43, 145202 (2010). 4  J. De Urquijo, A. Juarez, E. Basurto, and J. Hernandez-Avila, J. Phys. D: Appl. Phys. 40, 2205 (2007). 5 H. Kasuya, Y. Kawamura, H. Mizoguchi, Y. Nakamura, S. Yanabu, and N. Nagasaki, IEEE Trans. Dielectr. Electr. Insul. 17, 1196–1203 (2010). 6 L. G. Christophorou, J. K. Olthoff, and D. S. Green, NIST Tech. Note 6, 1–44 (1997); https://swap.stanford.edu/20110205200458/http://www.epa. gov/highgwp/electricpower-sf6/documents/new_report_final.pdf. 7 A. Lee and L. Frost, IEEE Trans. Plasma Sci. 8, 362–367 (1980). 8 A. Gleizes, I. Sakalis, M. Razafinimanana, and S. Vacquie, J. Appl. Phys. 61, 510–518 (1987). 9 H. Zhao, X. W. Li, K. Zhu, Q. Wang, H. Lin, and X. X. Guo, IEEE Trans. Dielectr. Electr. Insul. 23, 2657–2667 (2016). 10 H. Zhao, X. W. Li, and H. Lin, IEEE Trans. Power Delivery 32, 254–262 (2017). 11 J. Mantilla, N. Gariboldi, S. Grob, and M. Claessens, “Investigation of the insulation performance of a new gas mixture with extremely low GWP,” in Electrical Insulation Conference (EIC) (2014), pp. 469–473. 12 M. O. McLinden, R. A. Perkins, E. W. Lemmon, and T. J. Fortin, J. Chem. Eng. Data 60, 3646–3659 (2015). 13 C. Preve, R. Maladen, D. Piccoz, and J.-M. Biasse, “Validation method and comparison of SF6 alternative gases,” paper presented at the CIGRE Paris, 2016. 14 P. Simka and N. Ranjan, “Dielectric strength of C5 perfluoroketone,” in 19th International Symposium on High Voltage Engineering, Pilsen, Czech Republic (2015), pp. 23–28. 15 A. Murphy, J. Phys. D: Appl. Phys. 34, R151 (2001). 16 A. Gleizes, J. J. Gonzalez, and P. Freton, J. Phys. D: Appl. Phys. 38, R153–R183 (2005). 17 C. E. Moore, Atomic Energy Levels as Derived from the Analyses of Optical Spectra (U.S. Dept. of Commerce, National Bureau of Standards, 1949), Vol. 1. 18 C. E. Moore, Atomic Energy Levels as Derived from the Analyses of Optical Spectra (U.S. Dept. of Commerce, National Bureau of Standards, 1949), Vol. 2. 19 M. W. Chase, NIST-JANAF Thermochemical Tables (American Institute of Physics for the National Institute of Standards and Technology, 1998). 20 J. O. Hirschfelder and R. B. Bird, Molecular theory of gases and liquids: s.n. (Wiley, 1954). 21 A. Murphy, Plasma Chem. Plasma Process. 15, 279–307 (1995). 22 J. L. Zhang, J. D. Yan, A. B. Murphy, and W. Hall, IEEE Trans. Plasma Sci. 30, 706–719 (2002). 23 J. R. Stallcop, H. Partridge, A. Pradhan, and E. Levin, J. Thermophys. Heat Transfer 14, 480 (2000). 24 R. Devoto, Phys. Fluids (1958–1988) 10, 2105–2112 (1967). 25 X. Cui, “Research on contact erosion mechanism and material transfer characteristics under direct current arc,” Ph.D. thesis (Harbin Institute of Technology, China, 2014). 26 X. Li, Y. Deng, X. Jiang, H. Zhao, R. Zhuo, D. Wang, and M. Fu, High Voltage Eng. 43, 708–714 (2017). 27 Y. W. Fu, X. H. Wang, X. Li, A. J. Yang, G. H. Han, Y. H. Lu, Y. Wu, and M. Z. Rong, AIP Adv. 6, 16 (2016). 28 See http://kinetics.nist.gov/kinetics/index.jsp for chemical reaction mechanisms.