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Thermodynamic properties and transport coefficients of a twotemperature polytetrafluoroethylene vapor plasma for ablation-controlled discharge applications To cite this article: Haiyan Wang et al 2017 J. Phys. D: Appl. Phys. 50 395204
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Journal of Physics D: Applied Physics J. Phys. D: Appl. Phys. 50 (2017) 395204 (14pp)
https://doi.org/10.1088/1361-6463/aa7d68
Thermodynamic properties and transport coefficients of a two-temperature polytetrafluoroethylene vapor plasma for ablation-controlled discharge applications Haiyan Wang1,6, Weizong Wang2,5,6, Joseph D Yan3, Haiyang Qi1, Jinyue Geng4 and Yaowu Wu4 1
Pinggao Group Co. Ltd, Pingdingshan City, Henan 467001, People’s Republic of China Qian Xuesen Laboratory of Space Technology, China Academy of Space Technology, Beijing 100094, People’s Republic of China 3 Department of Electrical Engineering and Electronics, The University of Liverpool, Liverpool L69 3GJ, United Kingdom 4 Beijing Institute of Control Engineering, China Academy of Space Technology, Beijing 100094, People’s Republic of China 2
E-mail:
[email protected] Received 16 March 2017, revised 20 June 2017 Accepted for publication 4 July 2017 Published 11 September 2017 Abstract
Ablation-controlled plasmas have been used in a range of technical applications where local thermodynamic equilibrium (LTE) is often violated near the wall due to the strong cooling effect caused by the ablation of wall materials. The thermodynamic and transport properties of ablated polytetrafluoroethylene (PTFE) vapor, which determine the flowing plasma behavior in such applications, are calculated based on a two-temperature model at atmospheric pressure. To our knowledge, no data for PTFE have been reported in the literature. The species composition and thermodynamic properties are numerically determined using the two-temperature Saha equation and the Guldberg–Waage equation according to van de Sanden et al’s derivation. The transport coefficients, including viscosity, thermal conductivity and electrical conductivity, are calculated with the most recent collision interaction potentials using Devoto’s electron and heavy-particle decoupling approach but expanded to the thirdorder approximation (second-order for viscosity) in the frame of the Chapman–Enskog method. Results are computed for different degrees of thermal non-equilibrium, i.e. the ratio of electron to heavy-particle temperatures, from 1 to 10, with electron temperature ranging from 300 to 40 000 K. Plasma transport properties in the LTE state obtained from the present work are compared with existing published results and the causes for the discrepancy analyzed. The two-temperature plasma properties calculated in the present work enable the modeling of wall ablation-controlled plasma processes. Keywords: wall ablation, Teflon, non-equilibrium plasma, two temperature model, thermodynamic properties, transport coefficients (Some figures may appear in colour only in the online journal)
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Author to whom any correspondence should be addressed. Current address: University of Antwerp, BE-2610 Wilrijk-Antwerp, Belgium. 6 These authors contributed equally to this work. 1361-6463/17/395204+14$33.00
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© 2017 IOP Publishing Ltd Printed in the UK
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1. Introduction
Table 1. List of reactions considered in the present work.
Ablation-controlled plasmas are widely used in technological applications such as high current switching [1–3], soft x-ray generation [4], pulsed plasma thrusters (PPT) [5–7], electrothermal-chemical (ETC) launching [8, 9] and laser ablation [10, 11]. Polytetrafluoroethylene (Teflon, PTFE) is a polymer material that has been used in most of these applications. The compound materials vaporize when subjected to strong heating from the high-power plasma, and as a result a vapor mass flow is injected into the plasma. Thus the ablated vapor becomes part of the plasma and significantly influences the discharge process and plasma parameters such as temperature, velocity and pressure. To improve the process efficiency, a magneto hydrodynamic (MHD) model has been developed and applied to investigate the ablation characteristics of heated compound materials interacting with discharging plasma [1–3]. The assumption of local thermodynamic equilibrium (LTE), which is used in the MHD model of ablation-dominated arcs at high current, is no longer valid as a result of the large temper ature gradient (existing near a cold wall or when cold vapor is injected into the plasma) or insufficient electron number density to achieve efficient energy exchange between electrons and heavy species [12]. Under such circumstances, while electrons and heavy species are able to maintain their Maxwellian velocity distribution functions, the mean kinetic energy of electrons can be much higher than that of heavy particles. A two-temperature MHD model would thus be required, which has to be based on non-equilibrium thermodynamic and transport properties of the plasma [13, 14]. The description of the state of a two-temper ature plasma maintained in a polymer vapor involves complex microscopic processes such as dissociation reactions, excitation into different types of discrete energy levels (rotational, vibrational and electronic), and ionization of different atomic species, etc. A common approach to render the problem tractable is to use the principle of local chemical equilibrium (LCE) with different electron (Te) and heavy-particle (Th) temperatures [15, 16]. Existing work is limited to plasmas under LTE conditions, for only pure CF4, C2F6 and ablated PTFE vapor (C2F4)m [1, 18, 19]. To our knowledge, there has been no published work so far on the thermodynamic properties and transport coefficients of a two-temperature PTFE plasma. To fill this gap, the two-temperature plasma properties of evaporated Teflon are calculated in the present work. Results are presented and discussed mainly over an electron temperature range of 300 to 40 000 K, although calculations have been carried out under different pressures and higher electron temperatures up to 60 000 K. The most recent cross-sectional data with the highest accuracy specified in the literature have been used in the evaluation of the collision integrals. Results in LTE as an extreme case in the present work are compared with published data and the possible reasons for the discrepancies analyzed.
Number
Chemical reaction
Number
Chemical reaction
1 2 3 4 5 6
C2 F4 → C2 F2 + F2 C2 F2 → CF2 + C CF4 → CF3 + F CF3 → CF2 + F CF2 → CF + F CF → C + F C5 → C4 + C
12 13 14 15 16 17
F- → F + e F → F+ + e C → C+ + e F+ → F2+ + e C+ → C2+ + e
18
C2+ → C3+ + e CF3 → CF+ 3 +e CF2 → CF+ 2 +e CF → CF+ + e
7 8 9 10 11
C4 → C3 + C C3 → C2 + C C2 → C + C F2 → F + F
19 20 21
F2+ → F3+ + e
determine the species composition [20, 21]. The plasma of ablated PTFE vapor contains different species at different temperatures. Considering the possible temperature range, a total of 24 different species, including atoms, ions and molecular radicals as well as electrons, are included in the calcul ation: C2F4, C2F2, CF4, CF3, CF2, CF, C5, C4, C3, C2, C, F2, + + + + − 2+ 2+ 3+ 3+ F, CF+ 3 , CF2 , CF , C , F , F , C , F , C , F . Other molecular ions are excluded because of their low density and negligible effect on the thermodynamic and transport properties. A total of 21 independent reactions are taken into account (table 1) and described by the mass action law, i.e. Saha’s equation for ionization and the Gulberg–Waage law for dissociation reactions. Two forms of the mass action law exist for two-temper ature plasmas, represented by Potapov’s method [22] and Van de Sanden et al’s method [23]. Our previous work on twotemperature SF6 plasma showed that the difference in the two Saha equations leads to significant discrepancy in species composition and hence plasma properties [24]. For example, Potapov’s approach leads to larger variation in species concentration and plasma properties at a high degree of nonequilibrium (Te/Th), especially the specific heat at constant pressure and thermal conductivity, both of which are closely related to the energy associated with chemical reactions. For a long time the subject of the accurate form of the law of mass action has been a matter of debate. Giordano et al [25] were able to resolve the confusion surrounding the issue by explaining that the modified Saha laws in Potapov’s method and Van de Sanden et al’s method can each be correctly applied under defined thermodynamic constraints. However, to the best of our knowledge, there has been no experimental evidence that can be used to justify the conditions under which the approaches are valid. Based on the argument that in the extreme case of very high or very low electron number density laws governing dissociation and ionization must not depend on θ = Te/Th, Van de Sanden et al’s approach has been recommended by Gleizes et al through a comparative study of the composition of a two-temperature SF6 plasmas based on both approaches [26]. In view of the argument in [26], and also the fact that Van de Sanden’s approach has been widely cited in the literature as a reference case for chemical equilibrium calculations [27], this approach is also adopted in the present work. The Guldberg–Waage equation and generalized Saha
2. Mathematical models 2.1. Determination of plasma composition
The first step in the calculation of the thermodynamic properties and transport coefficients of a non-LTE plasma is to 2
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reaction energy for each chemical reaction as well as the spectroscopic data including the vibrational and rotational constants and the electronic configuration for the calculation of partition functions of molecules were taken from the JANAF Thermochemical Tables [31]. In addition to the law of mass action (Saha’s law and Gulberg–Waage’s law) as detailed above, the calculation of the species composition of the two-temperature plasma requires three additional equations to close the system of equations. They are based on conservation of chemical elements, Dalton’s law for the equation of state, and electrical quasineutrality. The complete set of equations is solved using the Newton–Raphson method to obtain well-converged results. The composition of the two-temperature plasma under study is obtained based on the assumption of LCE. In cases where the net mass transfer rates by diffusion or convection are larger than the rates of chemical reactions (including dissociation, ionization and recombination reactions), departures from LCE may develop [12]. Under such conditions, it is no longer possible to accurately calculate the local plasma composition with a relatively simple approach such as the law of mass action used in the present work. Since the local composition is affected by the transport of species from other regions in the plasma, a mass conservation equation needs to be solved for individual species, and the thermodynamic properties as well as the transport coefficients thus depend on not only the local temperature and pressure but also on the transport process and the chemical kinetics. A kinetic model which describes species formation or loss by various chemical reactions should be coupled with the mass, momentum and energy transport equations to describe the species concentration distribution. The rates of chemical reactions differ by many orders of magnitude, implying that a very wide range of time scales has to be considered at each location in the plasma, ranging from that of the fastest reaction to that of the slowest reaction or transport processes. This requires a prohibitively long computation time and is not practical, although some approximate methods have been developed to investigate the influence of chemical non-equilibrium parameters by taking into account a modified Saha equation assuming that chemical equilibrium is more important for the ionization reaction [32]. For the ablated PTFE vapor in particular the kinetic process is very complicated when chemical non-equilibrium occurs. As a result, we only include the thermal non-equilibrium effect in the computation of species composition as well as transport coefficients. Besides the chemical non-equilibrium effect, the condensation effect can also significantly influence the plasma properties. For a LTE plasma system, the Gibbs free energy minimization method is commonly used in multiphase plasma calculation, and the influence of solid carbon on the computed species composition properties of ablated PTFE vapor plasma were investigated in our previous work [18, 33]. The condensation effect can also be significant in a non-LTE plasma system, due to low heavy-species temperature Th. Recently André et al [34] presented a paper computing the species composition of a multiphase non-LTE air–aluminum plasma which showed the influence of the non-LTE effect on the phase
law are expressed for a dissociation reaction as ab ↔ a + b, where equilibrium is controlled by the heavy species kinetic temperature Th, and for ionization as ar+ ↔ a(r+1)+ + e, which is controlled by the electron temperature: 3/2 3/2 Qa Qb 2πkTh na nb ma mb Ed (1) = exp − nab Qab h2 mab kTex ne
3/2 EI, r+1 − δEI,r+1 nr+1 Qr+1 2me πkTe exp − =2 nr Qr h2 kTex
(2) where Q is the internal partition function, EI,r+ 1 and Ed are the ionization energy and dissociation energy, respectively, and k and h are, respectively, the Boltzmann constant and Planck constant. The subscript r represents r-times ionized species or molecules. ab, a, b and e denote, respectively, the reactant, two products of the dissociation reaction and electrons, ni and mi are the number density and mass of species i, and Tex is the excitation temperature of ionization of species ar+. δEI,r+ 1 is the lowering of the ionization energy when taking into account the shielding effects of both ions and electrons in the calculation of the Debye length [24]. The choice of this excitation temperature has been discussed widely in previous studies and is still a subject of debate [24]. The authors have taken the argument that the heavy-particle temperature Th is responsible for dissociation reactions and the electron temper ature Te controls the ionization reactions. The species partition functions are then computed according to the mathematical model presented in [20]. 2.1.1. Monatomic species. εn 5 there is an apparent shift of the fast rising part of the curve towards high electron temperatures. This is because dissociation reactions producing CF3, CF2 and CF as well as atoms are controlled by the heavy-particle temperature. To achieve a certain heavy-particle temperature requires an increased electron temperature when Te/Th increases. As a result, the ionization reactions which are controlled by the electron temperature are delayed until dissociation occurs. It is also clear that a higher electron number density can be obtained in non-LTE plasmas. One the one hand, electrons depend on ionization reactions, as described above. On the other hand, with a higher degree of non-equilibrium there are more high-energy electrons for ionization and there are more molecules or atoms in a unit volume of space to be ionized. The concurrence of these two conditions allows a higher electron number density to be generated. There are three important features in the change of the number density of atomic 8
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Figure 5. Mass density of PTFE plasmas as a function of electron temperature under different degrees of non-equilibrium at atmospheric pressure.
Figure 3. Electron number density as a function of electron temperature in PTFE plasmas under different degrees of nonequilibrium at atmospheric pressure.
ionization at an earlier stage of the dissociation period, thus reducing the highest number density. • Once the number density of fluorine atoms reaches its maximum value, the decaying profile curves follow a similar track, especially for those with Te/Th > 2. This implies that once ionization of fluorine atoms by electron impact becomes more important than dissociative generation of fluorine atoms, the heavy-particle temperature has a reduced influence on the dependence of the atomic fluorine density on the electron temperature . This reduction in influence becomes stronger as Te/Th increases, so that for Te/Th > 5, the number density decay curves become indistinguishable. Figure 4. Number density of fluorine atoms as a function of electron temperature in PTFE plasmas under different degrees of non-equilibrium at atmospheric pressure.
3.2. Thermodynamic properties
The mass density of PTFE plasmas with different degrees of non-equilibrium is given in figure 5. The mass density increases at a fixed electron temperature as θ increases due to delayed dissociation and ionization. The steepest slope for higher degrees of non-equilibrium (Te/Th > 5) can be explained by the rapid decrease in the number of heavy molecular weight particles due to dissociation and the ioniz ation, which are controlled by the heavy-particle temperature and electron temperature, respectively. The results for specific enthalpy are given in figure 6 for PTFE plasmas to show its dependence on the degree of non-equilibrium. The change in the specific enthalpy profile is mainly attributed to the chemical reactions and mass density (see equations (6)–(8)). When θ increases, dissociation is increasingly delayed, resulting in a slow increase of specific enthalpy with respect to electron temperature. The occurrence of dissociation and ionization over a narrower range of electron temperature leads to a rapid increase in specific enthalpy. Moreover, the specific enthalpy decreases with increasing θ at a given electron temperature. When dissociation is complete (at a higher electron temperature when θ increases), the specific enthalpy becomes only weakly dependent on the degree
fluorine, controlled by dissociation (as a generation mech anism) and ionization (as a loss mechanism). • Firstly, in equilibrium, electron temperature and heavyparticle temperature are equal and dissociation reactions lead to the generation of atomic fluorine at low electron temperature (2200 K) where ionization is weak. Thus dissociation results in a high peak value of fluorine atom number density. When the degree of non-equilibrium is high, such as Te/Th = 5, at the same heavy-particle temper ature of 2200 K for dissociation, the electron temperature will be 11 000 K (figure 4). Due to this ratio of five, the rapid increase in the number density of atomic fluorine occurs in a range of electron temperatures that is about five times higher. • Secondly, the peak values of the number density of fluorine atoms decreases when the degree of non-equilibrium increases. This is a direct result of enhanced ionization due to increased electron temperature during the dissociation stage. The generation rate of fluorine atoms by dissociation reactions is balanced by electron impact 9
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Figure 6. Specific enthalpy of PTFE plasmas as a function of electron temperature under different degrees of non-equilibrium at atmospheric pressure.
of non-equilibrium because the second and third ionization reactions depend only on electron temperature. The specific heat as function of electron temperature strongly depends on the degree of non-equilibrium, as presented in figure 7. For each of the curves the peak at lower temperature corresponds to dissociation and those at higher temperature correspond to ionization, as summarized in table 1. The peaks in the specific heat curves reflect the rapid change in the specific enthalpy curves. Indeed, the behavior of electron specific heat at constant pressure is closely related to the variation in electron number density, and a peak is produced each time a type of ionization takes place. Under thermal equilibrium conditions, the peaks of electron specific heat at around 12 500 and 27 500 K correspond to the first and second ionization, respectively, of atomic carbon. The peaks at around 17 500 and 34 000 K are contributed by the first and second ionization, respectively, of fluorine atoms. When thermal non-equilibrium exists, molecular ionization also contributes to the peaks of the electron specific heat. For example, for θ = 10 molecular ionization of CF2 and CF makes a significant contribution to the peaks of electron specific heat at electron temperatures around 17 500 and 28 000 K. For heavyparticle specific heat, when the degree of non-equilibrium is lower than two, the peaks are, respectively, contributed by multiple dissociations of CF4 and C5 as well as multiple ionizations of monatomic species. For θ ⩾ 2 it is difficult to separate the different contributions: the contributions of dissociation and ionization are superimposed. A cross-check among the influencing factors shows that when a sufficiently high electron temperature is reached in the high-θ cases, dissociation reactions which are controlled by the heavy-particle temperature do not yet generate enough reactants for ionization reactions to occur. Once dissociation temperatures are reached, products of molecules and atoms generated by dissociation are immediately ionized. The concurrent dissociation and ionization processes give rise to an extremely high peak of the specific heat curve. Molecular ionization,
Figure 7. Specific heat of PTFE plasmas as a function of electron temperature under different degrees of non-equilibrium at atmospheric pressure: (a) CPe, (b) CPh, (c) CPt.
which is negligible in plasmas at thermal equilibrium, plays an increasing role in the specific heat of a plasma when the degree of non-equilibrium becomes high. This is because molecules, mainly CF3, CF2 and CF, from dissociation are ionized due to the high electron temperature before they further dissociate into smaller molecules or atoms under the control of the heavy-particle temperature. Comparing results in figures 7(b) and (c), it is evident that heavy particles play a more important role in determining the total specific heat at constant pressure.
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Figure 8. Viscosity of PTFE plasmas as a function of electron temperature for different degrees of non-equilibrium at atmospheric pressure.
Figure 10. Different thermal conductivity components of PTFE
plasmas as a function of electron temperature with a degree of non-equilibrium of three at atmospheric pressure (λtot, total thermal conductivity; λtrh and λtre, translational components due to heavy particles and electrons, respectively; λre, reactive component; λin, internal component). 3.3.2. Electrical conductivity. The most significant fea-
ture of the electrical conductivity behavior of non-equilibrium plasmas in comparison with equilibrium ones is that it becomes lower than the equilibrium value for a certain temperature range then becomes higher than the latter when electron temperature continues to grow. The lowering of the electrical conductivity is especially manifested when Te/Th > 5. It is closely related to the delayed dissociation reactions and the consequent ionizations to produce electrons. Dissociation of molecules, which is controlled by the heavy-particle temperature, does not occur until the corresponding electron temperature is reached. This shifts the ionization towards higher electron temperatures as θ increases. Once dissociation starts, the electrical conductivity increases rapidly due to immediate ionization. As clearly shown in figure 3, the electron number density increases logarithmically with Te/Th at a fixed Te for Te > 15 000 K and it is always higher than the equilibrium value. Consequently, the electrical conductivity for Te > 15 000 K is always higher than the equilibrium value and increases with Te/Th.
Figure 9. Electrical conductivity of PTFE plasmas as a function of electron temperature with different degrees of non-equilibrium at atmospheric pressure.
3.3. Transport coefficients 3.3.1. Viscosity. For all cases with different degrees of non-equilibrium, the viscosity first increases with electron √ temperature up to Te = 10 000 K. This is because of the Th dependence of viscosity of neutral gases and the decrease in neutral–neutral collision integrals. Viscosity then decreases when Coulomb interaction, which is stronger than neutral– neutral interaction, starts to dominate. On the other dimension, when the degree of non-equilibrium increases, the viscosity peak is reduced and the rate of reduction with respect to the degree of non-equilibrium slows down at higher Te/Th. Indeed, viscosity is primarily a property of the heavy particles: for a given Te, if θ increases, Th decreases, resulting in a drop in the momentum transport and hence in a drop in the viscosity value. Furthermore, the electron temperature corresponding to the viscosity peak shifts slightly towards higher temperature when Te/Th increases because ionization occurs at a higher electron temperature but lower heavyparticle temperature.
3.3.3. Thermal conductivity. Different thermal conductiv-
ity components of the PTFE plasmas with a degree of nonequilibrium of three at atmospheric pressure are presented in figure 10. In the temperature range where dissociation and ionization take place (Te > 5000 K), the reactive term makes a major contribution. The translational contribution of electrons becomes important at higher temperatures (Te > 15 000 K). The translational and internal contribution of heavy particles is only important when Te Th) takes place in the plasma element adjacent to the wall surface due to the strong cooling effect of wall ablation which absorbs the heat emitted from the arc. Additionally, the non-LTE model and LTE model include the deviation of the plasma parameters and the ablation properties. For example, a 22% underestimate of the cumulative ablated mass over the whole discharge period by the non-LTE model has been obtained in a standard case compared with that by the LTE model. This indicates the need to consider the influence of the departure from LTE on the description of the ablationcontrolled arc discharge process. For this, the two-temperature plasma properties calculated in the present work enable the modeling of wall ablation-controlled plasma processes.
[1] Zhang J L, Yan J D, Murphy A B, Hall W and Fang M T C 2002 Computational investigation of arc behavior in an auto-expansion circuit breaker contaminated by ablated nozzle vapor IEEE Trans. Plasma Sci. 2 706–19 [2] Paul K C, Sakuta T, Takashima T and Ishikawa M 1997 The dynamic behaviour of wall-stabilized arcs contaminated by Cu and PTFE vapours J. Phys. D: Appl. Phys. 30 103 [3] Yang F, Wu Y, Rong M Z and Niu C P 2013 Low-voltage circuit breaker arcs—simulation and measurements J. Phys. D: Appl. Phys. 46 273001 [4] Hong D, Dussart R, Cachoncinlle C, Rosenfeld W, Gotze S, Pons J, Viladrosa R, Fleurier C and Pouvesle J M 2000 Study of a fast ablative capillary discharge dedicated to soft x-ray production Rev. Sci. Instrum. 71 15–9 [5] Schönherr T, Nees F, Arakawa Y, Komurasaki K and Herdrich G 2013 Characteristics of plasma properties in an ablative pulsed plasma thruster Phys. Plasmas 20 033503 [6] Keidar M, Boyd I D and Beilis I I 2000 Electrical discharge in the Teflon cavity of a coaxial pulsed plasma thruster IEEE Trans. Plasma Sci. 28 376–85 [7] Burton R L and Turchi P J 1998 Pulsed plasma thruster J. Propul. Power 14 716–35 [8] Kim S H, Yang K S, Lee Y H, Kim J S and Lee B H 2009 Electrothermal-chemical ignition research on 120 mm gun in Korea IEEE Trans. Magn. 45 341–6 [9] Keidar M and Boyd I D 2006 Ablation study in the capillary discharge of an electrothermal gun J. Appl. Phys. 99 053301 [10] Autrique D, Gornushkin I, Alexiades V, Chen Z, Bogaerts A and Rethfeld B 2013 Revisiting the interplay between ablation, collisional and radiative processes during ns-laser ablation Appl. Phys. Lett. 103 174102 [11] Wang Z B, Hong M H, Lu Y F, Wu D J, Lan B and Chong T C 2003 Femtosecond laser ablation of polytetrafluoroethylene (Teflon) in ambient air J. Appl. Phys. 93 6375 [12] Rat V, Murphy A B, Aubreton J, Elchinger M F and Fauchais P 2008 Treatment of non-equilibrium phenomena in thermal plasma flows J. Phys. D: Appl. Phys. 41 183001 [13] Wang W Z, Yan J D, Rong M Z and Spencer J W 2013 Theoretical investigation of the decay of an SF6 gas-blast arc using a two-temperature hydrodynamic model J. Phys. D: Appl. Phys. 46 065203 [14] Wang W Z, Kong L H, Geng J Y, Wei F Z and Xia G Q 2017 Wall ablation of heated compound-materials into nonequilibrium discharge plasmas J. Phys. D: Appl. Phys. 50 074005 [15] Wu Y et al 2016 Calculation of 2-temperature plasma thermo-physical properties considering condensed phases: application to CO2–CH4 plasma: part 1. Composition and thermodynamic properties J. Phys. D: Appl. Phys. 49 405203 [16] Niu C et al 2016 Calculation of 2-temperature plasma thermo-physical properties considering condensed phases: application to CO2–CH4 plasma: part 2. Transport coefficients J. Phys. D: Appl. Phys. 49 405204 [17] Chervy B, Riad H and Gleizes A 1996 Calculation of the interruption capability of SF6–CF4 and SF6–C2F6 mixtures. I. Plasma properties IEEE Trans. Plasma Sci. 24 198–217 [18] Wang W Z, Wu Y, Rong M Z, Éhn L and Černušák I 2012 Thermodynamic properties and transport coefficients of F2, CF4, C2F2, C2F4, C2F6, C3F6 and C3F8 plasmas J. Phys. D: Appl. Phys. 45 285201 [19] Kovitya P 1984 Thermodynamic and transport properties of ablated vapors of PTFE, alumina, Perspex and PVC in the temperature range 5000–30 000 K IEEE Trans. Plasma Sci. PS-12 38–42
Acknowledgments This work was supported by National Natural Science Foundation of China (grant no. 51407182), Beijing Natural Science Foundation (grant no. 3154044), the open project of State Key Laboratory of Electrical Insulation and Power Equipment (grant no. EIPE14208), along with Innovative Research Fund and Internship Project of Qian Xuesen Laboratory of Space Technology. This work was completed during the period when Dr Weizong Wang worked in the Qian Xuesen Laboratory of Space Technology. His current affiliation is University of Antwerp.
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[37] Ferziger J H and Kaper H G 1972 Mathematical Theory of Transport Processes in Gases (Amsterdam: North-Holland) [38] Devoto R S 1967 Third approximation to the viscosity of multicomponent mixtures Phys. Fluids 10 2704–6 [39] Bonnefoi C 1983 PhD Thesis Limoges University, France [40] Rat V, André P, Aubreton J, Elchinger M F, Fauchais P and Lefort A 2001 Transport properties in a twotemperature plasma: theory and application Phys. Rev. E 64 26409 [41] Zhang X N, Li H P, Murphy A B and Xia W D 2013 A numerical model of non-equilibrium thermal plasmas. I. Transport properties Phys. Plasmas 20 033508 [42] Colombo V, Ghedini E and Sanibondi P 2009 Twotemperature thermodynamic and transport properties of argon–hydrogen and nitrogen–hydrogen plasmas J. Phys. D: Appl. Phys. 42 055213 [43] Zhang X N, Li H P, Murphy A B and Xia W D 2015 Comparison of the transport properties of two-temperature argon plasmas calculated using different methods Plasma Sources Sci. Technol. 24 035011 [44] Butler J N and Brokaw R S 1957 Thermal conductivity of gas mixtures in chemical equilibrium J. Chem. Phys. 26 1636–43 [45] Bonnefoi C, Aubreton J and Mexmain J M 1985 Z. Naturforsch A 40 885–91 [46] Chen X and Li H P 2003 The reactive thermal conductivity for a two-temperature plasma Int. J. Heat Mass Transfer 46 1443–54 [47] Rat V, Andr´e P, Aubreton J, Elchinger M F, Fauchais P and Lefort A 2002 Two-temperature transport coefficients in argon–hydrogen plasmas—II: inelastic processes and influence of composition Plasma Chem. Plasma Process. 22 475–93 [48] Nemchinsky V 2005 Dissociation reactive thermal conductivity in a two-temperature plasma J. Phys. D: Appl. Phys. 38 3825–31 [49] Ghorui S, Heberlein J V R and Pfender E 2008 Thermodynamic and transport properties of twotemperature nitrogen–oxygen plasma Plasma Chem. Plasma Process. 28 553–82 [50] Wang W Z, Rong M Z, Yan J D and Wu Y 2002 The reactive thermal conductivity of thermal equilibrium and nonequilibrium plasmas: application to nitrogen IEEE Trans. Plasma Sci. 40 980–9 [51] Ramshaw J D 1993 Hydrodynamic theory of multicomponent diffusion and thermal diffusion in multitemperature gas mixtures J. Non-Equilib. Thermodyn. 18 121–34 [52] Ramshaw J D 1996 Simple approximation for thermal diffusion in ionized gas mixtures J. Non-Equilib. Thermodyn. 21 233–8 [53] Boulos M I, Fauchais P and Pfender E 1994 Thermal Plasmas: Fundamentals and Applications (New York: Plenum) [54] Laricchiuta A et al 2009 High temperature mars atmosphere. Part I: transport cross section Eur. Phys. J. D 54 607–12 [55] Murphy A B and Arundell C J 1994 Transport coefficients of argon, nitrogen, oxygen, argon–nitrogen, and argon–oxygen plasmas Plasma Chem. Plasma Process. 14 451–90 [56] Mason E A and Munn R J 1967 Transport coefficients of ionized gases Phys. Fluids 10 1827–32 [57] Devoto R S 1973 Transport properties of ionized gases Phys. Fluids 16 616–23 [58] Sokolova I 2000 High temperature gas and plasma transport properties of F2 and CF4 mixtures Fluid Phase Equilib. 174 213–20
[20] Wang W Z, Rong M Z, Wu Y, Spencer J W, Yan J D and Mei D H 2012 Thermodynamic and transport properties of two-temperature SF6 plasmas Phys. Plasmas 19 083506 [21] Wang W Z, Rong M Z, Yan J D, Murphy A B, and Spencer J W 2011 Thermophysical properties of nitrogen plasmas under thermal equilibrium and non-equilibrium conditions Phys. Plasmas 18 113502 [22] Potapov A V 1966 Chemical equilibrium of multi-temperature systems High Temp. 4 48–51 [23] van de Sanden M C M, Schram P P J M, Peeters A G, van der Mullen J A M and Kroesen G M W 1989 Thermodynamic generalization of the Saha equation for a two-temperature plasma Phys. Rev. A 40 5273–6 [24] Wang W Z, Rong M Z and Spencer J W 2013 Nonuniqueness of two-temperature Guldberg–Waage and Saha equations: influence on thermophysical properties of SF6 plasmas Phys. Plasmas 20 113504 [25] Giordano D and Capitelli M 1995 Two-temperature Saha equation—a misunderstood problem J. Thermophys. Heat Transfer 9 803–4 [26] Gleizes A, Chervy B and Gonzalez J J 1999 Calculation of a two-temperature plasma composition: bases and application to SF6 J. Phys. D: Appl. Phys. 32 2060–7 [27] Colombo V, Ghedini E and Sanibondi P 2011 Twotemperature thermodynamic and transport properties of carbon–oxygen plasmas Plasma Sources Sci. Technol. 20 035003 [28] Drellishak K S, Aeschliman D P and Cambel A B 1965 Partition functions and thermodynamic properties of nitrogen and oxygen plasmas Phys. Fluids 8 1590 [29] Bacri J and Raffanel S 1987 Calculation of some thermodynamic properties of air plasmas: internal partition functions, plasma composition, and thermodynamic functions Plasma Chem. Plasma Process. 7 53 [30] Ralchenko Y, Kramida A E, Reader J and NIST ASD Team 2008 NIST Atomic Spectra Database (Version 3.1.5) (Gaithersburg, MD: National Institute of Standards and Technology) (http://physics.nist.gov/PhysRefData/ASD/ levels_form.html) [31] Chase M W, Davies C A, Downey J R, Frurip D J, McDonald R A and Syverud A N 1985 JANAF Thermochemical Tables 3rd edn (Washington, DC: American Chemical Society) Chase M W, Davies C A, Downey J R, Frurip D J, McDonald R A and Syverud A N 1985 J. Phys. Chem. Ref. Data 14 1211–60 [32] Ghorui S, Heberlein J V R and Pfender E 2007 Thermodynamic and transport properties of twotemperature oxygen plasmas Plasma Chem. Plasma Process 27 267–91 [33] Wang W Z, Wu Y and Rong M Z 2014 Influence of ablated PTFE vapor entrainment on critical dielectric strength of hot SF6 gas IEEE Trans. Dielectr. Electr. Insul. 21 1478–85 [34] André P, Abbaoui M, Augeard A, Desprez P and Singo T 2016 Study of condensed phases, of vaporization temperatures of aluminum oxide and aluminum, of sublimation temperature of aluminum nitride and composition in an air aluminum plasma Plasma Chem. Plasma Process. 36 1161–75 [35] Hirschfelder J O, Curtis C F and Bird R B 1964 Molecular Theory of Gases and Liquids 2nd edn (New York: Wiley) [36] Chapman S and Cowling T G 1970 The Mathematical Theory of Non-Uniform Gases 3rd edn (Cambridge: Cambridge University Press)
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