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DOI 10.1007/s11090-014-9543-3
ORIGINAL PAPER
Transport Coefficients of High Temperature SF6–He
Mixtures Used in Switching Applications
as an Alternative to Pure SF6
Weizong Wang • Mingzhe Rong • Yi Wu
Received: 13 January 2014 / Accepted: 28 February 2014
Ó Springer Science+Business Media New York 2014
Abstract Sulfur hexafluoride (SF6) gas has a quite high global warming potential and
hence it is required that applying any substitute for SF6 gas. Much interest in the use of a
mixture of helium and SF6 as arc quenching medium were investigated indicating a high
performance of arc interruption. The calculated values of transport coefficients of mixtures
of SF6–He mixtures, at high temperatures are presented in this paper: to the knowledge of
the authors, related data have not been reported in the literature. The species composition
and thermodynamic properties are determined by the method of Gibbs free energy minimization, using standard thermodynamic tables. The transport properties including electron
diffusion coefficients, viscosity, thermal conductivity and electrical conductivity, are
evaluated by using the Chapman–Enskog method expanded up to the third-order
approximation (second-order for viscosity). Particular attention is paid to the collision
integral database by the use of the most accurate and recent cross-sections or interaction
potentials available in the literature. The calculations, which assume local thermodynamic
equilibrium, are performed in the temperature range from 300 to 30,000 K for different
pressures between 0.1 and 16 atm. An evaluation of the current interruption performance
by adding He into SF6 is discussed from a microscopic point of view. The properties with
regard to SF6–He mixtures calculated here are expected to be reliable because of the
improved collision integrals employed.
Keywords SF6–He mixtures Transport coefficients Switching application Arc
quenching medium
W. Wang (&)
Qian Xuesen Laboratory of Space Technology, China Academy of Space Technology,
Beijing 100094, People’s Republic of China
e-mail: [email protected]
W. Wang M. Rong Y. Wu
State Key Laboratory of Electrical Insulation and Power Equipment, Xi’an Jiaotong University,
Xi’an 710049, Shaanxi, People’s Republic of China
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Introduction
Sulfur hexafluoride (SF6) as the electric power industry’s presently preferred gaseous dielectric
and arc quenching medium is almost exclusively used in the transmission and distribution of
electrical energy. Of these applications, gas insulated circuit breakers and current interruption
equipments accounts for most of this amount [1, 2]. However, it has been shown that the strong
infrared absorption of SF6 and its long lifetime in the environment are the reasons for its
extremely high global warming potential which for a 100-year time horizon is estimated to be
*24,000 times greater (per unit mass) than that of CO2, the predominant contributor to the
greenhouse effect. Therefore, its impact on the environment has rekindled interest in finding
replacement gases used in high voltage electrical equipment [3–7]. Considering the relatively
poor dielectric strength of environment-friendly pure gases and gas mixtures such as air, an
alternative solution is to mix with electronegative gases, including SF6, at partial concentrations
of a few percent with another gas as possible substitute gases for pure SF6. Of these, SF6/He
mixtures seem to be good candidate, and are widely investigated because of their effectiveness
for arc interruption. For example, Grant et al. [8] investigated the recovery performance of
SF6–He mixtures indicating the performance of SF6–He mixtures which seem to be higher than
pure SF6 for virtually all mixture compositions from 75 to 25 % SF6.
For circuit breakers, the fast thermal and dielectric recovery of SF6 (short time constant for
increase in resistivity) which contributes to its high interruption capability is closely connected with its properties such as excellent thermal cooling ability and high dielectric
strength. However, recent investigation concerning on the critical breakdown field of hot
SF6–He mixtures has shown that adding He into SF6 hardly contributes to an enhancement of
the dielectric strength because helium is not an electronegative gas [9]. We should further
investigate the fundamental properties of SF6–He mixtures such as their thermodynamic
properties and transport coefficients and acquire the main effects important for a high current
interruption performance of SF6–He mixtures. There exist a large number of calculations of
species composition, thermodynamic properties and transport coefficients for pure SF6 [10–
18] and He [19–23] arc plasma under both local thermodynamic equilibrium and non-equilibrium conditions. However, no data related to the thermodynamic properties and transport
coefficients of high temperature SF6–He mixtures were reported in the literature.
This paper is, therefore, aimed at utilizing the available data to obtain a more reliable
calculation of the species composition, the thermodynamic properties and transport coefficients of SF6–He mixtures under the assumption of local thermodynamic equilibrium (LTE).
The first part of this work is thus devoted to the calculation of the plasma composition and
thermodynamic properties for SF6–He mixtures under different molar proportions in an
extended temperature range 300–30,000 K and a wide pressure range 0.10–16 atm, conditions which satisfy most thermal plasma modelling requirements. The second part of this
work recalls the bases of the Chapman–Enskog method and presents the selected collision
integrals allowing the determination of the transport coefficients (electron diffusion coefficients, viscosity, electrical conductivity and thermal conductivity). The last part gives a
discussion of the results based on an evaluation of the current interruption performance by
adding He into SF6 from a microscopic point of view and a conclusion is drawn as well.
Composition and Thermodynamic Properties
The determination of the species composition, which is a prerequisite to obtaining thermodynamic properties and transport coefficients of mixtures [24], was calculated as a
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function of temperature and pressure based on the method of minimizing the Gibbs energy
of a system [25, 26]. In the calculation, it is assumed that the mixture of high temperature
SF6–He gas is composed of a total of 28 different species including relevant atoms, ions
and molecules as well as electrons: SF6 species of SF6, SF5, SF4, SF3, SF2, SF, SSFF,
FSSF, F2, S2, F, S, SF?, SF-, S?, F?, S-, F-, S2?, F2?, S3?, F3?, S2?, F2? as well as
helium species of He, He?, He2? and e. Other molecular ions are neglected because of
their low amount appearing in the system. The Debye–Hückel correction was taken into
account and applied to the chemical potential of charged species, and to the total number
density of the plasma, as described by Kovitya [27]. The required thermodynamic data for
neutral atoms and positively-charge atomic ions were calculated from the internal partition
functions, which were derived from the energy level and degeneracy tabulated by the NIST
(National Institute of Standards and Technology) Atomic Spectra Database [28]. Different
extrapolation approaches which deal with the missing levels to complete the level series
have been developed in the literature, such as the traditional Ritz–Rydberg approximation
or the simplified approach. We have adopted a simplified method initially described by
Milone and Merlo [29] to compute the atomic partition function. This technique is based
on the grouping of atomic levels into several groups and shows good agreement with
reference calculations obtained by direct summation over a complete set obtained through
Ritz–Rydberg extrapolations [30–32]. This simplified method can lead to great convenience in the calculation of atomic partition function. Data for other species were taken
from the JANAF Thermochemical Tables in the form of polynomials whose coefficients
were fitted using a least-squares method and extended to higher temperature by means of
the formulas and the molecular data given with the table [33]. The relations used to
determine the composition are not all linear in the independent variables and therefore an
iteration procedure is generally required for their solution. The minimization method of
Gordon and McBride using Lagrange multipliers along with steepest descent Newton–
Raphson iteration is utilized to solve the non-linear equation system numerically [26].
Figure 1 presents the temperature dependence of specie number density of 50 % SF6
and 50 % He (in molar proportions) at atmospheric pressure. As the continuous dissociation of sulfur fluoride, the number density of atomic fluoride increases fairly rapidly
and then decreases at a high temperature due to its high ionization potential. Hence, the
free fluorine atom dominates in a wide temperature range from 1,700 to 15,000 K.
Ionization starts at around 3,000 K and the charged ions exist initially in the form of S2?
and F-. With further temperature increase, atomic sulfur gradually ionizes and the
concentration of free electrons rises. Helium exists almost in the form of atomic specie
in a wide temperature range where atomic Fluorine starts to ionize due to its much
higher ionization potential (24.5 eV) than that of atomic fluorine (17.422 eV). As a
result, the addition of helium into sulfur fluoride can inhibit the ionization of gaseous
mixture as we can find in Fig. 2 and hence reduce the ionization degree at the same
temperature.
Thermodynamic properties, such as enthalpy and specific heat can be determined
relatively simply once the composition is known, using the mass, using the standard
formulas. The detailed expressions for these physical quantities can be found in the
Ref. [34]. Figure 3 shows the evolution of the mass density under different mixing
ratios in SF6–He mixture (in molar proportions) at atmospheric pressure as a function
of temperature. Due to the pressure conservation and continuous dissociation and
ionization, the mass density experiences a gradual reduction with increasing temperature. Because helium has the lightest mass of all heavy species, the continuous addition
of helium into sulfur fluoride brings a monotonically decreasing mass density at a fixed
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Fig. 1 Temperature dependence of equilibrium composition of 50 % SF6 and 50 % He at atmospheric
pressure
temperature. A decrease in mass density is simply observed (for a given temperature
and pressure) with increasing helium proportion because this gas contains the light
element of helium.
The peaks in the specific heat at constant pressure as presented in Fig. 4 that originate
from the heats of the dissociation and ionization reactions. Taking the 5 % SF6 and 95 %
He mixture as an example, the peaks in the specific heat at constant pressure at atmospheric pressure correspond to successive dissociations of sulfur fluoride at around 1,600,
2,000 and 2,600 K, the first ionization of sulfur, fluorine and helium at around 10,000,
17,000 and 22,000 K. The peak related to the second ionization of sulfur is not apparent
due to the low concentration of S? in pure SF6. For SF6–He mixtures, the specific heat
peak due to first ionization of helium at around 22,000 K is superimposed on the one
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Fig. 2 Temperature dependence of equilibrium electron concentration in SF6–He mixture under different
mixing ratios (in molar proportions) at atmospheric pressure
Fig. 3 Temperature dependence of mass density under different mixing ratios in SF6–He mixture (in molar
proportions) at atmospheric pressure
associated with the second ionization of sulfur at around 28,000 K, as demonstrated in
Fig. 4.
The influence of pressure on specific heat at constant pressure is plotted in Fig. 5 for
50 % SF6 and 50 % He mixture. The curve peaks which are related to dissociation and
ionization are shifted to higher temperatures with decreasing amplitude. This behaviour is
general whatever the initial composition caused by delayed chemical reaction with the
rising pressure.
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Fig. 4 Temperature dependence of specific heat at constant pressure under different mixing ratio in SF6–He
mixture (in molar proportions) at atmospheric pressure
Fig. 5 Influence of pressure on specific heat at constant pressure for 50 % SF6 and 50 % He (in molar
proportions) at the temperature larger than 1,000 K
Collision Integrals
The calculation of transport coefficients, namely diffusion coefficients, electrical conductivity, thermal conductivities and viscosity, requires the knowledge of collision integrals, which take into account the pair interaction potential between two colliding species i
and j. They are statistical averages over a Maxwellian distribution of the binary collision
cross sections, and are defined as follows [35–37]:
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ðl;sÞ
Xij
sffiffiffiffiffiffiffiffiffiffi Z1
kT
¼
exp c2ij c2sþ3
Qlij ðgÞdcij
ij
2plij
ð1Þ
0
The transport cross sections Qlij(g) are evaluated by
Qlij ðgÞ
¼ 2p
Z1
1 cosl v b db
ð2Þ
0
where the parameters lij, v, g and b are the reduced mass, the angle by which the molecules
are deflected in the centre of gravity coordinate system, section, the relative velocity of the
two particles, and the impact parameter of the colliding species i and j, respectively. The
indices (l, s) are directly related to the order of approximation used for the transport
coefficients. The angle of deflection depends on the intermolecular potential of the colliding species.
It should be pointed out that in our current work only the ground states of species are
taken into account on transport processes although the electronically excited atoms poses
important influence. Recent studies indicate that the electronically excited states apparently
have much higher cross sections than the ground states and they can apparently affect the
transport coefficients especially at high pressure [38–40]. Therefore, the computed values
of reactive thermal conductivity in this study may require further improvement in the
future regardless of the fact that transport cross-sections of the excited states of all the
species with regard to the gaseous mixture of SF6/He, are not available in the literature at
present.
Heavy Species Interaction
For the neutral species interactions, only the elastic collision process is taken into account.
For interactions in which charge exchange occurs, collision integrals with odd order l take
into account both elastic and inelastic interaction by the empirical mixing rule [41].
Collision integrals between neutral and ion species interaction with even l are wholly
determined by the elastic interactions. The He–He interaction as well as elastic He–He?
interaction was described by the accurate new potentials determined from an ab initio
calculation as treated in previous work [42]. For other neutral species interactions and
neutral-ion interactions, an improvement of the Lennard–Jones potential in the framework
of a phenomenological approach developed by Capitelli et al. [43, 44] has been adopted to
evaluate related elastic collision process. This model potential can be defined in terms of
fundamental physical properties of involved interacting partners (polarizability a, charge,
number of electrons effective in polarization). Relevant species polarizability data
involving SF6 and helium species along with their source are respectively taken from
tabulated tables in our previous work [14, 42] and not given in detail here. No accurate
experimental data or theoretical calculations are available in the literature for the polarizability of higher order ions He2?, S2?, F2?, S3?, F3?. Hence, collision integrals for
elastic interactions involving these species have been derived using a polarization potential
model [45].
For both the interactions between S–S?, F–F? and He–He?, the charge-transfer collision integral were determined by a least-squares fit to calculated transport cross section
data as treated in previous work [42, 46]. The charge exchange cross-sections for collisions
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between unlike species (e.g.Y þ X ! X þ Y) are small compared to the elastic collision integrals, and are neglected in this paper. No accurate experimental data or theoretical
calculation of charge-exchange cross section are available in the literature for the interactions between other parent atom or molecule X and its ion X- or X?, their cross section
data were determined using an empirical formula [47].
Charged Species Interaction
The collision integrals for the charged–charged interactions were calculated using the
screened Coulomb potential. The Debye length takes into account the shielding effects of
both ions and electrons [48, 49].
Electron-Neutral Interaction
The collision integrals for interactions between electrons and neutral species have been
calculated as a function of temperature by straightforward integration of the Q1(E),
Q2(E) and Q3(E) cross-sections as a function of electron energy. When Q2(E) and
Q3(E) are not available, their ratios to the momentum transfer cross-section Q1(E) can be
determined by numerical integration of differential elastic cross sections (DCS), if these
are available. The differential cross sections dr/dX can be numerically integrated over all
scattering angles to obtain the transport cross sections as a function of the interaction
energy. For the interactions e–F, e–S and e–He, we applied the collision integrals used in
our previous work [42, 46]. Some interactions e–X2 (X = S, F) were treated according to
the works of André et al. [50] who estimated the momentum-transfer cross-sections Qe-X2
from available momentum-transfer cross-sections Qe–X. For other electron–neutral interactions for which no available experimental or calculated data are available in the literature, the cross-sections were estimated by assuming that the cross-sections are independent
of energy and dominated by polarization effects [51]. Because of the very small number
densities of these neutral species in the plasmas as well as the dominant electron–ion
interaction with much larger collision cross section as temperature rises, these simplifications did not affect the transport coefficients relevant with electron transport.
Determination of Transport Coefficients
Transport coefficients are calculated using the classical Chapman–Enskog method, which
has been exhaustively detailed in the literature [35–37]. The distribution function of the
different species is assumed to be the Maxwellian distribution function perturbed by a firstorder perturbation function. The latter is developed in terms of a series of Sonine polynomials and then expressed by means of the expansion coefficients, bringing about a
linearization of the Boltzmann equation and introducing systems of linear equations. The
solution of these linear equations to a selected order of approximation allows one to obtain
transport coefficients which are governed by elastic collisions between all the species
represented through effective collision integrals. The order chosen in the calculation
determines the dimensions of the system of linear equations with which the distribution
function and the Boltzmann equation are solved with an approximate expansion expression. This paper utilizes the third-order approximation for transport properties except
viscosity, for which the second-order approximation is considered. For thermal
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conductivity, besides the translational component, the contributions from the chemical
reactions and internal energy should also be taken into account respectively by Meador and
Stanton’s derivation [52] and the Hirschfelder–Eucken approximation [53–55].
The equilibrium properties of pure SF6 and He plasmas have been studied widely in the
literature, since they are very important for many applications. There are few experimental
measurements of transport coefficients at high temperatures, so it is important to check the
consistency of our equilibrium calculations with other theoretical results. Our calculated
transport coefficients for both types of plasmas have been compared with a wide database
in our previous work [42, 46] and not presented here in order to avoid a repeat. Generally
good agreement was found with most data for pure SF6 and He plasmas showing that the
collision integrals used here is reliable.
Diffusion Coefficients
Due to large number of the ordinary diffusion coefficients required to describe plasmas
(one for each pair of species), only the values of the electrons thermal diffusion coefficient
are presented in Fig. 6. The influence of the pressure on thermal conductivity is illustrated
in Fig. 7. With the rise of helium concentration, electron thermal diffusion coefficient
decreases sincerely below 22,000 K. Above 22,000 K, the addition of helium into SF6
increases the electron thermal diffusion coefficients. The electron thermal diffusion
coefficient depends appreciably on the pressure. However, the dependence is significantly
reduced at lower temperature owing to the very low concentration of electrons in the
mixtures.
Viscosity
The dependence of the viscosity on pressure and the mixing ratios in SF6–He mixture is
much more pronounced, as shown in Figs. 8 and 9. The viscosity increases with
Fig. 6 Temperature dependence of electron thermal diffusion coefficient under different mixing ratios in
SF6–He mixture (in molar proportions) at atmospheric pressure
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Fig. 7 Temperature dependence of electron thermal diffusion under different mixing ratio in SF6–He
mixture (in molar proportions) at atmospheric pressure
Fig. 8 Temperature dependence of viscosity under different mixing ratios in SF6–He mixture (in molar
proportions) at atmospheric pressure
temperature when neutral species dominate, and decreases when significant ionization
occurs as a result of the large collision integrals for the Coulomb interaction. In the rising
stage of viscosity, the addition of helium into sulfur fluoride brings a slightly rising
viscosity value due to the smaller neutral–neutral interaction collision integrals involving
helium specie. The location of viscosity curve peaks depends on ionization energies and on
masses of species. For pure SF6, the peak corresponds to the ionization of atomic sulfur at
around 12,000 K. However, the maximum value is related to the ionization of atomic
helium for pure He. The peak location greatly depends on the mixing ratios of SF6 and He
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Fig. 9 Influence of pressure on viscosity for 50 % SF6 and 50 % He (in molar proportions)
which influence the ionization degree of gaseous mixture. With the addition of helium into
sulfur fluoride, the peak of viscosity gradually shifts to a higher temperature with a
decreasing value due to the smaller He–He? elastic collision integral than that of S–S?. In
the decreasing state of viscosity, the addition of helium into sulfur fluoride causes a rising
value mainly due to the decreasing ionization degree and charged species. Figure 9 indicates that the viscosity at a given temperature increases with pressure, at least at those
pressures for which ionization is significant. This is because the degree of ionization
decreases for increased pressure, so the Coulomb interactions become less important.
Thermal Conductivity
The temperature dependence of the thermal conductivity of SF6–He mixture under different proportions is compared in Fig. 10 with that of pure sulfur fluoride and pure
helium. The addition of helium into sulfur fluoride increases the total thermal conductivity below 1,200 K and in the temperature range above 3,000 K. This behaviour can
favour thermal cooling effect of arc plasma by enhanced thermal conduction regardless
of the decreased reactive component of thermal conductivity in the temperature range
between 1,200 and 3,000 K. It is also noted that with the molar proportion of helium
lower than 50 % in the gaseous mixture, the total thermal conductivity in this temperature range has no large difference with that of pure SF6 indicating the potential of
replacing SF6 by SF6/He mixtures in high-voltage circuit breakers with certain mixing
ratios.
Figure 11 shows the different components of thermal conductivity for 50 % mixtures
of SF6 and He (in molar proportions) at atmospheric pressure. Below 1,200 K, the
translational component of heavy species contributes to most of the total thermal conductivity. With increasing temperature, the reactive component gradually plays a significant role due to the continuous dissociation and ionization especially in the
temperature range between 1,200 and 3,000 K in which the dissociation of SFx (x = 1,
6) takes place. The heavy species translational component increases slowly until around
11,000 K because the collision integrals for the interactions between neutral species
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Fig. 10 Temperature dependence of total thermal conductivity under different mixing ratio in SF6–He
mixture (in molar proportions) at atmospheric pressure
Fig. 11 Temperature dependence of the components of thermal conductivity of 50 % SF6 and 50 % He (in
molar proportions) at atmospheric pressure
decrease; after a plateau it then decreases slowly owing to the occurrence of ionization.
The contribution of electron translation to the total thermal conductivity, which is
affected mainly by the elastic collisions between electrons and ions, shows a monotonously rising trend and surpasses that of heavy species for temperatures exceeding
11,000 K. The internal component contributes little to the total thermal conductivity in
the whole temperature range considered here.
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Fig. 12 Influence of pressure on total thermal conductivity for 50 % SF6 and 50 % He (in molar
proportions)
Figure 12 shows the influence of pressure on thermal conductivity for 50 % SF6 and
50 % He (in molar proportions). As the temperature rises, the peaks that correspond to the
dissociation and ionization are shifted to higher temperatures for the same reason as
discussed in the case of specific heat. Above 18,000 K, a decreasing pressure brings a
decreasing number density of electrons and ions and hence a decreasing total thermal
conductivity.
Electrical Conductivity
At low temperatures, the electric conductivity varies almost proportionally to the square of
the electron number density and the influence of electron impact cross section between
electrons and neutral species is small because of a low ionization degree. As presented in
Fig. 13 and Table 1, the electrical conductivity of mixtures containing a few percent of
helium is slightly lower than that of pure sulfur fluoride below 22,000 K due to reduced
electron number density with the addition of He into SF6. Above 22,000 K, the collisions
between charged particles become the main interactions. The addition of He into SF6
decreases the contribution of collision integrals between electrons and ions especially
when the formation of multiply-charged ions occurs and leads to a decreased electrical
conductivity. Moreover, it is noted that even 50 % molar proportion of He will not
apparently change the value of electrical conductivity as a result that the fluoride species
are dominant in the gaseous mixture when continuous dissociation of SF6 occurs.
The electrical conductivity decreases as the pressure increases at temperatures below
about 11,000 K whereas the opposite effect is observed at high temperatures as shown in
Fig. 14. At low temperatures, the interactions between electrons and neutral species mainly
contribute to the electron mobility. Increasing pressures prohibit the ionization and
decrease the ionization degree. At higher temperatures, the interactions between electron
and charged species are predominant. The rising electrons number density with increasing
pressures leads to an increasing electrical conductivity.
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Fig. 13 Temperature dependence of electrical conductivity under different mixing ratio in SF6–He mixture
(in molar proportions) at atmospheric pressure
Table 1 Electrical conductivity of SF6–He mixtures at atmospheric pressure (S/m)
Temperature
(K)
Pure He
95 % He ?
5 % SF6
50 % He ?
50 % SF6
25 % He ?
75 % SF6
3,500
4,000
–
0.08576
0.27861
0.34372
–
0.90869
2.812
3.4014
4,500
–
5.8516
17.127
5,000
–
21.17
5,500
6.87E - 05
62.746
6,000
4.36E - 04
146.56
321.98
348.84
365.20
6,500
0.01701
288.05
567.04
604.52
626.45
7,000
0.1044
495.81
880.11
925.12
950.81
64.804
154.58
19.995
66.558
171.04
Pure SF6
0.39465
3.8412
21.996
78.925
181.33
Discussion and Conclusion
In this paper, a considerable effort has been devoted to the calculation of transport coefficients of SF6–He mixtures in local thermodynamic equilibrium for temperatures from 300
to 30,000 K and pressures from 0.1 to 16 atm, which are conditions relevant to switching
applications in high voltage circuit breakers. To our knowledge, this work fills the lack of
data in the literature. The plasma composition was determined by the minimization of the
Gibbs free energy, and thermodynamic properties were presented in detail. For the calculation of transport coefficients, use was made of collision integrals obtained by recent
intermolecular interaction studies. A reliable database of high-order collision integrals
involving all important neutral–neutral, neutral–ion, electron–neutral and charged interactions was developed especially for the interactions between SF6 species and helium
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Fig. 14 Influence of pressure on electrical conductivity for 50 % SF6 and 50 % He (in molar proportions)
species. Validation of the transport coefficients for pure SF6 and He determined using these
collision integrals, which was carried out in our previous work by comparing with available data in the literature, shows that these interactions are reliable. The properties with
regard to SF6–He mixtures calculated here are expected to be reliable because of the
improved collision integrals employed and can provide accurate reference data for use in
the simulation of plasmas in high voltage circuit breaker.
It should be noted that the assumption of local thermodynamic equilibrium, which
current properties computation and magnetohydrodynamic simulation of switching arcs
was strongly based on in the high current phase, is no longer valid in the current zero
period. When arc temperature decays too rapidly under gas blast with a very strong
quenching rates of heavy species temperature, the species in the chemical system do not
have enough time to reach equilibrium because the reaction rate is finite, chemical nonequilibrium may occur in the arc system. When the electron number density is not high
enough to allow sufficient transfer of energy between the electrons and heavy species, thus
causing electron temperature being substantially higher than that of heavy species and a
thermally non-equilibrium takes place. A kinetic model [56–58] and two-temperature
model [59] was respectively developed in the literature to describe the plasma state under
both chemically non-equilibrium and thermally conditions. Both non-equilibrium effects
can lead to an overpopulated concentration of electrons at a fixed gas temperature and
hence a larger electrical conductivity compared to the LTE condition [14, 15, 57]. The
detailed analysis of the influence of non-equilibrium effects on plasma properties of SF6
and He mixture is not given here due to its relatively complicated mechanism.
From the fundamental properties of high temperature SF6–He mixtures, a qualitative
evaluation of the interruption capability of the mixtures studied here can be proposed. For
arc and current interruption, the dielectric, and thermal cooling properties of the gas are
important. Characterization of the cooling capacity of an interrupting gaseous medium
involves consideration of the specific heat and thermal conductivity of the gas as well as
low-temperature electrical conductivity. Our previous investigation indicates that the
addition of He to SF6 contributes virtually nothing to the dielectric strength of the mixture
in the temperature range below 4,000 K because helium is a non-electronegative gas and
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does not attach electrons. However, from our current calculation, adding the light helium
gas into sulfur fluoride can efficiently increase the specific heat and thermal at the very of
gaseous mixtures at high temperatures (above 3,000 K) and at the relatively lower temperatures (below 12,000 K). In the temperature range where continuous dissociation of SF6
takes place, the gaseous mixture with molar proportion of helium no lower than 50 % still
maintains at a high level of specific heat at constant pressure and thermal conductivity
which is not significantly different than those of pure SF6. Low-temperature electrical
conductivity is another effect important for the current interruption especially thermal or
post-arc phase. Due to a much higher ionization potential of helium, its addition into SF6
shows a lower low-temperature electrical conductivity. Both high thermal cooling effect
and low low-temperature electrical conductivity can favour the thermal recovery of circuit
breaker during current interruption corresponding to the post-arc phase. Moreover, helium
is an inert gas and does not react chemically with either SF6, or the gas impurities present
in commercial SF6, or the system components. There is no such gas fast recovery problem
for SF6–He as other replacement gas like CF3I which cannot quickly reassemble, preferably to form their original molecular structure during the cooling process. For the latter,
some chemical products or physical systems must be included within the high voltage
circuit breaker in order to eliminate specific byproducts (iodine and graphite). Based our
computation analysis and other investigation in the literature, a mixture of SF6 and helium
has shown promise when used in gas insulated circuit breakers, and should be investigated
further.
Acknowledgments This work was supported by the Foundation for Innovative Research Groups of the
National Natural Science Foundation of China under Grant No. 51221005 and by the Chinese Government
Scholarship program for postgraduates and the Dual Collaborative PhD Degree Program between Xi’an
Jiaotong University and University of Liverpool.
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