The dielectric strength of dissociated binary and ternary gas mixtures containing helium, hydrogen, and nitrogen for cryogenic power applications is reported. The compositions of the dissociated gas species in the temperature range of 77–5000 K at 1.0–2.0 MPa are obtained by minimizing the Gibbs free energy assuming local chemical equilibrium. The resulting mole fractions of the dissociated gas species that vary as a function of temperature and pressure are used for calculating the density-reduced critical electric field representing the dielectric strength. The results suggest that the He-H2-N2 mixture has higher dielectric strength than the He-H2 and He-N2 mixtures, but NH3 would potentially accumulate over multiple arcing and cooling cycles and potentially cause long-term issues in cryogenic switchgear applications. On the other hand, the binary alternatives, the He-H2 and He-N2 mixtures, show lower dielectric strength than the ternary gas mixture but will maintain their original gas properties even over multiple arcing and cooling cycles. The results also show that the dielectric strength of the He-H2-N2 and He-H2 mixtures decreases substantially with increasing temperature whereas that of the He-N2 mixture stays nearly unchanged. The results of this study are useful for the fundamental understanding of gas dielectrics under arcing conditions in cryogenic switchgear applications and the development of resilient cryogenic power systems.
I. INTRODUCTION
Superconducting and cryogenic power systems offer much needed volumetric and gravimetric power density enhancements that enable advanced designs for higher system efficiency in future electric aircrafts and ships.1–3 Especially, an integrated all-cryogenic power system design is preferred as it minimizes the number of transitions of power from cryogenic to ambient environments, which are the major sources of heat load that increase the capital costs of cryogenic infrastructures and operational costs due to higher fuel consumption.4 The materialization of all-cryogenic power systems requires advanced protection systems, in which the development of compact and effective cryogenic switchgear technology is essential. As a part of this effort, we have been conducting research in the fields of cryogenic power electronics,5 cryogenic passive component research,6 high-temperature superconducting (HTS) cable design,7 cryogenic switchgear design,8 and the associated cooling technology and improved cryogenic dielectric media research.9–13
In this paper, we report the dielectric properties of dissociated cryogenic gas mixtures as switchgear technology involves wide temperature operations associated with arcing and cooling events. High temperature generated by arcs dissociates the initial gas mixture and forms various compositions of new gas species. As the dissociation process is temperature and pressure dependent, the dielectric strength of the dissociated mixture also varies with temperature and pressure. Generally, the dielectric strength weakens with increasing temperatures as large molecular gases that show stronger dielectric properties dissociate into smaller molecules that have weaker dielectric properties. The understanding of the dielectric strength variation in a switchgear is important since unwanted phenomena such as restrikes could occur at high temperatures due to reduced dielectric strength.
The compositions of the dissociated gas mixtures over the temperature range of 77–5000 K and pressures at 1.0–2.0 MPa are calculated based on the Gibbs free energy minimization method. Then the dielectric strength of the gas mixtures is represented in terms of the density-reduced critical electric field, which is obtained by equating the density-reduced ionization and attachment coefficients. In the study, we initially discuss the dielectric strength variation of the dissociated He-H2-N2 gas mixture over the temperature and pressure conditions. We selected the He-H2-N2 mixture since our previous studies reported the mixture as the most promising candidate for cryogenic power applications among potential cryogenic gas media owing to its unrivaled dielectric performance in normal cryogenic operating conditions (i.e., pre-arcing conditions).10,11 Under post-arcing conditions, however, the recombination process of the dissociated He-H2-N2 mixture may cause issues by forming NH3 in the system over numerous switching operations. To address the issue, we also report the dissociated gas compositions as well as the dielectric strength of He-H2 and He-N2 mixtures over the studied temperature and pressure conditions as potential binary alternatives to the ternary mixture of He-H2-N2. The results of the He-H2-N2, He-H2, and He-N2 mixtures commonly show a decreasing trend in dielectric strength with increasing temperature although the degree of change in dielectric strength varies by the gas mixture and the range of temperature.
II. DISSOCIATED GAS MIXTURES
As the initial step of the study, we calculate the compositions of dissociated gas species by minimizing the Gibbs free energy. The widely utilized method produces the composition data of dissociated gas mixtures in local chemical equilibrium as a function of temperature and pressure.14–19 For the Gibbs free energy minimization process, possible dissociated gas species need to be predetermined. For the He-H2-N2 mixture, He, H2, N2, NH3, NH2, NH, N, and H are assumed as the potential products. For the He-H2 mixture, He, H2, H, and for the He-N2 mixture, He, N2, and N are taken into account as possible dissociated gas species. The required thermodynamic data of each gas species that are required for the study are retrieved from the NIST database.20
Figure 1 shows the composition of the dissociated He-H2-N2 gas mixture as a function of temperature and pressure. The initial concentration of N2 in the mixture at 77 K is determined according to gas pressure. The maximum mole fraction of N2 is used as long as condensation does not occur. As a result, 4, 6, and 9 mol. % of N2 are used at 2.0, 1.5, and 1.0 MPa, respectively. Also, as reported in our previous studies,9–11 we limit the concentration of H2 to 7 mol. %, the estimated maximum concentration that is considered non-flammable in any mixture with air.21 Although Fig. 1 suggests that a substantial amount of NH3 exists at temperatures below 500 K, note that the formation of NH3 from the He-H2-N2 mixture is unlikely to occur with no arcing since the reaction kinetics are slow at low temperatures. However, the concentration of NH3 is likely to be considerable after an arcing event. This is because the temperature of a gas mixture near an arc column can be elevated to several thousands of kelvin, by which a substantial portion of the original gas mixture (i.e., He-H2-N2) would dissociate into atomic or smaller molecular gases such as N and H. Subsequently, as temperature decreases after the arc is quenched, some of the dissociated gas species would recombine and potentially form NH3 as the gas mixture reaches the local chemical equilibrium. As temperatures increases beyond 1000 K, the mole fractions of atomic and smaller molecular gas species including NH2, NH, N, and H increase rapidly while the mole fraction of NH3 becomes insignificant.
The compositions of dissociated He-H2-N2 mixtures at temperatures and pressures between 77 and 5000 K and 1.0–2.0 MPa.
The compositions of dissociated He-H2-N2 mixtures at temperatures and pressures between 77 and 5000 K and 1.0–2.0 MPa.
III. DIELECTRIC STRENGTH OF THE DISSOCIATED GAS MIXTURES
The composition of the gas mixtures obtained for all temperature and pressure conditions is used for calculating the dielectric strength of the gas mixtures in terms of the density-reduced critical electric field, which is obtained by equating the density-reduced ionization and attachment coefficients.10,11 The ionization and attachment coefficients are obtained by solving the Boltzmann equation with the two-term approximation method assuming local electron kinetics based on the electron scattering cross section data and the mole fraction of all gas species comprising the dissociated gas mixtures at a given temperature and pressure condition. More details regarding the two-term approximation method are available in our previous studies9–12 as well as in the following Refs. 29–31. It should be noted that we only account for electron kinetics in this study due to the lack of sufficient cross section data of ions although ion kinetics may play an important role in arcing conditions. The sources of the retrieved electron scattering cross section data are listed in Table I. Cross section data that are unavailable have been substituted by those of similar gas species for the analysis as reported in previous studies.32,33 In the present study, the unavailable cross section data of NH2 and NH are substituted by those of NH3 and N except for the ionization cross sections of both NH2 and NH, which are retrieved from the data reported by Joshipura et al.24
Electron scattering cross section data.
Collision . | Source . | Collision . | Source . |
---|---|---|---|
e–He | Reference 22 | e–NH2 | References 23 and 24 |
e–H2 | References 22 and 25 | e–NH | References 26 and 24 |
e–N2 | Reference 27 | e–N | Reference 26 |
e–NH3 | Reference 23 | e–H | Reference 28 |
Figures 2(a) and 2(b) show the density-reduced ionization and attachment coefficients at the two extreme temperatures of 77 K and 5000 K. For all three gas pressures investigated (1.0, 1.5, and 2.0 MPa), the ionization coefficient is not substantially different while the attachment coefficient is orders of magnitude larger at 77 K [Fig. 2(a)] than at 5000 K [Fig. 2(b)]. The substantially high attachment coefficient at 77 K is due to the higher mole fractions of H2 and NH3 at lower temperatures. The electron attaching properties of H2 and NH3 absorb and remove free electrons from the gas mixture, which is one of the main contributing factors of dielectric strength enhancement in gases. On the other hand, the lower attachment coefficient at 5000 K is due to the lower mole fractions of H2 and NH3 leading to fewer electron attaching processes. The E/N values, at which the ionization and attachment coefficients are equivalent, are the density-reduced critical electric field [(E/N)cr]. These values have been widely used in representing the dielectric strength of gas mixtures.9–11,30,31,34,35 However, (E/N)cr should not be directly considered as an actual breakdown voltage. In fact, (E/N)cr is derived solely based on the coefficients of electron kinetics. Note that according to Townsend's theory, breakdown voltage not only depends on the dielectric properties of gas media but also depends on the surface properties of electrodes including the secondary electron emission coefficient, which varies by numerous factors such as electrode material, temperature, and gas type. As shown by the arrows in Figs. 2(a) and 2(b), the E/N values, at which the ionization and attachment coefficients cross-over, are higher at 77 K than at 5000 K for all gas pressures. The results indicate that the dielectric strength of the mixture is stronger at lower temperatures.
Density-reduced ionization and attachment coefficients, and density-reduced critical electric field of He-H2-N2 mixtures. (a) Temperature: 77 K and (b) temperature: 5000 K.
Density-reduced ionization and attachment coefficients, and density-reduced critical electric field of He-H2-N2 mixtures. (a) Temperature: 77 K and (b) temperature: 5000 K.
By calculating the density-reduced ionization and attachment coefficients based on the gas mixture composition data in the temperature range of 77–5000 K at 1.0–2.0 MPa (Fig. 1), and equating the two coefficients, (E/N)cr values can be obtained as a function of temperature and pressure as shown in Fig. 3. The results show that (E/N)cr is substantially higher at temperatures below 500 K, which is due to the high concentration of NH3 in the respective temperature range. As the temperature increases from 500 K to 1000 K, NH3 concentration drops rapidly and so does the (E/N)cr value. In the temperature range of 1000–3000 K, the concentration of NH3 is significantly low and that of H increases. (E/N)cr stays almost at the same value between 1000 and 2500 K because the variation of NH3 and H is insignificant. At temperatures between 2500 and 3000 K, (E/N)cr gradually decreases due to the increasing concentration of H and the reduction of H2. Above 3000 K, (E/N)cr decreases more rapidly as H2 significantly decreases while the concentrations of H, N, NH, and NH2 further increase.
The main reason for the difference in the (E/N)cr values of 1.0–2.0 MPa is in the initial mole fraction difference of N2, in which higher mole fraction was allowed in lower pressure conditions. Moreover, it should be noted that the high concentration of NH3 in the low temperature range is unlikely to occur at normal cryogenic operation, but likely to occur as dissociated gas species recombine after an arcing event. Hence, the dielectric strength of the original gas mixture of He-H2-N2 under cryogenic conditions before an arcing event, in which NH3 does not exist, would be close to the (E/N)cr values between 1000 and 2000 K in Fig. 3.
Density-reduced critical electric field of dissociated He-H2-N2 mixtures as a function of pressure and temperature.
Density-reduced critical electric field of dissociated He-H2-N2 mixtures as a function of pressure and temperature.
IV. POTENTIAL LONG-TERM ISSUES OF THE TERNARY MIXTURE AND THE BINARY ALTERNATIVES
Although the He-H2-N2 mixture has been the most promising dielectric gas media for cryogenic power electronics, HTS cables, and HTS machines, it may introduce potential issues in applications that encounter arcing such as cryogenic switchgear. As discussed earlier in the study, multiple arcing and cooling cycles in a switchgear may gradually accumulate and freeze NH3 in the system, which will require frequent gas replacements to maintain its original dielectric performance.
As the alternative cryogenic media of the He-H2-N2 mixture, binary gas mixtures such as He-H2 or He-N2 can be used. To confirm how the binary gas mixtures dissociate at higher gas temperatures and to check whether the recombination process will result in the initial binary gas mixtures, we again use the Gibbs free energy minimization method to calculate the composition of the dissociated binary gas mixtures over the temperature range of 77–5000 K, at pressures between 1.0 and 2.0 MPa. Subsequently, the mole fractions of the dissociated gas species as well as the cross section data of each gas species are used to calculate the density-reduced critical electric field over the studied temperature and pressure conditions.
Figures 4(a) and 4(b) show the composition of the dissociated He-H2 and He-N2 mixtures as a function of temperature and pressure obtained by minimizing the Gibbs free energy. Both figures show that the composition of He remains unchanged while H2 and N2 dissociate into H and N, respectively, at high temperature. The dissociation process of H2 becomes significant above 2500 K, in which the mole fraction of H exceeds that of H2 above 3500 K. On the other hand, the dissociation process of N2 is relatively insignificant in the studied temperature range. Although the dielectric strength of the binary gas mixtures at normal cryogenic operating conditions is lower than that of the ternary mixture, the advantage of using the He-H2 and He-N2 mixtures is that the dissociated gas species would recombine to its initial composition and retain its initial physical properties even after multiple arcing and cooling cycles.
The compositions of dissociated gas mixtures at temperatures and pressures between 77 and 5,000 K and 1.0–2.0 MPa. (a) He-H2 mixture and (b) He-N2 mixture.
The compositions of dissociated gas mixtures at temperatures and pressures between 77 and 5,000 K and 1.0–2.0 MPa. (a) He-H2 mixture and (b) He-N2 mixture.
The dielectric strength represented by the density-reduced critical electric field corresponding to the compositions of the dissociated binary gas mixtures shown in Figs. 4(a) and 4(b) is presented in Figs. 5(a) and 5(b), respectively. Similar to the case of the ternary He-H2-N2 mixture shown in Fig. 3, the (E/N)cr values of the He-H2 mixture decrease substantially with increasing temperature. The decreasing (E/N)cr values corresponds to the gas composition of Fig. 4(a), in which a significant decrease in H2 and a significant increase in H are observed above 2500 K. In contrast, as shown in Fig. 5(b), the (E/N)cr values of the He-N2 mixture remain almost unchanged over the entire temperature range. The steady trend is due to the insignificant amount of N2 dissociation within the studied temperature range as shown in Fig. 4(b). It should be noted that the (E/N)cr values corresponding to 1.0–2.0 MPa are mainly different because the initial composition of N2 is higher at lower pressures to maximize the dielectric strength at normal cryogenic operating conditions, yet limited such that condensation does not occur: N2 is limited to 4, 6, and 9 mol. % at 2.0, 1.5, and 1.0 MPa, respectively.
Density-reduced critical electric field of dissociated gas mixtures as a function of pressure and temperature. (a) He-H2 mixture and (b) He-N2 mixture.
Density-reduced critical electric field of dissociated gas mixtures as a function of pressure and temperature. (a) He-H2 mixture and (b) He-N2 mixture.
V. CRITICAL ELECTRIC FIELD
In this section, we present the dielectric strength in terms of the critical electric field (Ecr). As stated earlier, (E/N)cr is widely used for representing the dielectric strength of gas mixtures. However, Ecr shows the dielectric strength more directly since it is not normalized by density N. We multiply (E/N)cr with the particle number density N obtained at the pressure and temperature conditions based on N = P/k/T, where P is pressure, k is the Boltzmann constant, and T is temperature. Figures 6(a)–6(c) show the Ecr values of the ternary gas mixture (He-H2-N2) and the binary gas mixtures (He-H2 and He-N2). In all three gas mixtures, the highest dielectric strength is shown at 2.0 MPa and the lowest at 1.0 MPa. Furthermore, in all three gas mixtures, the dielectric strength decreases with increasing temperature due to the increasing dissociation process at higher temperatures.
Critical electric field of dissociated gas mixtures as a function of pressure and temperature. (a) He-H2-N2 mixture, (b) He-H2 mixture, and (c) He-N2 mixture.
Critical electric field of dissociated gas mixtures as a function of pressure and temperature. (a) He-H2-N2 mixture, (b) He-H2 mixture, and (c) He-N2 mixture.
VI. CONCLUSIONS
In summary, we presented the dielectric strength of dissociated cryogenic gas mixtures over the temperature range of 77–5000 K and the pressure range of 1.0–2.0 MPa. The gas composition data obtained in this study suggested that the recombination process of a hot dissociated He-H2-N2 gas mixture would generate NH3, which could cause potential long-term challenges in the operation of a cryogenic switchgear. To address the challenge, we discussed the He-H2 and He-N2 mixtures as the binary alternatives and confirmed their dissociated gas composition and estimated the dielectric strength variation over the studied temperature and pressure range. The gas composition results showed that the binary alternatives are free from the long-term challenges associated with the NH3 generation but have lower dielectric strength than the ternary mixture. The (E/N)cr values showed that the dielectric strength gradually decreases with increasing temperature in the case of He-H2 mixture while that of He-N2 remains relatively constant over the entire temperature range. Furthermore, the Ecr results commonly showed that the higher dielectric strength is obtained at higher pressures and lower temperatures regardless of the gas mixture. The data presented in this paper provide guidance for the dielectric design of cryogenic switchgear as well as other applications that involve arc discharge.
ACKNOWLEDGMENTS
This work was supported by the Office of Naval Research (ONR).