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Transport Coefficients of Two-temperature Lithium Plasma for Space Propulsion Applications

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Abstract

Lithium has been proposed as an attractive metal propellant for advanced electric propulsion. In our current work, transport coefficients including the viscosity, thermal conductivity, and electrical conductivity of lithium plasma under both the equilibrium and non-equilibrium conditions are calculated based on a two-temperature model. The collision integrals used in calculating the transport coefficients are significantly more accurate than values used in previous theoretical studies, resulting in more reliable values of the transport coefficients. Results are computed for different degrees of thermal non-equilibrium, i.e. the ratio of electron to heavy particle temperatures, from 1 to 15, with the electron temperature ranging from 300 to 60,000 K in a wide pressure range from 0.0001 to 100 atm. We compare our calculated results with existing published results and discrepancies are found and explained.

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References

  1. Kodys AD, Choueiri EY (2005) A critical review of the state-of-the-art in the performance of applied-field magnetoplasmadynamic thrusters. In: 41st AIAA/ASME/SAE/ASEE joint propulsion conference (Tucson, AZ) AIAA-2005-2447, p 1–23

  2. Coogan W, Hepler MA, Choueiri E (2016) Measurement of the applied-field component of the thrust of a lithium Lorentz force accelerator. In: 52nd AIAA/ASME/SAE/ASEE joint propulsion conference AIAA propulsion and energy forum, AIAA 2016-4537

  3. Xisto CM, Páscoa JC, Oliveira PJ, Nicolini DA (2012) A hybrid pressure density-based algorithm for the Euler equations at all Mach number regimes. Int J Numer Methods Fluids 70:961–976

    Article  Google Scholar 

  4. Sleziona PC, Auweter-Kurtz M, Schrade HO, (1988) numerical codes for cylindrical MPD thrusters. In: Proceedings of 20th international electric propulsion conference, no. IEPC 88-038

  5. Hirschfelder JO, Curtis CF, Bird RB (1964) Molecular theory of gases and liquids, 2nd edn. Wiley, New York

    Google Scholar 

  6. Murphy AB, Arundell CJ (1994) Transport coefficients of argon, nitrogen, oxygen, argon–nitrogen, and argon–oxygen plasmas. Plasma Chem Plasma Process 14:451–490

    Article  CAS  Google Scholar 

  7. Capitelli M, Celiberto R, Gorse C, Giordano D (1995) Transport properties of high temperature air components: a review. Plasma Chem Plasma Process 16:S269–S302

    Article  Google Scholar 

  8. Murphy AB (1995) Transport coefficients of air, argon–air, nitrogen–air, and oxygen–air plasmas. Plasma Chem Plasma Process 15:279–307

    Article  CAS  Google Scholar 

  9. Pousse J, Chervy B, Bilodeau JF, Gleizes A (1996) Thermodynamic and transport properties of argon/carbon and helium/carbon mixtures in fullerene synthesis. Plasma Chem Plasma Process 16:605–634

    Article  CAS  Google Scholar 

  10. Murphy AB (1997) Transport coefficients of helium and argon–helium plasmas. IEEE Trans Plasma Sci 25:809–814

    Article  CAS  Google Scholar 

  11. Murphy AB (2000) Transport coefficients of hydrogen and argon–hydrogen plasmas. Plasma Chem Plasma Process 20:279–297

    Article  CAS  Google Scholar 

  12. Cressault Y, Gleizes A (2004) Thermodynamic properties and transport coefficients in Ar–H2–Cu plasma. J Phys D Appl Phys 37:560–572

    Article  CAS  Google Scholar 

  13. Sourd B, Aubreton J, Elchinger MF, Labrot M, Michon U (2006) High temperature transport coefficients in E/C/H/N/O mixtures. J Phys D Appl Phys 39:1105–1119

    Article  CAS  Google Scholar 

  14. Tanaka Y, Yamachi N, Matsumoto S, Kaneko S, Okabe S, Shibuya M (2008) Thermodynamic and transport properties of CO2, CO2–O2, and CO2–H2 mixtures at temperatures of 300 to 30000 K and pressures of 0.1 to 10 MPa. Electr Eng Japan 163:18–29

    Article  Google Scholar 

  15. Cressault Y, Hannachi R, Teulet Ph, Gleizes A, Gonnet JP, Battandier JY (2008) Influence of metallic vapours on the properties of air thermal plasmas. Plasma Sour Sci Technol 17:035016

    Article  Google Scholar 

  16. Wang WZ, Murphy AB, Yan JD, Rong MZ, Spencer JW, Fang MTC (2011) Thermophysical properties of high-temperature reacting mixtures of carbon and water in the range 400–30,000 K and 0.1–10 atm: I. Equilibrium composition and thermodynamic properties. Plasma Chem Plasma Process 32:75–96

    Article  Google Scholar 

  17. Wang WZ, Rong MZ, Murphy AB, Wu Y, Spencer JW, Yan JD, Fang MTC (2011) Thermophysical properties of carbon–argon and carbon–helium plasmas. J Phys D Appl Phys 44:355207

    Article  Google Scholar 

  18. Wang WZ, Wu Y, Rong MZ, Éhn L, 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

    Article  Google Scholar 

  19. Wang WZ, Yan JD, Rong MZ, Murphy AB, Spencer JW, Fang MTC (2012) Thermophysical properties of high temperature reacting mixtures of carbon and water in the range 400–30,000 K and 0.1–10 atm: II. Transport coefficients. Plasma Chem Plasma Process 32:495–518

    Article  Google Scholar 

  20. Wang WZ, Wu Y, Rong MZ, Yang F (2012) Theoretical computation studies for transport properties of air plasmas. Acta Phys Sin 61:105201

    Google Scholar 

  21. Wang WZ, Rong MZ, Wu Y, Yan JD (2014) Fundamental properties of high-temperature SF6 mixed with CO2 as a replacement for SF6 in high-voltage circuit breakers. J Phys D Appl Phys 47:255201

    Article  Google Scholar 

  22. Rat V, Murphy AB, Aubreton J, Elchinger MF, Fauchais P (2008) Treatment of non-equilibrium phenomena in thermal plasma flows. J Phys D Appl Phys 41:183001

    Article  Google Scholar 

  23. Girard R, Gonzalez JJ, Gleizes A (1999) Modelling of a two-temperature SF6 arc plasma during extinction. J Phys D Appl Phys 32:1229–1238

    Article  CAS  Google Scholar 

  24. Gonzalez JJ, Girard R, Gleizes A (2000) Decay and post-arc phases of a SF6 arc plasma: a thermal and chemical non-equilibrium model. J Phys D Appl Phys 33:2759–2768

    Article  CAS  Google Scholar 

  25. Trelles JP, Chazelas C, Vardelle A, Heberlein JVR (2009) Arc Plasma Torch Modeling. J Thermal Spray Technol 18:728–752

    Article  Google Scholar 

  26. Colombo V, Ghedini E, Boselli M, Sanibondi P, Concetti A (2011) 3D static and time-dependent modelling of a dc transferred arc twin torch system. J Phys D Appl Phys 44:194005

    Article  Google Scholar 

  27. Ghorui S, Heberlein JVR, Pfender E (2007) Non-equilibrium modelling of an oxygen-plasma cutting torch. J Phys D Appl Phys 40:1966–1976

    Article  CAS  Google Scholar 

  28. Trelles JP, Heberlein JVR, Pfender E (2007) Non-equilibrium modelling of arc plasma torches. J Phys D Appl Phys 40:5937

    Article  CAS  Google Scholar 

  29. Wang WZ, Yan JD, Rong MZ, Spencer JW (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

    Article  Google Scholar 

  30. Wang WZ, Kong LH, Geng JY, Wei FZ, Xia GQ (2017) Wall ablation of heated compound-materials into non-equilibrium discharge plasmas. J Phys D Appl Phys 50:074005

    Article  Google Scholar 

  31. Devoto RS (1967) Third approximation to the viscosity of multicomponent mixtures. Phys Fluids 10:2704–2706

    Article  CAS  Google Scholar 

  32. Bonnefoi C (1983) Ph.D. thesis, Limoges University, France

  33. Rat V, André P, Aubreton J, Elchinger MF, Fauchais P, Lefort A (2001) Transport properties in a two-temperature plasma: theory and application. Phys Rev E 64:26409

    Article  CAS  Google Scholar 

  34. Zhang XN, Li HP, Murphy AB, Xia WD (2013) A numerical model of non-equilibrium thermal plasmas. I. Transport properties. Phys Plasmas 20:033508

    Article  Google Scholar 

  35. Zhang XN, Li HP, Murphy AB, Xia WD (2015) Comparison of the transport properties of two-temperature argon plasmas calculated using different methods. Plasma Sour Sci Technol 24:035011

    Article  Google Scholar 

  36. Ghorui S, Heberlein JVR, Pfender E (2008) Thermodynamic and transport properties of two-temperature nitrogen-oxygen plasma. Plasma Chem Plasma Process 28:553–582

    Article  CAS  Google Scholar 

  37. Wu Y et al (2016) Calculation of 2-temperature plasma thermos-physical properties considering condensed phases: application to CO2–CH4 plasma: part 1. Composition and thermodynamic properties. J Phys D Appl Phys 49:405203

    Article  Google Scholar 

  38. Miller EM, Sandler SI (1973) Transport properties of two-temperature partially ionized argon. Phys Fluids 16:491–493

    Article  CAS  Google Scholar 

  39. Kannappan D, Bose TK (1977) Transport properties of a two-temperature argon plasma. Phys Fluids 20:1668–1673

    Article  CAS  Google Scholar 

  40. Rat V, Andre P, Aubreton J (2002) Transport coefficients including diffusion in a two-temperature argon plasma. J Phys D Appl Phys 35:981–991

    Article  CAS  Google Scholar 

  41. Kannappan DB, Bose TK (1980) Transport properties of a two-temperature helium plasma. Phys Fluids 23:1473–1474

    Article  CAS  Google Scholar 

  42. Wang HY et al (2017) Thermodynamic properties and transport coefficients of two temperature PTFE vapour plasma for ablation controlled discharge applications. J Phys D Appl Phys. doi:10.1088/1361-6463/aa7d68

    Google Scholar 

  43. Wang HX, Sun SR, Chen SQ (2012) Calculation of two-temperature transport coefficients of helium plasma. Acta Phys Sin 61:195203

    Google Scholar 

  44. Rat V, Andre P, Aubreton J, Elchinger MF, Fauchais P, Lefort A (2002) Two-temperature transport coefficients in argon–hydrogen plasmas: I. Elastic processes and collision integrals. Plasma Chem Plasma Process 22:453–474

    Article  CAS  Google Scholar 

  45. Niu CP 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

    Article  Google Scholar 

  46. Wang WZ, Rong MZ, Wu Y, Spencer JW, Yan JD, Mei DH (2012) Thermodynamic and transport properties of two-temperature SF6 plasmas. Phys Plasmas 19:3–18

    CAS  Google Scholar 

  47. Wang WZ, Rong MZ, Yan JD, Murphy AB, Spencer JW (2011) Thermophysical properties of nitrogen plasmas under thermal equilibrium and non-equilibrium conditions. Phys Plasmas 18:113502

    Article  Google Scholar 

  48. Aubreton J, Elchinger MF, Rat V (2004) Two-temperature transport coefficients in argon–helium thermal plasmas. J Phys D Appl Phys 37:34–41

    Article  CAS  Google Scholar 

  49. Colombo V, Ghedini E, Sanibondi P (2009) Two-temperature thermodynamic and transport properties of argon–hydrogen and nitrogen–hydrogen plasmas. J Phys D Appl Phys 42:055213

    Article  Google Scholar 

  50. Colombo V, Ghedini E, Sanibondi P (2011) Two-temperature thermodynamic and transport properties of carbon–oxygen plasmas. Plasma Sour Sci Technol 20:03500

    Google Scholar 

  51. Wang HX, Chen SQ, Chen X (2012) Thermodynamic and transport properties of two-temperature lithium plasmas. J Phys D Appl Phys 45:165202

    Article  Google Scholar 

  52. Murphy AB (2001) Thermal plasmas in gas mixtures. J Phys D Appl Phys 34:151–173

    Article  Google Scholar 

  53. Potapov AV (1966) Chemical equilibrium of multi-temperature systems. High Temp 4:48–51

    Google Scholar 

  54. van de Sanden MCM, Schram PPJM, Peeters AG, van der Mullen JAM, Kroesen GMW (1989) Thermodynamic generalization of the Saha equation for a two-temperature plasma. Phys Rev A 40:5273–5276

    Article  Google Scholar 

  55. Giordano D (1998) Equivalence of energy, entropy, and thermodynamic potentials in relation to the thermodynamic equilibrium of multitemperature gas mixtures. Phys Rev E 58:3098–3112

    Article  CAS  Google Scholar 

  56. Giordano D, Capitelli M (2001) Nonuniqueness of the two-temperature Saha equation and related considerations. Phys Rev E 65:16401

    Article  Google Scholar 

  57. White WB, Johnson SM, Dantzig GB (1958) Chemical equilibrium in complex mixtures. J Chem Phys 28:751

    Article  CAS  Google Scholar 

  58. Andre P (1995) Partition functions and concentrations in plasmas out of thermal equilibrium. IEEE Trans Plasma Sci 23:453–458

    Article  CAS  Google Scholar 

  59. Andre P, Abbaoui M, Lefort A, Parizet MJ (1996) Numerical method and composition in multi-temperature plasmas: application to an Ar-H2 mixture. Plasma Chem Plasma Process 16:379–398

    Article  CAS  Google Scholar 

  60. Chen X, Han P (1999) On the thermodynamic derivation of the Saha equation modified to a two-temperature plasma. J Phys D Appl Phys 32:1711–1718

    Article  Google Scholar 

  61. Giordano D, Capitelli M (1995) Two-temperature Saha equation—a misunderstood problem. J Thermophys Heat Transfer 9:803–804

    Article  CAS  Google Scholar 

  62. Andre P, Aubreton J, Elchinger MF, Rat V, Fauchais P, Lefort A, Murphy AB (2004) A statistical mechanical view of the determination of the composition of multi-temperature plasmas. Plasma Chem Plasma Process 24:435–446

    Article  CAS  Google Scholar 

  63. Wang WZ, Rong MZ, Spencer JW (2013) Nonuniqueness of two-temperature Guldberg–Waage and Saha equations: influence on thermophysical properties of SF6 plasmas. Phys Plasmas 20:113504

    Article  Google Scholar 

  64. Ralchenko Y, Kramida AE, Reader J, NIST ASD Team 2008 NIST atomic spectra database (version 3.1.5). National Institute of Standards and Technology, Gaithersburg, MD http://physics.nist.gov/PhysRefData/ASD/levels_form.html

  65. Zavitsas AA (2003) The potential energy curve of the ground state of lithium X1Σ +g Li2. J Mol Spectrosc 221:67–71

    Article  CAS  Google Scholar 

  66. Kutzelnigg W, Staemmler V, Oelus M (1972) Potential curve of the lowest triplet state of Li2. Chem Phys Lett 13:496–500

    Article  CAS  Google Scholar 

  67. Jasika P, Wilczyński J, Sienkiewicz JE (2007) Calculation of adiabatic potentials of Li2 +. Eur Phys J Special Topics 144:85–91

    Article  Google Scholar 

  68. Lorents DC, Black G, Heinz O (1965) Charge transfer between Li ions and Li atoms in the 14-1000-eV energy region. Phys Rev A 137:1049

    Article  CAS  Google Scholar 

  69. Li TC, Liu CH, Qu YC et al (2015) Resonant charge transfer in slow Li+–Li(2s) collisions. Chin Phys B 24:103401

    Article  Google Scholar 

  70. Johnson WR, Safronova UI, Derevianko A, Safronova MS (2008) Relativistic many-body calculation of energies, lifetimes, hyperfine constants, and polarizabilities in 7Li. Phys Rev A 77:022510

    Article  Google Scholar 

  71. Bray I (1998) Private Communication

  72. Williams W, Trajmar S, Bozinis D (1976) Electron scattering from Li at 5.4, 10, 20 and 60 eV impact energies. J Phys B At Mol Phys 9:1529–1536

    Article  CAS  Google Scholar 

  73. Mason EA, Munn RJ (1967) Transport coefficients of ionized gases. Phys Fluids 10:1827–1832

    Article  Google Scholar 

  74. Devoto RS (1973) Transport properties of ionized gases. Phys Fluids 16:616–623

    Article  CAS  Google Scholar 

  75. Ghorui S, Das AK (2013) Collision integrals for charged-charged interaction in two-temperature non-equilibrium plasma. Phys Plasmas 20:093504

    Article  Google Scholar 

  76. Chapman S, Cowling TG (1970) The mathematical theory of non-uniform gases, 3rd edn. Cambridge University Press, Cambridge

    Google Scholar 

  77. Ferziger JH, Kaper HG (1972) Mathematical theory of transport processes in gases. North-Holland, Amsterdam

    Google Scholar 

  78. Wang WZ, Rong MZ, Yan JD, Wu Y (2002) The reactive thermal conductivity of thermal equilibrium and nonequilibrium plasmas: application to nitrogen. IEEE Trans Plasma Sci 40:980–989

    Article  Google Scholar 

  79. Xi Chen, Li HP (2003) The reactive thermal conductivity for a two-temperature plasma. Int J Heat Mass Transfer 46:1443–1454

    Article  Google Scholar 

  80. Boulos MI, Fauchais P, Pfender E (1994) Thermal plasmas: fundamentals and applications. Plenum, New York

    Book  Google Scholar 

  81. Holland PM, Biolsi L, Rainwater JC (1986) Theoretical calculation of the transport properties of monatomic lithium vapor. J Chem Phys 85:4011–4018

    Article  CAS  Google Scholar 

  82. Gleizes A, Chervy B, Gonzalez JJ (1999) Calculation of a two-temperature plasma composition: bases and application to SF6. J Phys D Appl Phys 32:2060–2067

    Article  CAS  Google Scholar 

  83. Davies RH, Mason EA, Munn RJ (1965) High-temperature transport properties of alkali metal vapors. Phys Fluids 8:444–452

    Article  CAS  Google Scholar 

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 11675040), Natural Science Foundation of Liaoning Province (Grant No. 201602175), and the Fundamental Research Funds for the Central Universities of China (Grant No. DUT15ZD (G) 01).

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Xia, G., Han, Y., Wu, Q. et al. Transport Coefficients of Two-temperature Lithium Plasma for Space Propulsion Applications. Plasma Chem Plasma Process 37, 1505–1522 (2017). https://doi.org/10.1007/s11090-017-9837-3

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