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Theoretical computation studies for transport properties of air plasmas

Wang Wei-Zong Wu Yi Rong Ming-Zhe Yang Fei

Theoretical computation studies for transport properties of air plasmas

Wang Wei-Zong, Wu Yi, Rong Ming-Zhe, Yang Fei
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  • The thermophysical properties of arc plasma provide reliable micro-theoretical foundations and parameter inputs for the numerical simulation of the air arc discharge process. Based on the assumption of the local thermodynamic equilibrium, the computation of transport properties including electron diffusion coefficient, viscosity, thermal conductivity and electrical conductivity is performed by using the Chapman-Enskog method and expanding the sonine polynomial up to the third-order approximation (second-order for viscosity) in a pressure (0.120 atm) and temperature range (30040000 K) conditions which satisfy most thermal plasma modelling requirements. The most recent data on potential interactions and elastic differential cross sections for interacting particles are utilized to determine the collision integrals, resulting in more accurate and reliable values of transport properties than those given in the previous literature.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51177124), the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 51007072), and the Ph.D. Programs Foundation of Ministry of Education of China (Grant No. 20110201130006).
    [1]

    Gong J Q, Gong Y, Liu J Y, Zhang P Y 2002 Acta Phys. Sin. 51 291 (in Chinese) [宫继全, 宫野, 刘金远, 张鹏云 2002 物理学报 51 291]

    [2]

    Rong M Z, Wu Y, Fei Y, Sun Z Q, Wang W Z, Wang X H 2008 Proceeding of the XVII International Conference on Gas Discharges and Their Applications Cardiff, UK

    [3]

    Wu Y, Rong M Z, Yang F, Murphy A B, Ma Q, Sun Z Q, Wang X H 2008 IEEE Trans. Plasma Sci. 36 1074

    [4]

    Wu Y, Rong M Z, Yang F, Wang X H, Ma Q, Wang W Z 2008 Acta Phys. Sin. 57 5761 (in Chinese) [吴翊, 荣命哲, 杨飞, 王小华, 马强, 王伟宗 2008 物理学报 57 5761]

    [5]

    Rong M Z, Wu Y, Yang F, Murphy A B, Wang W Z, Guo J 2010 IEEE Trans. Plasma Sci. 38 2306

    [6]

    Yang F, Rong M Z, Wu Y, Shi Q, Liu Z C, Ma R G, Chen S 2011 Acta Phys. Sin. 60 055208 (in Chinese) [杨飞, 荣命哲, 吴翊, 史强, 刘增超, 马瑞光, 陈胜 2011 物理学报 60 055208]

    [7]

    Wang W Z, Rong M Z, Murphy A B, Wu Y, Su H B, Yang F 2010 High Voltage Engineering 36 2777 (in Chinese) [王伟宗, 荣命哲, Murphy A B, 吴翊, 苏海博, 杨飞 2010 高电压技术 36 2777]

    [8]

    Zheng J, Gu Y J, Chen Q F, Chen Z Y 2010 Acta Phys. Sin. 59 7472 (in Chinese) [郑君, 顾云军, 陈其峰, 陈志云 2010 物理学报 59 7472]

    [9]

    Fauchais P, Boulos M I, Pfender E 1994 Thermal Plasmas-Fundamentals and Applications (Vol. 1) (New York: Plenum) p213

    [10]

    Schreiber P W, Hunter A M, Benedetto K R 1973 AIAA J. 11 2696

    [11]

    Bacri J, Raffanel S 1989 Plasma Chem. Plasma Process. 9 133

    [12]

    Murphy A B 1995 Plasma Chem. Plasma Process. 15 279

    [13]

    Capitelli M, Colonna G, Gorse G, Angola A D 2000 Eur. Phys. J. D 11 279

    [14]

    Capitelli M, Colonna G, Gorse G, Angola A D 2008 Eur. Phys. J. D 46 129

    [15]

    Hirschfelder J O, Curtis C F, Bird R B 1964 Molecular Theory of Gases and Liquids (2nd Ed.) (New York: Wiley)

    [16]

    Chapman S, Cowling T G 1970 The Mathematical Theory of Non-uniform Gases (3rd Ed.) (Cambridge: Cambridge University Press)

    [17]

    Devoto R S 1967 Phys. Fluids 10 2105

    [18]

    Devoto R S 1966 Phys. Fluids 9 1230

    [19]

    Rat V, Andre' P, Aubreton J, Elchinger M F, Fauchais P, Lefort A 2002 J. Phys. D: Appl. Phys. 35 981

    [20]

    Devoto R S 1973 Phys. Fluids 16 616

    [21]

    Devoto R S 1967 Phys. Fluids 10 2704

    [22]

    Meador W E, Stanton L D 1965 Phys. Fluids 8 1694

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    Monchick L, Yun K S, Mason E A 1963 J. Chem. Phys. 39 654

    [24]

    Hirschfelder J O 1957 Chem. Phys. 26 282

    [25]

    Stallcop J R, Partridge H, Levin E 2000 Phys. Rev. A 62 062709

    [26]

    Stallcop J R, Partridge H, Levin E 2000 Phys. Rev. A 64 042722

    [27]

    Levin E, Partridge H, Stallcop H R 1990 J. Thermophys. Heat Transfer 4 469

    [28]

    Abbaspour M, Goharshadi E K, Emampour J S 2006 Chem. Phys. 326 620

    [29]

    Ali M, Amir H J 2004 Bull. Chem. Soc. Jpn. 77 1297

    [30]

    Slavícek P, Kalus R, Paska P 2003 J. Chem. Phys. 119 2102

    [31]

    Wright M J, Levin E 2005 J. Thermophys. Heat Transfer 19 127

    [32]

    Brunetti B, Liuti G, Luzzatti E, Pirani F, Volpi G G 1983 J. Chem. Phys. 79 273

    [33]

    Pirani F, Vecchiocattivi F 1981 Chem. Phys. 59 387

    [34]

    Brunetti B, Liuti G, Luzzatti E, Pirani F, Vecchiocattivi F 1981 J. Chem. Phys. 74 6734

    [35]

    Aubreton J, Bonnefoi C, Mexmain J M 1986 Rev. Phys. Appl. 21 365

    [36]

    Capitelli M, Cappelletti D, Colonna G, Gorse C, Laricchiuta A, Liuti G, Longo S, Pirani F 2007 Chem. Phys. 338 62

    [37]

    Laricchiuta A, Colonna G, Bruno D, Celiberto R, Gorse C, Pirani F, Capitelli M 2007 Chem. Phys. Lett. 445 133

    [38]

    Andrea L, Federico P 2008 J. Mol. Struct. (Theochem) 857 22

    [39]

    Lupinetti C, Thakkar A J 2005 J. Chem. Phys. 122 044301

    [40]

    Duijnen P T V, Swart M 1998 J. Phys. Chem. A 102 2399

    [41]

    Das A K, Thakkar A J 1998 J. Phys. B At. Mol. Opt. Phys. 31 2215

    [42]

    Murphy A B, Arundell C J 1994 Plasma Chem. Plasma Process. 14 451

    [43]

    Stallcop J R, Partridge H, Levin E 1991 Chem. Phys. 95 6429

    [44]

    Aubreton J, Bonnefoi C, Mexmain J M 1986 J. Appl. Phys. Rev. 21 365

    [45]

    Barata J A S 2007 Nucl. Instrum. Meth. Phys. Res. A 580 14

    [46]

    Danailov D M, Viehland L A, Johnsen R, Wright T G, Dickinson A S 2008 J. Chem. Phys. 128 134302

    [47]

    BrostrOm L, Larsson M, Mannervik S, Sonneka D 1991 J. Chern. Phys. 94 2734

    [48]

    Meier P, Sandemant R J, Andrews M 1974 J. Phys. B: At. Mol. Phys. 7 L339

    [49]

    Me'rawa M, Be'gue' D, Pouchan C 2003 J. Mol. Str. (Theochem) 633 157

    [50]

    Sourd B, Aubreton J, Elchinger M F, Labrot M, Michon U 2006 J. Phys. D: Appl. Phys. 39 1105

    [51]

    Thakkar A, Das A K 2001 J. Mol. Str. (Theochem) 547 233

    [52]

    Yevseyev A V, Radtsig A A, Smirnov B M 1982 J. Phys. B: At. Mol. Phys. 15 4437

    [53]

    Kihara T, Taylor M H, Hirschfelder J O 1960 Phys. Fluids 3 715

    [54]

    Mehrdad A, Constantine E T 2005 Atom. Data Nucl. Data Tables 91 8

    [55]

    Itikawa Y 2009 J. Phys. Chem. Ref. Data 38 1

    [56]

    Sullivan J P, Gibson J C, Gulley R G, Buckman S J 1995 J. Phys. B 28 4319

    [57]

    Linert I, King G C, Zubek M 2004 J. Phys. B 37 4681

    [58]

    Machado L, Ribeiro E M S, Lee M T, Fujimoto M M, Brescansin L M 1999 Phys. Rev. A 60 1199

    [59]

    Tabata T, Shirai C T, Sataka M, Kubo H A 2006 Atom. Data Nucl. Data Tables 92 375

    [60]

    Muse J, Silva H, Lopes M C A, Khakoo M A 2008 J. Phys. B: At. Mol. Opt. Phys. 41 095203

    [61]

    Gote M, Ehrhardt H 1995 J. Phys. B: At. Mol. Opt. Phys. 28 3957

    [62]

    Hayashi M 1989 NATO ASI Series B 220 333

    [63]

    Mojarrabi M, Gulley R J, Middleton A G, Cartwright D C, Teubner P J O, Buckman S J, Brunger M J 1995 J. Phys. B 28 487

    [64]

    Williams J F, Allen L J 1989 J. Phys. B: At. Mol. Opt. Phys. 22 3529

    [65]

    Thomas L D, Nesbet R K 1975 Phys. Rev. A 12 1729

    [66]

    Blaha M, Davis J 1975 Phys. Rev. A 12 2319

    [67]

    Itikawa Y, Ichimura A 1990 J. Phys. Chem. Ref. Data 19 637

    [68]

    Mason E A, Munn R J 1967 Phys. Fluids 10 1827

    [69]

    Devoto R S 1973 Phys. Fluids 16 616

    [70]

    Murphy A B 2001 J. Phys. D: Appl. Phys. 34 151

  • [1]

    Gong J Q, Gong Y, Liu J Y, Zhang P Y 2002 Acta Phys. Sin. 51 291 (in Chinese) [宫继全, 宫野, 刘金远, 张鹏云 2002 物理学报 51 291]

    [2]

    Rong M Z, Wu Y, Fei Y, Sun Z Q, Wang W Z, Wang X H 2008 Proceeding of the XVII International Conference on Gas Discharges and Their Applications Cardiff, UK

    [3]

    Wu Y, Rong M Z, Yang F, Murphy A B, Ma Q, Sun Z Q, Wang X H 2008 IEEE Trans. Plasma Sci. 36 1074

    [4]

    Wu Y, Rong M Z, Yang F, Wang X H, Ma Q, Wang W Z 2008 Acta Phys. Sin. 57 5761 (in Chinese) [吴翊, 荣命哲, 杨飞, 王小华, 马强, 王伟宗 2008 物理学报 57 5761]

    [5]

    Rong M Z, Wu Y, Yang F, Murphy A B, Wang W Z, Guo J 2010 IEEE Trans. Plasma Sci. 38 2306

    [6]

    Yang F, Rong M Z, Wu Y, Shi Q, Liu Z C, Ma R G, Chen S 2011 Acta Phys. Sin. 60 055208 (in Chinese) [杨飞, 荣命哲, 吴翊, 史强, 刘增超, 马瑞光, 陈胜 2011 物理学报 60 055208]

    [7]

    Wang W Z, Rong M Z, Murphy A B, Wu Y, Su H B, Yang F 2010 High Voltage Engineering 36 2777 (in Chinese) [王伟宗, 荣命哲, Murphy A B, 吴翊, 苏海博, 杨飞 2010 高电压技术 36 2777]

    [8]

    Zheng J, Gu Y J, Chen Q F, Chen Z Y 2010 Acta Phys. Sin. 59 7472 (in Chinese) [郑君, 顾云军, 陈其峰, 陈志云 2010 物理学报 59 7472]

    [9]

    Fauchais P, Boulos M I, Pfender E 1994 Thermal Plasmas-Fundamentals and Applications (Vol. 1) (New York: Plenum) p213

    [10]

    Schreiber P W, Hunter A M, Benedetto K R 1973 AIAA J. 11 2696

    [11]

    Bacri J, Raffanel S 1989 Plasma Chem. Plasma Process. 9 133

    [12]

    Murphy A B 1995 Plasma Chem. Plasma Process. 15 279

    [13]

    Capitelli M, Colonna G, Gorse G, Angola A D 2000 Eur. Phys. J. D 11 279

    [14]

    Capitelli M, Colonna G, Gorse G, Angola A D 2008 Eur. Phys. J. D 46 129

    [15]

    Hirschfelder J O, Curtis C F, Bird R B 1964 Molecular Theory of Gases and Liquids (2nd Ed.) (New York: Wiley)

    [16]

    Chapman S, Cowling T G 1970 The Mathematical Theory of Non-uniform Gases (3rd Ed.) (Cambridge: Cambridge University Press)

    [17]

    Devoto R S 1967 Phys. Fluids 10 2105

    [18]

    Devoto R S 1966 Phys. Fluids 9 1230

    [19]

    Rat V, Andre' P, Aubreton J, Elchinger M F, Fauchais P, Lefort A 2002 J. Phys. D: Appl. Phys. 35 981

    [20]

    Devoto R S 1973 Phys. Fluids 16 616

    [21]

    Devoto R S 1967 Phys. Fluids 10 2704

    [22]

    Meador W E, Stanton L D 1965 Phys. Fluids 8 1694

    [23]

    Monchick L, Yun K S, Mason E A 1963 J. Chem. Phys. 39 654

    [24]

    Hirschfelder J O 1957 Chem. Phys. 26 282

    [25]

    Stallcop J R, Partridge H, Levin E 2000 Phys. Rev. A 62 062709

    [26]

    Stallcop J R, Partridge H, Levin E 2000 Phys. Rev. A 64 042722

    [27]

    Levin E, Partridge H, Stallcop H R 1990 J. Thermophys. Heat Transfer 4 469

    [28]

    Abbaspour M, Goharshadi E K, Emampour J S 2006 Chem. Phys. 326 620

    [29]

    Ali M, Amir H J 2004 Bull. Chem. Soc. Jpn. 77 1297

    [30]

    Slavícek P, Kalus R, Paska P 2003 J. Chem. Phys. 119 2102

    [31]

    Wright M J, Levin E 2005 J. Thermophys. Heat Transfer 19 127

    [32]

    Brunetti B, Liuti G, Luzzatti E, Pirani F, Volpi G G 1983 J. Chem. Phys. 79 273

    [33]

    Pirani F, Vecchiocattivi F 1981 Chem. Phys. 59 387

    [34]

    Brunetti B, Liuti G, Luzzatti E, Pirani F, Vecchiocattivi F 1981 J. Chem. Phys. 74 6734

    [35]

    Aubreton J, Bonnefoi C, Mexmain J M 1986 Rev. Phys. Appl. 21 365

    [36]

    Capitelli M, Cappelletti D, Colonna G, Gorse C, Laricchiuta A, Liuti G, Longo S, Pirani F 2007 Chem. Phys. 338 62

    [37]

    Laricchiuta A, Colonna G, Bruno D, Celiberto R, Gorse C, Pirani F, Capitelli M 2007 Chem. Phys. Lett. 445 133

    [38]

    Andrea L, Federico P 2008 J. Mol. Struct. (Theochem) 857 22

    [39]

    Lupinetti C, Thakkar A J 2005 J. Chem. Phys. 122 044301

    [40]

    Duijnen P T V, Swart M 1998 J. Phys. Chem. A 102 2399

    [41]

    Das A K, Thakkar A J 1998 J. Phys. B At. Mol. Opt. Phys. 31 2215

    [42]

    Murphy A B, Arundell C J 1994 Plasma Chem. Plasma Process. 14 451

    [43]

    Stallcop J R, Partridge H, Levin E 1991 Chem. Phys. 95 6429

    [44]

    Aubreton J, Bonnefoi C, Mexmain J M 1986 J. Appl. Phys. Rev. 21 365

    [45]

    Barata J A S 2007 Nucl. Instrum. Meth. Phys. Res. A 580 14

    [46]

    Danailov D M, Viehland L A, Johnsen R, Wright T G, Dickinson A S 2008 J. Chem. Phys. 128 134302

    [47]

    BrostrOm L, Larsson M, Mannervik S, Sonneka D 1991 J. Chern. Phys. 94 2734

    [48]

    Meier P, Sandemant R J, Andrews M 1974 J. Phys. B: At. Mol. Phys. 7 L339

    [49]

    Me'rawa M, Be'gue' D, Pouchan C 2003 J. Mol. Str. (Theochem) 633 157

    [50]

    Sourd B, Aubreton J, Elchinger M F, Labrot M, Michon U 2006 J. Phys. D: Appl. Phys. 39 1105

    [51]

    Thakkar A, Das A K 2001 J. Mol. Str. (Theochem) 547 233

    [52]

    Yevseyev A V, Radtsig A A, Smirnov B M 1982 J. Phys. B: At. Mol. Phys. 15 4437

    [53]

    Kihara T, Taylor M H, Hirschfelder J O 1960 Phys. Fluids 3 715

    [54]

    Mehrdad A, Constantine E T 2005 Atom. Data Nucl. Data Tables 91 8

    [55]

    Itikawa Y 2009 J. Phys. Chem. Ref. Data 38 1

    [56]

    Sullivan J P, Gibson J C, Gulley R G, Buckman S J 1995 J. Phys. B 28 4319

    [57]

    Linert I, King G C, Zubek M 2004 J. Phys. B 37 4681

    [58]

    Machado L, Ribeiro E M S, Lee M T, Fujimoto M M, Brescansin L M 1999 Phys. Rev. A 60 1199

    [59]

    Tabata T, Shirai C T, Sataka M, Kubo H A 2006 Atom. Data Nucl. Data Tables 92 375

    [60]

    Muse J, Silva H, Lopes M C A, Khakoo M A 2008 J. Phys. B: At. Mol. Opt. Phys. 41 095203

    [61]

    Gote M, Ehrhardt H 1995 J. Phys. B: At. Mol. Opt. Phys. 28 3957

    [62]

    Hayashi M 1989 NATO ASI Series B 220 333

    [63]

    Mojarrabi M, Gulley R J, Middleton A G, Cartwright D C, Teubner P J O, Buckman S J, Brunger M J 1995 J. Phys. B 28 487

    [64]

    Williams J F, Allen L J 1989 J. Phys. B: At. Mol. Opt. Phys. 22 3529

    [65]

    Thomas L D, Nesbet R K 1975 Phys. Rev. A 12 1729

    [66]

    Blaha M, Davis J 1975 Phys. Rev. A 12 2319

    [67]

    Itikawa Y, Ichimura A 1990 J. Phys. Chem. Ref. Data 19 637

    [68]

    Mason E A, Munn R J 1967 Phys. Fluids 10 1827

    [69]

    Devoto R S 1973 Phys. Fluids 16 616

    [70]

    Murphy A B 2001 J. Phys. D: Appl. Phys. 34 151

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  • Received Date:  06 June 2011
  • Accepted Date:  28 May 2012
  • Published Online:  20 May 2012

Theoretical computation studies for transport properties of air plasmas

  • 1. School of Electrical Engineering, Xi'an Jiaotong University, State Key Laboratory of Electrical Insulation and Power Equipment, Xi'an 710049, China;
  • 2. Department of Electrical Engineering and Electronics, The University of Liverpool, Brownlow Hill, Liverpool L69 3GJ, UK
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 51177124), the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 51007072), and the Ph.D. Programs Foundation of Ministry of Education of China (Grant No. 20110201130006).

Abstract: The thermophysical properties of arc plasma provide reliable micro-theoretical foundations and parameter inputs for the numerical simulation of the air arc discharge process. Based on the assumption of the local thermodynamic equilibrium, the computation of transport properties including electron diffusion coefficient, viscosity, thermal conductivity and electrical conductivity is performed by using the Chapman-Enskog method and expanding the sonine polynomial up to the third-order approximation (second-order for viscosity) in a pressure (0.120 atm) and temperature range (30040000 K) conditions which satisfy most thermal plasma modelling requirements. The most recent data on potential interactions and elastic differential cross sections for interacting particles are utilized to determine the collision integrals, resulting in more accurate and reliable values of transport properties than those given in the previous literature.

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