Advertisement

Simulating Turbulent Thermal Plasma Flows for Nanopowder Fabrication

  • Masaya ShigetaEmail author
Review Article
  • 43 Downloads

Abstract

This article presents descriptions of theoretical models and numerical methods for simulating turbulent thermal plasma flow with nanopowder growth. Turbulence models must express turbulent and laminar states because both states co-exist with thermal plasmas showing large density variation and transport properties. Time-dependent 3D simulations are conducted based on Large Eddy Simulation using a dynamic Smagorinsky model. Results show significant difference depending on temporal and spatial discretization schemes and velocity–pressure coupling algorithms. Simulation results demonstrate that advanced numerical methods with high-order accuracy should be used for long and robust computations capturing steep gradients of nanopowder concentration and plasma temperature and 3D dynamic motions of multiscale vortices, which are turbulent features of thermal plasma flows with low Mach numbers. A thermal plasma jet generates a double-layer structure of inner high-temperature thick vortex rings and outer low-temperature thin vortex rings near the nozzle exit. Flowing downstream, these vortices interact, deform, and break up. Consequently, plasma transits to a complex thermal flow. The widely spreading distribution of multiscale vortices agrees with experimental observations, which are not simulated using conventional methods. Nanopowder is generated from material vapour by nucleation and condensation at interfacial regions between plasma and cold gas. Those regions include numerous vortices. Therefore, the vortices convey the nanopowder, producing a complex distribution of nanopowder. Simultaneously, the nanopowder diffuses and increases in size, decreasing in number by interparticle coagulation. Cross-correlation analysis suggests that a nanopowder distribution distant from a plasma jet can be controlled through temperature fluctuation control at the upstream plasma fringe.

Keywords

Thermal plasma Nanopowder Numerical simulation Turbulent flow Vortex structure 

List of Symbols

CP

Specific heat at constant pressure

D

Diffusion coefficient

d

Diameter

g

Number of monomers

I

Unit matrix

J

Homogeneous nucleation rate

Kth

Thermophoresis coefficient

kB

Boltzmann’s constant

h

Enthalpy

l

Mean free path

m

Mass

N

Number of datasets

n

Concentration

P

Pressure

Qrad

Radiation loss

Rcross

Cross-correlation coefficient

T

Temperature

S

Velocity gradient tensor

s

Surface area

u

Velocity vector

v

Volume

x

Axial position

y

Radial position in Cartesian coordinate system

z

Radial position in Cartesian coordinate system

Greek Letters

ρ

Density

η

Viscosity

λ

Thermal conductivity

Φ

Viscous dissipation

σ

Surface tension

τ

Time lag

Superscript

tr

Transposition

Subscripts

0

Anchoring point

c

Critical state

p

Particle

s

Saturation state

v

Vapour

Notes

Acknowledgements

This work was partly supported by the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (B) (KAKENHI: Grant No. 18H01371). Numerical results were obtained using supercomputing resources at the Cyberscience Center, Tohoku University. The author is grateful to Mr. Takeshi Yamashita of Tohoku University, as well as Mr. Takashi Soga and Mr. Kenta Yamaguchi of NEC Solution Innovators, Ltd. for improving the solver code.

Supplementary material

Supplementary material 1 (MP4 2394 kb)

Supplementary material 2 (MP4 2681 kb)

References

  1. 1.
    Boulos MI, Fauchais P, Pfender E (1994) Thermal plasmas fundamentals and applications, vol 1. Plenum Press, New YorkCrossRefGoogle Scholar
  2. 2.
    Sato T, Shigeta M, Kato D, Nishiyama H (2001) Mixing and magnetic effects on a nonequilibrium argon plasma jet. Int J Therm Sci 40:273–278CrossRefGoogle Scholar
  3. 3.
    Shigeta M, Sato T, Nishiyama H (2004) Computational simulation of a particle-laden RF inductively coupled plasma with seeded potassium. Int J Heat Mass Transf 47:707–716CrossRefGoogle Scholar
  4. 4.
    Shigeta M, Nishiyama H (2005) Numerical analysis of metallic nanoparticle synthesis using RF inductively coupled plasma flows. Trans ASME J Heat Transf 127:1222–1230CrossRefGoogle Scholar
  5. 5.
    Tanaka Y, Muroya Y, Hayashi K, Uesugi Y (2006) Simultaneous control of numerical enhancement of N atoms and decrease in heat flux into reaction chamber using Ar–N2 pulse-modulated induction thermal plasmas. Appl Phys Lett 89:031501CrossRefGoogle Scholar
  6. 6.
    Shigeta M (2018) Numerical study of axial magnetic effects on a turbulent thermal plasma jet for nanopowder production using 3D time-dependent simulation. J Flow Control Meas Vis 6:107–123CrossRefGoogle Scholar
  7. 7.
    Trelles JP (2019) Nonequilibrium phenomena in (quasi-)thermal plasma flows. Plasma Chem Plasma Process.  https://doi.org/10.1007/s11090-019-10046-1 CrossRefGoogle Scholar
  8. 8.
    Fauchais P (2004) Understanding plasma spraying. J Phys Appl Phys 41:053001Google Scholar
  9. 9.
    Heberlein J, Murphy AB (2008) Thermal plasma waste treatment. J Phys D Appl Phys 41:053001CrossRefGoogle Scholar
  10. 10.
    Murphy AB, Tanaka M, Yamamoto K, Tashiro S, Sato T, Lowke JJ (2009) Modelling of thermal plasmas for arc welding: the role of the shielding gas properties and of metal vapour. J Phys D Appl Phys 42:194006CrossRefGoogle Scholar
  11. 11.
    Shigeta M, Tanaka M (2019) Visualization of electromagnetic-thermal-fluid phenomena in arc welding. Jpn J Appl Phys 59:SA0805CrossRefGoogle Scholar
  12. 12.
    Colombo V, Concetti A, Ghedini E, Dallavalle S, Vancini M (2009) High-speed imaging in plasma arc cutting: a review and new developments. Plasma Sources Sci Technol 18:023001CrossRefGoogle Scholar
  13. 13.
    Shigeta M, Murphy AB (2011) Thermal plasmas for nanofabrication. J Phys D Appl Phys 44:174025CrossRefGoogle Scholar
  14. 14.
    Kim KS, Kim TH (2019) Nanofabrication by thermal plasma jets: from nanoparticles to low-dimensional nanomaterials. J Appl Phys 125:070901CrossRefGoogle Scholar
  15. 15.
    Mostaghimi J, Boulos MI (2015) Thermal plasma sources: how well are they adopted to process needs? Plasma Chem Plasma Process 35:421–436CrossRefGoogle Scholar
  16. 16.
    Siegel RW (1993) Synthesis and properties of nanophase materials. Mater Sci Eng, A 168:189–197CrossRefGoogle Scholar
  17. 17.
    Watanabe T, Nezu A, Abe Y, Ishii Y, Adachi K (2003) Formation mechanism of electrically conductive nanoparticles by induction thermal plasmas. Thin Solid Films 435:27–32CrossRefGoogle Scholar
  18. 18.
    Watanabe T, Okumiya H (2004) Formation mechanism of silicide nanoparticles by induction thermal plasmas. Sci Technol Adv Mater 5:639–646CrossRefGoogle Scholar
  19. 19.
    Shigeta M, Watanabe T (2007) Growth mechanism of silicon-based functional nanoparticles fabricated by inductively coupled thermal plasmas. J Phys D Appl Phys 40:2407–2419CrossRefGoogle Scholar
  20. 20.
    Ryu T, Sohn HY, Hwang KS, Fang ZZ (2009) Chemical vapor synthesis (CVS) of tungsten nanopowder in a thermal plasma reactor. Int J Refract Metal Hard Mater 27:149–154CrossRefGoogle Scholar
  21. 21.
    Shigeta M, Watanabe T (2016) Effect of precursor fraction on silicide nanopowder growth under thermal plasma conditions: a computational study. Powder Technol 288:191–201CrossRefGoogle Scholar
  22. 22.
    Tanaka Y, Tsuke T, Guo W, Uesugi Y, Ishijima T, Watanabe S, Nakamura K (2012) A large amount synthesis of nanopowder using modulated induction thermal plasmas synchronized with intermittent feeding of raw materials. J Phys Conf Ser 406:012001CrossRefGoogle Scholar
  23. 23.
    Kodama N, Tanaka Y, Kita K, Uesugi Y, Ishijima T, Watanabe S, Nakamura K (2014) A method for large-scale synthesis of Al-doped TiO2 nanopowder using pulse-modulated induction thermal plasmas with time-controlled feedstock feeding. J Phys D Appl Phys 47:195304CrossRefGoogle Scholar
  24. 24.
    Kambara M, Kitayama A, Homma K, Hideshima T, Kaga M, Sheem K-Y, Ishida S, Yoshida T (2014) Nano-composite Si particle formation by plasma spraying for negative electrode of Li ion batteries. J Appl Phys 115:143302CrossRefGoogle Scholar
  25. 25.
    Kodama N, Tanaka Y, Kita K, IshisakaY Uesugi Y, Ishijima T, Sueyasu S, Nakamura K (2016) Fundamental study of Ti feedstock evaporation and the precursor formation process in inductively coupled thermal plasmas during TiO2 nanopowder synthesis. J Phys D Appl Phys 49:305501CrossRefGoogle Scholar
  26. 26.
    Kambara M, Hamazaki S, Kodama N, Tanaka Y (2019) Efficient modification of Si/SiOx nanoparticles by pulse-modulated plasma flash evaporation for an improved capacity of lithium-ion storage. J Phys D Appl Phys 52:325502CrossRefGoogle Scholar
  27. 27.
    Girshick SL, Chiu C-P, Muno R, Wu CY, Yang L, Singh SK, McMurry PH (1993) Thermal plasma synthesis of ultrafine iron particles. J Aerosol Sci 24:367–382CrossRefGoogle Scholar
  28. 28.
    Bilodeau JF, Proulx P (1996) A mathematical model for ultrafine iron powder growth in thermal plasma. Aerosol Sci Technol 24:175–189CrossRefGoogle Scholar
  29. 29.
    Desilets M, Bilodeau JF, Proulx P (1997) Modelling of the reactive synthesis of ultra-fine powders in a thermal plasma reactor. J Phys D Appl Phys 30:1951–1960CrossRefGoogle Scholar
  30. 30.
    Cruz ACD, Munz RJ (1997) Vapor phase synthesis of fine particles. IEEE Trans Plasma Sci 25:1008–1016CrossRefGoogle Scholar
  31. 31.
    Aristizabal F, Munz RJ, Berk D (2006) Modeling of the production of ultrafine aluminium particles in rapid quenching turbulent flow. J Aerosol Sci 37:162–186CrossRefGoogle Scholar
  32. 32.
    Goortani BM, Proulx P, Xue S, Mendoza-Gonzalez NY (2007) Controlling nanostructure in thermal plasma processing: moving from highly aggregated porous structure to spherical silica nanoparticles. Powder Technol 175:22–32CrossRefGoogle Scholar
  33. 33.
    Mendoza-Gonzalez NY, Goortani BM, Proulx P (2007) Numerical simulation of silica nanoparticles production in an RF plasma reactor: effect of quench. Mater Sci Eng C 27:1265–1269CrossRefGoogle Scholar
  34. 34.
    Shigeta M, Watanabe T (2008) Numerical investigation of cooling effect on platinum nanoparticle formation in inductively coupled thermal plasmas. J Appl Phys 103:074903CrossRefGoogle Scholar
  35. 35.
    Shigeta M, Watanabe T (2008) Two-dimensional analysis of nanoparticle formation in induction thermal plasmas with counterflow cooling. Thin Solid Films 516:4415–4422CrossRefGoogle Scholar
  36. 36.
    Vorobev A, Zikanov O, Mohanty P (2008) Modelling of the in-flight synthesis of TaC nanoparticles from liquid precursor in thermal plasma jet. J Phys D Appl Phys 41:085302CrossRefGoogle Scholar
  37. 37.
    Vorobev A, Zikanov O, Mohanty P (2008) A co-condensation model for in-flight synthesis of metal-carbide nanoparticles in thermal plasma jet. J Therm Spray Technol 17:956–965CrossRefGoogle Scholar
  38. 38.
    Colombo V, Ghedini E, Gherardi M, Sanibondi P, Shigeta M (2012) A two-dimensional nodal model with turbulent effects for the synthesis of Si nano-particles by inductively coupled thermal plasmas. Plasma Sources Sci Technol 21:025001CrossRefGoogle Scholar
  39. 39.
    Pfender E, Fincke J, Spores R (1991) Entrainment of cold gas into thermal plasma jets. Plasma Chem Plasma Process 11:529–543CrossRefGoogle Scholar
  40. 40.
    Shigeta M (2019) Modeling and simulation of a turbulent-like thermal plasma jet for nanopowder production. IEEJ Trans Electric Electron Eng 14:16–28CrossRefGoogle Scholar
  41. 41.
    Shigeta M, Tanaka M, Ghedini E (2019) Numerical analysis of the correlation between arc plasma fluctuation and nanoparticle growth–transport under atmospheric pressure. Nanomaterials 9:1736CrossRefGoogle Scholar
  42. 42.
    Shigeta M (2012) Time-dependent 3-D simulation of an argon RF inductively coupled thermal plasma. Plasma Sources Sci Technol 21:055029CrossRefGoogle Scholar
  43. 43.
    Shigeta M (2016) Turbulence modelling of thermal plasma flows. J Phys D Appl Phys 49:493001CrossRefGoogle Scholar
  44. 44.
    Hlína J, Šonský J, Něnička V, Zachar A (2005) Statistics of turbulent structures in a thermal plasma jet. J Phys D Appl Phys 38:1760–1768CrossRefGoogle Scholar
  45. 45.
    Hlína J, Gruber J, Šonský J (2006) Application of a CCD camera to investigations of oscillations in a thermal plasma jet. Meas Sci Technol 17:918–922CrossRefGoogle Scholar
  46. 46.
    Hlína J, Chvála F, Šonský J, Gruber J (2008) Multi-directional optical diagnostics of thermal plasma jets. Meas Sci Technol 19:015407CrossRefGoogle Scholar
  47. 47.
    Hlína J, Šonský J (2010) Time-resolved tomographic measurements of temperatures in a thermal plasma jet. J Phys D Appl Phys 43:055202CrossRefGoogle Scholar
  48. 48.
    Viilu A (1962) An experimental determination of the minimum reynolds number for instability in a free jet. J Appl Mech 29:506–508CrossRefGoogle Scholar
  49. 49.
    Dorier J-L, Gindrat M, Hollenstein C, Salito A, Loch M, Barbezat G (2001) Time-resolved imaging of anodic arc root behavior during fluctuations of a DC plasma spraying torch. IEEE Trans Plasma Sci 29:494–501CrossRefGoogle Scholar
  50. 50.
    Duan Z, Heberlein J (2002) Arc instabilities in a plasma spray torch. J Therm Spray Technol 11:44–51CrossRefGoogle Scholar
  51. 51.
    Ghorui S, Tiwari N, Meher KC, Jan A, Bhat A, Sahasrabudhe SN (2015) Direct probing of anode arc root dynamics and voltage instability in a dc non-transferred arc plasma jet. Plasma Sources Science and Technology 24: 065003 (10 pages)CrossRefGoogle Scholar
  52. 52.
    Guisbiers G, Kazan M, Overschelde OV, Wautelet M, Pereira S (2008) Mechanical and thermal properties of metallic and semiconductive nanostructures. J Phys Chem C 112:4097–4103CrossRefGoogle Scholar
  53. 53.
    Nemchinsky VA, Shigeta M (2012) Simple equations to describe aerosol growth. Model Simul Mater Sci Eng 20:045017CrossRefGoogle Scholar
  54. 54.
    Girshick SL, Chiu C-P, McMurry PH (1990) Time-dependent aerosol models and homogeneous nucleation rates. Aerosol Sci Technol 13:465–477CrossRefGoogle Scholar
  55. 55.
    Phanse GM, Pratsinis SE (1989) Theory for aerosol generation in laminar flow condensers. Aerosol Sci Technol 11:100–119CrossRefGoogle Scholar
  56. 56.
    Murphy AB (1996) A comparison of treatments of diffusion in thermal plasmas. J Phys D Appl Phys 29:1922–1932CrossRefGoogle Scholar
  57. 57.
    Talbot L, Cheng RK, Schefer RW, Willis DR (1980) Thermophoresis of particles in a heated boundary layer. J Fluid Mech 101:737–758CrossRefGoogle Scholar
  58. 58.
    Launder BE, Spalding DB (1974) The numerical computation of turbulent flows. Comput Methods Appl Mech Eng 3:269–289CrossRefGoogle Scholar
  59. 59.
    McKelliget J, Szekely J, Vardelle M, Fauchais P (1982) Temperature and velocity fields in a gas stream exiting a plasma torch. A mathematical model and its experimental verification. Plasma Chem Plasma Process 2:317–332CrossRefGoogle Scholar
  60. 60.
    Lee YC, Pfender E (1987) Particle dynamics and particle heat and mass transfer in thermal plasmas. Part III thermal plasma jet reactors and multiparticle injection. Plasma Chem Plasma Process 7:1–27CrossRefGoogle Scholar
  61. 61.
    El-Hage M, Mostaghimi J, Boulos MI (1989) A turbulent flow model for the rf inductively coupled plasma. J Appl Phys 65:4178–4185CrossRefGoogle Scholar
  62. 62.
    Ramshaw JD, Chang CH (1992) Computational fluid dynamics modeling of multicomponent thermal plasmas. Plasma Chem Plasma Process 12:299–325CrossRefGoogle Scholar
  63. 63.
    Ye R, Proulx P, Boulos MI (2000) Particle turbulent dispersion and loading effects in an inductively coupled radio frequency plasma. J Phys D Appl Phys 33:2154–2162CrossRefGoogle Scholar
  64. 64.
    Shigeta M, Sato T, Nishiyama H (2003) Numerical simulation of a potassium-seeded turbulent RF inductively coupled plasma with particles. Thin Solid Films 435:5–12CrossRefGoogle Scholar
  65. 65.
    Ahmed I, Bergman TL (2000) Three-dimensional simulation of thermal plasma spraying of partially molten ceramic agglomerates. J Therm Spray Technol 9:215–224CrossRefGoogle Scholar
  66. 66.
    Hur M, Hong SH (2002) Comparative analysis of turbulent effects on thermal plasma characteristics inside the plasma torches with rod- and well-type cathodes. J Phys D Appl Phys 35:1946–1954CrossRefGoogle Scholar
  67. 67.
    Ramachandran K, Nishiyama H (2002) Three-dimensional effects of carrier gas and particle injections on the thermo-fluid fields of plasma jets. J Phys D Appl Phys 35:307–317CrossRefGoogle Scholar
  68. 68.
    Ramachandran K, Kikukawa N, Nishiyama H (2003) 3D modeling of plasma–particle interactions in a plasma jet under dense loading conditions. Thin Solid Films 435:298–306CrossRefGoogle Scholar
  69. 69.
    Ramachandran K, Nishiyama H (2004) Fully coupled 3D modeling of plasma–particle interactions in a plasma jet. Thin Solid Films 457:158–167CrossRefGoogle Scholar
  70. 70.
    Li H-P, Chen X (2001) Three-dimensional modelling of a dc non-transferred arc plasma torch. J Phys D Appl Phys 34:L99–L102CrossRefGoogle Scholar
  71. 71.
    Li H-P, Pfender E, Chen X (2003) Application of Steenbeck’s minimum principle for three-dimensional modelling of DC arc. J Phys D Appl Phys 36:1084–1096CrossRefGoogle Scholar
  72. 72.
    Guo Z, Yin S, Liao H, Gu S (2015) Three-dimensional simulation of an argon–hydrogen DC non-transferred arc plasma torch. Int J Heat Mass Transf 80:644–652CrossRefGoogle Scholar
  73. 73.
    Park JM, Kim KS, Hwang TH, Hong SH (2004) Three-dimensional modeling of arc root rotation by external magnetic field in nontransferred thermal plasma torches. IEEE Trans Plasma Sci 32:479–487CrossRefGoogle Scholar
  74. 74.
    Mariaux G, Vardelle A (2005) 3-D time-dependent modelling of the plasma spray process. Part 1: flow modelling. Int J Therm Sci 44:357–366CrossRefGoogle Scholar
  75. 75.
    Kim KS, Park JM, Choi S, Kim J, Hong SH (2008) Comparative study of two- and three-dimensional modeling on arc discharge phenomena inside a thermal plasma torch with hollow electrodes. Phys Plasmas 15:023501CrossRefGoogle Scholar
  76. 76.
    Martinez B, Mariaux G, Vardelle A, Barykin G, Parco M (2009) Numerical Investigation of a hybrid HVOF-plasma spraying process. J Therm Spray Technol 18:909–920CrossRefGoogle Scholar
  77. 77.
    Yakhot V, Orszag SA, Thangam S, Gatski TB, Speziale CG (1992) Development of turbulence models for shear flows by a double expansion technique. Phys Fluids A 4:1510–1520CrossRefGoogle Scholar
  78. 78.
    Colombo V, Concetti A, Ghedini E (2008) Three-dimensional time-dependent modeling of a DC transferred arc twin-torch system. IEEE Trans Plasma Sci 36:1038–1039CrossRefGoogle Scholar
  79. 79.
    Launder BE, Reece GJ, Rodi W (1975) Progress in the development of a Reynolds-stress turbulence closure. J Fluid Mech 68:537–566CrossRefGoogle Scholar
  80. 80.
    Colombo V, Ghedini E (2005) Time dependent 3-D simulation of a non-transferred arc plasma torch: anode attachment and downstream region effects. In: Proceedings of 17th international symposium on plasma chemistry, unpaginated CD, Toronto, CanadaGoogle Scholar
  81. 81.
    Colombo V, Concetti A, Ghedini E (2007) Time dependent 3D large eddy simulation of a DC non-transferred arc plasma spraying torch with particle injections. In: Proceedings of 16th IEEE international pulsed power conference, vol 2, Albuquerque, USA, pp 1565–1568Google Scholar
  82. 82.
    Marchand C, Chazelas C, Mariaux G, Vardelle A (2007) Liquid precursor plasma spraying: modeling the interactions between the transient plasma jet and the droplets. J Therm Spray Technol 16:705–712CrossRefGoogle Scholar
  83. 83.
    Vardelle A, Chazelas C, Marchand C, Mariaux G (2008) Modeling time-dependent phenomena in plasma spraying of liquid precursors. Pure Appl Chem 80:1981–1991CrossRefGoogle Scholar
  84. 84.
    Colombo V, Concetti A, Ghedini E, Gherardi M, Sanibondi P (2011) Three-dimensional time-dependent large eddy simulation of turbulent flows in an inductively coupled thermal plasma torch with a reaction chamber. IEEE Trans Plasma Sci 39:2894–2895CrossRefGoogle Scholar
  85. 85.
    Jeništa J, Takana H, Nishiyama H, Bartlová M, Aubrecht V, Křenek P, Hrabovský M, Kavka T, Sember V, Mašláni A (2011) Integrated parametric study of a hybrid-stabilized argon–water arc under subsonic, transonic and supersonic plasma flow regimes. J Phys D Appl Phys 44:435204CrossRefGoogle Scholar
  86. 86.
    Shigeta M (2013) Three-dimensional flow dynamics of an argon RF plasma with dc jet assistance: a numerical study. J Phys D Appl Phys 46:015401CrossRefGoogle Scholar
  87. 87.
    Trelles JP (2014) Identification of coherent flow structures in non-equilibrium plasmas. IEEE Trans Plasma Sci 42:2852–2853CrossRefGoogle Scholar
  88. 88.
    Trelles JP, Modirkhazeni SM (2014) Variational multiscale method for nonequilibrium plasma flows. Comput Methods Appl Mech Eng 282:87–131CrossRefGoogle Scholar
  89. 89.
    Meillot E, Vincent S, Bot CL, Sarret F, Caltagirone JP, Bianchi L (2015) Numerical simulation of unsteady ArH2 plasma spray impact on a moving substrate. Surf Coat Technol 268:257–265CrossRefGoogle Scholar
  90. 90.
    Bhigamudre VG, Trelles JP (2019) Characterization of the arc in crossflow using a two-temperature nonequilibrium plasma flow model. J Phys D Appl Phys 52:015205CrossRefGoogle Scholar
  91. 91.
    Patanker SV, Spalding DB (1972) A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. Int J Heat Mass Transf 15:1787–1806CrossRefGoogle Scholar
  92. 92.
    Oliveira PJ, Issa RI (2001) An improved PISO algorithm for the computation of buoyancy-driven flows. Numer Heat Transf B 40:473–493CrossRefGoogle Scholar
  93. 93.
    Komurasaki S (2012) A hydrothermal convective flow at extremely high temperature. In: Proceedings of 7th international conference on computational fluid dynamics ICCFD7-3001, Kohala Coast, USAGoogle Scholar
  94. 94.
    Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipes in C the art of scientific computing, 2nd edn. Cambridge University Press, CambridgeGoogle Scholar
  95. 95.
    Watanabe T, Honda T, Kanzawa A (1989) Concentration of a plasma energy flow by a blowing gas. Int Chem Eng 29:663–670Google Scholar
  96. 96.
    Matsushita Y (2011) Outflow boundary condition in the finite volume method for unsteady-state fluid flow computation with variable density. Comput Therm Sci 3:531–537CrossRefGoogle Scholar
  97. 97.
    Smagorinsky J (1963) General circulation experiments with the primitive equations: I. The basic experiment. Mon Weather Rev 91:99–164CrossRefGoogle Scholar
  98. 98.
    Germano M, Piomelli U, Moin P, Cabot WH (1991) A dynamic subgridscale eddy viscosity model. Phys Fluids A 3:1760–1765CrossRefGoogle Scholar
  99. 99.
    Lilly DK (1992) A proposed modification of the Germano subgridscale closure method. Phys Fluids A 4:633–635CrossRefGoogle Scholar
  100. 100.
    Martín MP, Piomelli U, Candler GV (2000) Subgrid-scale models for compressible large-eddy simulations. Theoret Comput Fluid Dyn 13:361–376Google Scholar
  101. 101.
    Kobayashi H (2005) The subgrid-scale models based on coherent structures for rotating homogeneous turbulence and turbulent channel flow. Phys Fluids 17:045104CrossRefGoogle Scholar
  102. 102.
    Kobayashi H (2006) Large eddy simulation of magnetohydrodynamic turbulent channel flows with local subgrid-scale model based on coherent structures. PhysFluids 18:045107Google Scholar
  103. 103.
    Menart J, Lin L (1998) Numerical study of high-intensity free-burning arc. J Thermophys Heat Transf 12:500–506CrossRefGoogle Scholar
  104. 104.
    Japan Institute of Metals (1993) Metal data book. Maruzen, TokyoGoogle Scholar
  105. 105.
    Hunt JCR, Wray AA, Moin P (1988) Eddies, streams, and convergence zones in tur-bulent flows. In: Center for turbulence research proceedings of the summer program, pp 193–208Google Scholar
  106. 106.
    Leparoux M, Schreuders C, Shin JW, Siegman S (2005) Induction plasma synthesis of carbide nano-powders. Adv Eng Mater 7:349–353CrossRefGoogle Scholar
  107. 107.
    Rao N, Girshick SL, Heberlein J, McMurry P, Jones S, Hansen D, Micheel B (1995) Nanoparticle formation using a plasma expansion process. Plasma Chem Plasma Process 15:581–606CrossRefGoogle Scholar
  108. 108.
    Leparoux M, Kihn Y, Paris S, Schreuders C (2008) Microstructure analysis of RF plasma synthesized TiCN nanopowders. Int J Refract Metal Hard Mater 26:277–285CrossRefGoogle Scholar
  109. 109.
    Leparoux M, Schreuders C, Fauchais P (2008) Improved plasma synthesis of Si-nanopowders by quenching. Adv Eng Mater 10:1147–1150CrossRefGoogle Scholar
  110. 110.
    Berlinger B, Benker N, Weinbruch S, L’Vov BV, Ebert M, Koch W, Ellingsen DG, Thomassen Y (2011) Physicochemical characterisation of different welding aerosols. Anal Bioanal Chem 399:1773–1780PubMedCrossRefGoogle Scholar
  111. 111.
    Shigeta M, Watanabe T (2010) Growth model of binary alloy nanopowders for thermal plasma synthesis. J Appl Phys 108:043306CrossRefGoogle Scholar
  112. 112.
    Shigeta M, Watanabe T, Nishiyama H (2004) Numerical investigation for nano-particle synthesis in an RF inductively coupled plasma. Thin Solid Films 457:192–200CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2020

Authors and Affiliations

  1. 1.Joining and Welding Research InstituteOsaka UniversityIbaraki-shiJapan

Personalised recommendations