Simulating Turbulent Thermal Plasma Flows for Nanopowder Fabrication

  • Masaya ShigetaEmail author
Review Article


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.


Thermal plasma Nanopowder Numerical simulation Turbulent flow Vortex structure 

List of Symbols


Specific heat at constant pressure


Diffusion coefficient




Number of monomers


Unit matrix


Homogeneous nucleation rate


Thermophoresis coefficient


Boltzmann’s constant




Mean free path




Number of datasets






Radiation loss


Cross-correlation coefficient




Velocity gradient tensor


Surface area


Velocity vector




Axial position


Radial position in Cartesian coordinate system


Radial position in Cartesian coordinate system

Greek Letters






Thermal conductivity


Viscous dissipation


Surface tension


Time lag






Anchoring point


Critical state




Saturation state





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)


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Authors and Affiliations

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

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