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Numerical Modeling in Radio Frequency Suspension Plasma Spray of Zirconia Powders

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Abstract

A comprehensive model was developed to investigate the suspension spraying for a radio frequency (RF) inductively coupled plasma torch. Firstly, the electromagnetic field is solved with the Maxwell equations and validated by the analytical solutions. Secondly, the plasma field with different power inputs is simulated by solving the governing equations of the fluid flow coupled with the RF heating. Then, the suspension droplets embedded with nano particles are modeled in a Lagrangian manner, considering feeding, collision, heating and evaporation of the suspension droplets, as well as tracking, acceleration, melting and evaporation of the nano or agglomerate particles. The non-continuum effects and the influence of the evaporation on the heat transfer are considered. This particle model predicts the trajectory, velocity, temperature and size of the in-flight nano- or agglomerate particles. The effects of operating conditions and intial inputs on the particle characteristics are investigated. The statistical distributions of multiple particles’ size, velocity, temperature are also discussed for the cases with and without consideration of suspension droplets collision.

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Abbreviations

A :

Magnetic vector potential (A H m−1)

B :

Magnetic flux density (T)

C p :

Specific heat (J kg−1 K−1)

C D :

Drag coefficient

D :

Diffusion coefficients (m2 s−1)

E :

Electric field (V m−1)

f :

Frequency (Hz)

F :

Lorentz force (N m−3)

H :

Magnetic field (A m−1)

h :

Heat transfer coefficient

J :

Current density (A m−2)

Kn :

Knudsen number

k :

Thermal conductivity (W m−1 K−1)

L m :

Latent heat of fusion (J kg−1)

L v :

Latent heat of evaporation (J kg−1)

m :

Mass

Nu :

Nusselt number

Pr :

Prandtl number, Pr = ν/α

Q J :

Joule heating (W m−3)

Q conv :

Convection heat (W m−3)

Q rad :

Radiation heat loss (W m−3)

Q vap :

Vaporization heat (W m−3)

R :

Radius (nm)

Sh :

Sherwood number

r :

Radial coordinate (m)

t :

Time (s)

T :

Particle temperature (K)

V, U, W:

Velocity vector (m s−1)

x :

Axial coordinate (m)

η :

Viscosity (kg s−1 m−1)

θ :

Azimuthal coordinate

θ inject :

Injection angle

μ 0 :

Permeability in vacuum, 4π × 10−7 (H m−1)

σ :

Electrical conductivity S (m−1)

ω:

Angular frequency rad (s−1)

c :

Cell

f :

Film surrounding particle surface

w :

Vicinity of the particle surface

l :

Liquid

g :

Gas

p :

Particle

so :

Solid

sl :

Solvent

v :

Vapor

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Acknowledgments

This work was supported by a grant from the Major State Basic Research Development Program of China (973 Program) under contract No. 2011CB706501, the National Natural Science Foundation of China with Grant No. 11072216 and No. 11002136.

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Authors and Affiliations

  1. China Jiliang University, 310018, Hangzhou, People’s Republic of China

    Lijuan Qian & Jianzhong Lin

  2. State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, 310027, Hangzhou, People’s Republic of China

    Jianzhong Lin & Hongbin Xiong

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  1. Lijuan Qian
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Correspondence to Jianzhong Lin.

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Qian, L., Lin, J. & Xiong, H. Numerical Modeling in Radio Frequency Suspension Plasma Spray of Zirconia Powders. Plasma Chem Plasma Process 30, 733–760 (2010). https://doi.org/10.1007/s11090-010-9247-2

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