Modeling Microstructure Formation in Yttria-Stabilized Zirconia (YSZ) Droplet with High Impact Velocity in Supersonic Plasma Spray


In plasma spraying, copious heterogeneous nucleation starts when a molten ceramic droplet spreads on a cold surface under rapid cooling. Some nuclei will survive and grow, eventually forming a splat of grains of distinct crystalline orientations. This paper aims to predict the dynamic process of yttria-stabilized zirconia (YSZ) droplet impact with solidification microstructure formation under various plasma spray conditions. A diffuse interface model was developed to track the evolving liquid–gas and solid–liquid interfaces. Continuously dense YSZ droplet impacts with different impacting angles were conducted, along with a hollow droplet impact. Results reveal that competitive growth among crystals is limited in the planar solidification, and that columnar structure dominates all the tests performed owing to a large thermodynamic driving force, and that given the rapid spreading of YSZ droplets along a solid surface, solidification may be safely assumed to take place mostly after spreading. Besides, typical crystal growth velocities are around 1 m/s, and local equilibrium can be assumed in the bulk.

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\({\mathbf{u}}\) :

Velocity (m/s)

t :

Time (s)

p :

Pressure (Pa)

\(\rho\) :

Density (kg/m3)

\(\varvec{\sigma}\) :

Newtonian stress tensor (Pa)

\({\mathbf{g}}\) :

Gravitational acceleration (m/s2)

G :

Chemical potential (J/m3)

c :

Order parameter for the flow field

c P :

Specific heat (J/kg K)

T :

Temperature (K)

\(\rho_{\text{l}}\) :

Liquid density (kg/m3)

\(L_{\text{l}}\) :

Latent heat of fusion (kJ/kg)

\(\phi\) :

Order parameter for the solidification field

\(\mu\) :

Dynamic viscosity (Pa s)

M :

Phase field mobility (m3 s/kg)

f :

Bulk free energy density (J/m3)

\(\xi\) :

Interface thickness (m)

\(\gamma\) :

Surface tension (N/m)

\(\tau_{\phi }\) :

Kinetic time constant (s) for the solidification field

\(u\) :

Reduced temperature

s :

Coupling strength (m)

\(\theta\) :

Orientation field

\(\varepsilon_{\theta }\) :

Gradient energy coefficient (m) for the orientation field

P :

Kinetics of θ

\(\tau_{\theta }\) :

Kinetic time constant (s) for the orientation field

d :

Mushy region constant

\(F_{\text{l}}\) :

Liquid fraction

\(f_{\text{w}}\) :

Wall free energy density (J/m2)

\(d_{0}\) :

Thermal capillary length (m)

D :

Thermal diffusivity (m2/s)

\(\varepsilon_{4}\) :

Antistrophic strength

\(\mu\) :

Rotation rate of grains (m)

\(\beta\) :

Grain boundary mobility

\(Cn\) :

Cahn number

\(\mu_{\text{e}}\) :

Effective viscosity (Pa s)

k :

Thermal conductivity (W/m K)

\(\tilde{\varepsilon }_{\phi }\) :

Gradient energy coefficient (m) for the solidification field


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Correspondence to Ben Q. Li.

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Shen, M., Li, B.Q. & Bai, Y. Modeling Microstructure Formation in Yttria-Stabilized Zirconia (YSZ) Droplet with High Impact Velocity in Supersonic Plasma Spray. J Therm Spray Tech (2020).

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  • droplet impact
  • hollow droplet
  • plasma spray
  • polycrystalline growth
  • solidification