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

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Abstract

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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Abbreviations

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

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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Authors and Affiliations

  1. State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi, People’s Republic of China

    Mingguang Shen

  2. Department of Mechanical Engineering, University of Michigan, Dearborn, MI, 48128, USA

    Ben Q. Li

  3. State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi, People’s Republic of China

    Yu Bai

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  1. Mingguang Shen
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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 29, 1695–1707 (2020). https://doi.org/10.1007/s11666-020-01060-3

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  • DOI: https://doi.org/10.1007/s11666-020-01060-3

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