Abstract
Numerical models have been developed using computational fluid dynamics (CFD) analysis program FLUENT V6.02© to investigate the effect of the substrate on the behavior of the plasma flow fields and in-flight particles. Simulations are performed for cases where flat substrates are either present or absent, for the former, the substrate is oriented perpendicularly or inclined to the torch axis. It is shown that although the presence of perpendicular or inclined substrate significantly influences the plasma flow fields at the vicinity of the substrate, the particle behavior remain relatively unaffected. The insignificant effect of the substrate on particle behavior is qualitatively verified by experimental observation using SprayWatch© imaging diagnostics equipment. Images captured by the equipment confirm that the particles travel through the plasma plume with high momentum and show no sudden change in theirtrajectories right before impacting the substrate. Both the numerical and experimental findings show that the freestream model is sufficiently detailed for future work of this nature.
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Abbreviations
- A :
-
Cross section area (m2)
- B :
-
Empirical constant (=9.81)
- C D :
-
Drag coefficient
- C μ :
-
Empirical constant (=0.09)
- C 1ε :
-
Empirical constant (=1.44)
- C 2ε :
-
Empirical constant (=1.92)
- C p :
-
Specific heat capacity (J/kg K)
- D :
-
Diffusion coefficient (m2/s)
- D p :
-
Particle diameter (m)
- E :
-
Arc voltage (V)
- G κ :
-
Product of the eddy viscosity and viscous dissipation terms
- H f :
-
Latent heat of fusion (J/kg)
- h :
-
Enthalpy (J/kg)
- h :
-
Heat transfer coefficient (W/m2 K)
- I :
-
Arc current (A)
- K :
-
von Kármán constant (=0.42)
- k :
-
Thermal conductivity (W/mK)
- m :
-
Mass (kg)
- n p :
-
Number of particles
- p :
-
Pressure (Pa)
- \(P_{\rm in}^{\prime\prime\prime}\) :
-
Constant heat source (W/m3)
- \(\dot{q}\) :
-
Heat flux (W/m2)
- S ϕ :
-
Source term
- T :
-
Temperature (K)
- T A :
-
Plasma temperature at adjacent element to the wall (K)
- T b :
-
Boiling point (K)
- T i :
-
Turbulent intensity (%)
- T m :
-
Melting point (K)
- T w :
-
Substrate temperature (K)
- t :
-
Time (s)
- u :
-
Velocity vector (m/s)
- u′:
-
Velocity vector fluctuation (m/s)
- U :
-
Velocity magnitude (m/s)
- U A :
-
Plasma velocity at adjacent element to the wall (m/s)
- u, v, w :
-
Velocity components in x, y and z directions, respectively (m/s)
- V :
-
Volume (m3)
- Y n :
-
Mass fraction
- y :
-
Distance from element to the wall (m)
- y A :
-
Distance from adjacent element to the wall (m)
- Subscripts :
-
- ∞:
-
Far field region
- l:
-
Laminar state
- p:
-
Particle
- t:
-
Turbulent state
- Greek symbols :
-
- α:
-
Thermal diffusivity (m2/s)
- ε:
-
Turbulent
- η:
-
Torch efficiency (%)
- Γϕ :
-
Diffusion coefficient
- κ:
-
Turbulent kinetic energy (m2/s2)
- κA :
-
Turbulent kinetic energy at adjacent element to the wall (m2/s2)
- μ:
-
Dynamic viscosity (kg/ms)
- ν:
-
Kinematic viscosity (m2/s)
- ϕ:
-
Process variable
- ρ:
-
Density (kg/m3)
- τ:
-
Shear stress (Pa)
- τw :
-
Wall shear stress (Pa)
- ς:
-
Liquid fraction
- Dimensionless numbers :
-
- Pr :
-
Prandtl number: \(Pr = \frac{\nu}{\alpha}\)
- Re :
-
Reynolds number: \(Re = \frac{\rho uD}{\mu}\)
- Re r :
-
Relative Reynolds number: \(Re_{\rm r}=\frac{\rho D_{p}(\boldsymbol{u}-\boldsymbol{u}_{p})}{\mu}\)
- U * :
-
Dimensionless mean velocity
- y * :
-
Dimensionless distance from element to the wall
- \(y^{\ast}_{T}\) :
-
Dimensionless thermal sublayer thickness
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Kang, C.W., Ng, H.W. & Yu, S.C.M. Comparative Study of Plasma Spray Flow Fields and Particle Behavior Near to Flat Inclined Substrates. Plasma Chem Plasma Process 26, 149–175 (2006). https://doi.org/10.1007/s11090-006-9009-3
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DOI: https://doi.org/10.1007/s11090-006-9009-3