Abstract
A mathematical model is developed to describe the plasma spray process in which particular attention is paid to the fluid flow and temperature fields in the plasma jet, the plasma/particle interaction, and the heat transfer phenomena associated with the deposition process. On the basis of the heat transfer analysis it was possible to define the limiting conditions for satisfactory operation of the deposition process in terms of basic process variables. For high deposition rates, high levels of superheat, and low thermal conductivity of the deposit, the limiting condition is set by the rate at which heat may be removed by the substrate. For large particle sizes and materials with high melting points the limiting condition is determined by the need to transfer sufficient thermal energy to the particles so that they arrive at the substrate in a fully molten state. Wherever possible, the model predictions were compared with experimental measurements and good agreement was obtained.
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Abbreviations
- C :
-
Specific heat
- C1 to C3 :
-
Constants in turbulence model
- C D :
-
Drag coefficient
- C′ D :
-
Drag coefficient modified for nonisothermal conditions
- D :
-
Diameter
- h :
-
Heat transfer coefficient from plasma to target
- H* :
-
Particle superheat
- k :
-
Turbulent kinetic energy per unit volume
- K :
-
Thermal conductivity
- L :
-
Latent heat of sprayed material
- L* :
-
Dimensionless latent heat of particle
- M :
-
Mass Nu Nusselt number
- P :
-
Pressure
- q t :
-
Heat flux from plasma jet to target
- Q :
-
Heat content
- r :
-
Radial coordinate (distance from axis of symmetry)
- R :
-
Radius
- Re:
-
Particle Reynolds number
- S:
-
Source term in conservation equations
- S*:
-
Ratio of coating and substrate properties
- t :
-
Time
- T :
-
TemperatureAxial velocity
- U, U C :
-
Spray velocity (rate of increase of coating thickness)
- v:
-
Radial velocity
- x :
-
Axial coordinate in target (origin at target/coating interface)
- x′ :
-
Axial coordinate in target (origin at surface of coating)
- X :
-
Coating thickness
- X 0 :
-
Thickness of solid coating when liquid layer appears
- Y :
-
Thickness of coating + thickness of target
- z:
-
Axial coordinate (origin at torch exit)
- a:
-
Thermal diffusivity
- e:
-
Dissipation rate of turbulence energy
- η* :
-
Solidification rate constant
- fi :
-
Viscosity (molecular viscosity if no subscript attached)
- v :
-
Kinematic viscosity
- ρ:
-
Density
- σ :
-
Prandtl number
- av :
-
Property value at mean film temperature
- b :
-
Value at edge of boundary layer in plasma
- c :
-
Coating
- de :
-
Value at edge of boundary layer around particle eff Effective
- g :
-
Gas (plasma)
- mp :
-
Melting point of particle
- p :
-
Particle
- R :
-
Radiation
- s:
-
Substrate (target)
- t :
-
Turbulent
- T :
-
Temperature
- w :
-
Wall (surface of solid target or solid coating)
- 0:
-
Value at torch exit (for plasma model)
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El-Kaddah, N., McKelliget, J. & Szekely, J. Heat transfer and fluid flow in plasma spraying. Metall Trans B 15, 59–70 (1984). https://doi.org/10.1007/BF02661063
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DOI: https://doi.org/10.1007/BF02661063