Thermal Spray Process Simulation
Theory: heating and melting in flight
Overview
Our sprayed coating contains unmelted particles and too much porosity.
A particle's flight from gun to substrate takes less than a millisecond. In that time its core must exceed the melting point and absorb the latent heat; otherwise it hits solid, bouncing off or stacking with gaps. Particles are small enough to treat as uniform in temperature, so heating rate is set by convection from the gas. Heat enters through surface area (diameter squared) while the mass to heat scales with volume (diameter cubed), so time to melt scales with diameter squared. Large particles become sharply harder to melt, making the powder's upper size limit critical.
Time to melt
T_g is gas temperature, T_m melting point, L latent heat and T̄ the mean particle temperature during heating (midway between initial and melting). The first term is heating to the melting point, the second melting.
Particle Biot number and flight time
x_sd is spray distance and v_p particle velocity. With Biot numbers above 0.1, particles tend to melt at the surface while the core stays solid.
Schoop's metal spraying
Thermal spraying was invented by Schoop in Switzerland in the early 20th century. He is said to have been inspired by seeing lead pellets fired from a toy gun flatten and stick to a wall. The first method blew molten metal with compressed air; later came wire melted in a gas flame, electric arc, plasma and HVOF, with ever hotter, faster heat sources — an evolution toward higher-melting materials and denser coatings.
Worked examples
Example 1: plasma spray (mean gas 8,000 K, conductivity 1.0 W/mK, particles 150 m/s, 0.1 m → 0.67 ms flight)
| Material | Biot | 20 μm | 40 μm | 60 μm | Max fully melted |
|---|---|---|---|---|---|
| Nickel | 0.014 | 0.04 ms | 0.18 ms | 0.40 ms | 77 μm |
| Alumina | 0.17 | 0.07 ms | 0.29 ms | 0.65 ms | 61 μm |
| WC-Co (Co melting) | 0.013 | 0.04 ms | 0.18 ms | 0.40 ms | 78 μm |
Properties: nickel (density 8,900 kg/m³, specific heat 500 J/kgK, melting point 1,728 K, latent heat 298 kJ/kg), alumina (3,950, 1,200, 2,327 K, 1,070 kJ/kg).
Example 2: HVOF (gas 2,800 K, conductivity 0.15 W/mK, particles 500 m/s, 0.2 m → 0.40 ms)
| Material | 20 μm | 40 μm | Max fully melted |
|---|---|---|---|
| Nickel | 1.3 ms | 5.4 ms | 11 μm |
| Alumina | 3.4 ms | 13.7 ms | 7 μm |
| WC-Co (Co melting) | 1.4 ms | 5.7 ms | 11 μm |
With HVOF hardly any particle melts. Does that still form a coating?
Yes. HVOF doesn't melt particles fully; it drives softened particles at very high speed and uses their kinetic energy to deform and bond them. The quiescent-gas formula (Nu = 2) underestimates heating — relative velocity raises heat transfer several-fold and surfaces are partly molten — but not melting fully is actually an advantage. Cemented carbide WC-Co degrades when overheated as carbides decompose, so firing it cool with HVOF yields hard, dense coatings. Melting alumina ceramic into a coating, by contrast, requires plasma. Even there, 60 μm alumina is borderline, and real plasma cools sharply away from its axis, so powders are often classified to about 10–45 μm.
Simulation workflow
- Compute gas flow and temperature in the gun and jet (plasma properties vary strongly with temperature).
- Track many particles with a size distribution and injection position and velocity.
- Compute heating, melting and velocity per particle and tally impact states.
- Estimate porosity and adhesion from splat spreading and solidification.
- Compute residual stress from coating and substrate temperature histories.
“The mean particle size melted fine”
An alumina coating had many unmelted particles, yet a calculation at the 30 μm mean size showed full melting, leaving the cause unclear. The powder's size distribution revealed about 10% by weight above 60 μm. Melting time scales with diameter squared, so 60 μm takes four times as long as 30 μm and can't melt in flight. Classifying out the large particles greatly reduced unmelted particles and porosity. Calculating only at the mean misses the few large particles that cause trouble.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Mean size only | Unmelted large particles missed | Track the size distribution |
| Constant gas properties | Heating badly wrong | Temperature-dependent properties |
| Uniform temperature at high Bi | Solid core missed | Resolve conduction inside |
| Fixed spray distance assumed | Re-solidification missed | Check state at impact |
| Ignoring substrate temperature | Wrong residual stress | Compute thermal history |
I'd like to learn related topics.
Related pages include additive manufacturing thermal analysis, casting thermal analysis, quenching simulation, induction hardening and furnace simulation.
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