# 17.5: Case Study - Thermal Spraying

- Page ID
- 8280

Thermal spraying is widely used to produce high quality coatings, mostly ceramic or metallic, and, to a lesser extent, for purposes of repair or to build up a shaped component. It is most commonly carried out by feeding powder into a high temperature, high velocity gas stream, where the particles gain heat and momentum (and may or may not closely approach the temperature and/or velocity of the surrounding gas).

Particles are carried by the gas stream towards a substrate, on which they are expected to impinge, deform and adhere. The issue of whether a particle in a fluid stream is likely to strike an obstacle is covered in the previous page: it's controlled by the Stokes number. As explained there, very fine particles are unlikely to strike surfaces. During thermal spraying, velocities are quite high (u ~100 m s^{-1}), favouring impact, but obstacles (substrates) are relatively large (D >~10 mm), with the opposite effect (giving the particle more time to change direction). An estimate of minimum particle size for impact (by setting Stk ~ 1), for a particle with a typical density (~3 × 10^{3} kg m^{3}), is given by

\[ d_{min} \approx \sqrt{ \frac{18 \pi D}{\Delta \rho u} } \approx \sqrt{ \frac{18(310^{-5})(0.01)}{(3 \times 10^3)(100)} } \approx 5 \mu \text{m} \]

In general, therefore, thermal spraying is not carried out with fine particles and a typical size range would be ~20-100μm.

The treatment on the previous page can also be used to explore times and distances over which particles will be accelerated to velocities close to that of the gas (which may itself be dropping off with distance ahead of the torch). The expression (for the characteristic time for a particle to change its velocity (so that it's close to that of the gas) leads to times of ~10 ms and 40 ms for particle diameters of 50 μm and 100 μm. Gas velocities in thermal spraying range from several tens of m s^{-1} to (supersonic) speeds of several hundred m s^{-1}. Taking 100 m s^{-1} as representative, the distances needed for particles with these two sizes to approach that speed (assuming linear acceleration over the above periods) are about 0.5 m and 2 m. This is, of course, a crude estimate, and there is no need for the particle velocity to closely approach that of the gas, but it does show that a relatively large "stand-off" distance may be needed for particles to reach peak velocity.

The other main issue is heat transfer from gas to particle. This is complex, but can be simplified by use of a heat transfer coefficient (interfacial thermal conductance), h_{i}, which relates the heat flux into a particle to the temperature difference between particle surface and nearby gas. The value of h_{i} can be expressed as K_{g} / δ, where K_{g}is gas conductivity and δ the thickness of a thermal boundary layer in the gas around the particle. The value of δ depends on relative velocity, gas viscosity, particle size and shape etc, so generalisations are difficult. Typically, however, h_{i} ranges from ~100 kW m^{-2} K^{-1} (fine particle, high relative velocity) to ~1 kW m^{-2} K^{-1} (coarse particle, low relative velocity). Since K_{g} for most gases is ~0.02 W m^{-2} K^{-1}, corresponding boundary layer thicknesses are ~0.2 μm and ~20 μm.

A value of hi allows estimation of heating rates, and also of whether particles remain isothermal or develop large internal thermal gradients. The latter can be decided from the value of the Biot number (ratio of conductance of interface to that of the particle):

\[ \text{Bi} \approx \frac{h_i}{K/L} \approx \frac{h_i(d/2)}{K_p} \]

Using the figures above, and taking K_{p} to be ~5 W m^{-2} K^{-1} (ceramic), Bi for a fine particle (d~5 μm) is ~0.05, while for a large particle (d~100 μm) it is ~0.01. These are both <<1, implying that all (thermally-sprayed) particles remain isothermal during the process (since the thermal resistance of the particle interior is small relative to that of the interface). This will be even more strongly the case for metallic particles (higher K_{p }

\[ h_i \Delta (4 \pi (d/2)^2) = c \left ( \frac{dT}{dt} \right ) \left ( \frac{4}{3} \pi (d/2)^3 \right ) \]

\[ \therefore \frac{dT}{dt} = \frac{6 h_i \Delta T}{c d} \]

If ΔT (initial value) is ~1,000 K, and specific heat, c, is ~3 ×10^{6} J m^{-3} K^{-1}, then the heating rate is ~4 × 10^{7} K s^{-1} for a fine particle and ~2 ×10^{4} K s^{-1} for a coarse one. These are both high rates, but particle size clearly has a strong effect. With typical flight times of the order of a few tens of ms, even 100 μm particles will become heated, but perhaps only by a few hundred K. For this reason, large particles (>100 μm) are rarely used in thermal spraying and, particularly for materials with high melting points (eg ceramics), it's often necessary for particles to be relatively small (<~50 μm), as well as making the gas temperature as high as possible.

The simulation below, in which these relationships are used to estimate both the particle temperature and its Stokes number on reaching the substrate, allows exploration of the conditions needed to ensure that a deposit is formed (ie that the particles will strike the substrate while molten), for some selected materials.