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Plasma spraying is widely used for coating deposition and advanced material forming. To control the plasma spraying process, one should be able to evaluate on line the key physical process variables, including the bulk temperature of particles (Pfender and Chang, 1998; Moreau, 1998; Fincke et al., 2001; Fauchais, 2004; Fauchais et al., 2006; Streibl et al., 2006). The particle temperature is usually determined experimentally from the ratio of the thermal radiation detected at two closely related wavelengths (two-color pyrometry). As a result, the so-called color temperature is obtained. It the case of a semitransparent particle, the color temperature is intermediate between the surface temperature and the center temperature of the particle, but it may not coincide with the bulk (volume-averaged) temperature. The difference between the measured value of color temperature and the bulk temperature may be considerable because of the great temperature difference inside the particles of oxides, which are characterized by very small thermal conductivity. The temperature profiles inside the particles were analyzed long ago by Yoshida and Akasi (1977) and Fiszdon (1979), but the semitransparency of oxide particles was ignored, even in a more recent paper by Wan et al. (1999). The particle semitransparency in thermal spraying was first taken into account by Dombrovsky and Ignatiev (2001, 2003).

Particle concentration in a plasma spray jet is usually small; therefore, particles do not interact with each other, and their influence on plasma parameters is not large. On the other hand, the optical thickness of the jet is small, and thermal radiation can be easily taken into account in the heat balance for a single particle. The resulting equations for a particle moving along the jet axis are as follows:

(1a)
(1b)
(1c)

The latent heat of melting is treated here as an equivalent increase in the specific heat capacity in the narrow temperature interval near the melting temperature (δ is the Dirac function). The value of the heat generation rate on the right-hand side of the energy equation is determined by use of an MDP0 approximation. We will not give here the semi-empirical relations for the drag coefficient CD and Nusselt number Nu. The corresponding equations as well as approximations of the thermal properties of argon plasma and typical profiles of the plasma velocity and temperature along the jet axis can be found in a paper by Dombrovsky and Ignatiev (2003) and in the book by Kundas et al. (1998). The numerical results for aluminum oxide particles are presented below. The following approximate relation for the absorption coefficient of molten aluminum oxide was used in the calculations (Dombrovsky, 1996):

(2)

where λ is expressed in microns and T is in Kelvin. The calculated temperature for a particle of radius a = 25 μm is shown in Figs. 1 and 2. One can see the great temperature difference inside the particle during the melting. Note that the radiation effect on particle temperature is insignificant. It is much less than that predicted by the opaque particle model. The calculations for particles of zirconium dioxide give similar results, but the temperature difference in a particle of the same size appears to be much greater (Dombrovsky and Ignatiev, 2001, 2003). We consider an example of aluminum oxide because of more reliable data for the temperature dependence of the absorption coefficient of the melt.

Figure 1. Calculated temperature of aluminum oxide particle in plasma jet: 1, without radiation; 2, with radiation; a, surface; b, average (bulk) temperature; c, center

Figure 2. Calculated temperature profiles in aluminum oxide particle at two different cross sections of plasma jet: 1, without radiation; 2, with radiation

Consider the relationship between the calculated color temperature Tc and the bulk temperature T of aluminum oxide particle. The latter quantity is defined as

(3)

The calculated values of Tc and T for a particle of radius a = 25 μm moving along the plasma jet axis are shown in Fig. 3. It is interesting that the variation of particle color temperature along the jet axis is not monotonic. This result is explained by the strong increase in the absorption coefficient of aluminum oxide with temperature. The considerable difference between measured color temperature and bulk temperature of particles in plasma spraying should be taken into account in optical diagnostics of plasma spraying process. Some suggestions of estimates of bulk temperature from experimental data were reported by Dombrovsky and Ignatiev (2003). It was also shown that one can evaluate the absorption coefficient of a particle substance aλ(T) by using the measurements of particle color temperature in a plasma jet.

Figure 3. Comparison of color temperature Tc (1) and bulk temperature T (2) of an aluminum oxide particle in a plasma jet

REFERENCES

Dombrovsky, L. A., Radiation Heat Transfer in Disperse Systems, Begell House, New York and Redding, CT, 1996.

Dombrovsky, L. A. and Ignatiev, M. B., Inclusion of Nonisothermality of Particles in the Calculations and Diagnostics of Two-Phase Jets Used for Spray Deposition of Coatings, High Temp., vol. 39, no. 1, pp. 134–141, 2001.

Dombrovsky, L. A. and Ignatiev, M. B., An Estimate of the Temperature of Semitransparent Oxide Particles in Thermal Spraying, Heat Transfer Eng., vol. 24, no. 2, pp. 60–68, 2003.

Fauchais, P., Understanding Plasma Spraying, J. Phys. D, vol. 37, no. 9, pp. R86–R108, 2004.

Fauchais, P., Montavon, G., Vardelle, M., and Cedelle, J., Developments in Direct Current Plasma Spraying, Surf. Coat. Tech., vol. 201, no. 5, pp. 1908–1921, 2006.

Fincke, J. R., Haggard, D. C., and Swank, W. D., Particle Temperature Measurement in the Thermal Spray Process, J. Thermal Spray Tech., vol. 10, no. 2, pp. 255–266, 2001.

Fiszdon, J. K., Melting of Powder Grains in a Plasma Flame, Int. J. Heat Mass Transfer, vol. 22, no. 5, pp. 749–761, 1979.

Kundas, S. P., Dostanko, A. P., Il'ushenko, A. F., Kuz'menkov, A. N., Lugscheder, E., and Eritt, U., Computer Simulation of Plasma Spraying Process, Bestprint, Minsk. 1998 (in Russian).

Moreau, C., Towards a Better Control of Thermal Spray Process, Proc. of 15th Int. Therm. Spray Conf., Nice, France, x, pp. 1681–1693, 1998.

Pfender, E. and Chang, C. H., Plasma Spray Jets and Plasma-Particulate Interaction: Modeling and Experiments, Proc. of 15th Int. Therm. Spray Conf., Nice, France, x, pp. 315–327, 1998.

Streibl, T., Vaidya, A., Friis, M., Srinivasan, V., and Sampath, S., A Critical Assessment of Particle Temperature Distributions During Plasma Spraying: Experimental Results for YSZ, Plasma Chem. Plasma Process., vol. 26, no. 1, pp. 73–102, 2006.

Wan, Y. P., Prasad, V., Wang, G. X., Sampath, S., and Fincke, G. R., Model of Power Particle Heating, Melting, Resolidification, and Evaporation in Plasma Spraying Processes, ASME J. Heat Transfer, vol. 121, no. 3, pp. 691–699, 1999.

Yoshida, T. and Akasi, K., Particle Heating in a Radio-Frequency Plasma Torch, J. Appl. Phys., vol. 48, no. 6, pp. 2252–2260, 1977.

References

  1. Dombrovsky, L. A., Radiation Heat Transfer in Disperse Systems, Begell House, New York and Redding, CT, 1996.
  2. Dombrovsky, L. A. and Ignatiev, M. B., Inclusion of Nonisothermality of Particles in the Calculations and Diagnostics of Two-Phase Jets Used for Spray Deposition of Coatings, High Temp., vol. 39, no. 1, pp. 134–141, 2001.
  3. Dombrovsky, L. A. and Ignatiev, M. B., An Estimate of the Temperature of Semitransparent Oxide Particles in Thermal Spraying, Heat Transfer Eng., vol. 24, no. 2, pp. 60–68, 2003.
  4. Fauchais, P., Understanding Plasma Spraying, J. Phys. D, vol. 37, no. 9, pp. R86–R108, 2004.
  5. Fauchais, P., Montavon, G., Vardelle, M., and Cedelle, J., Developments in Direct Current Plasma Spraying, Surf. Coat. Tech., vol. 201, no. 5, pp. 1908–1921, 2006.
  6. Fincke, J. R., Haggard, D. C., and Swank, W. D., Particle Temperature Measurement in the Thermal Spray Process, J. Thermal Spray Tech., vol. 10, no. 2, pp. 255–266, 2001.
  7. Fiszdon, J. K., Melting of Powder Grains in a Plasma Flame, Int. J. Heat Mass Transfer, vol. 22, no. 5, pp. 749–761, 1979.
  8. Kundas, S. P., Dostanko, A. P., Il'ushenko, A. F., Kuz'menkov, A. N., Lugscheder, E., and Eritt, U., Computer Simulation of Plasma Spraying Process, Bestprint, Minsk. 1998 (in Russian).
  9. Moreau, C., Towards a Better Control of Thermal Spray Process, Proc. of 15th Int. Therm. Spray Conf., Nice, France, x, pp. 1681–1693, 1998.
  10. Pfender, E. and Chang, C. H., Plasma Spray Jets and Plasma-Particulate Interaction: Modeling and Experiments, Proc. of 15th Int. Therm. Spray Conf., Nice, France, x, pp. 315–327, 1998.
  11. Streibl, T., Vaidya, A., Friis, M., Srinivasan, V., and Sampath, S., A Critical Assessment of Particle Temperature Distributions During Plasma Spraying: Experimental Results for YSZ, Plasma Chem. Plasma Process., vol. 26, no. 1, pp. 73–102, 2006.
  12. Wan, Y. P., Prasad, V., Wang, G. X., Sampath, S., and Fincke, G. R., Model of Power Particle Heating, Melting, Resolidification, and Evaporation in Plasma Spraying Processes, ASME J. Heat Transfer, vol. 121, no. 3, pp. 691–699, 1999.
  13. Yoshida, T. and Akasi, K., Particle Heating in a Radio-Frequency Plasma Torch, J. Appl. Phys., vol. 48, no. 6, pp. 2252–2260, 1977.
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