Appendix B
Radiation Transport in Thermal Barrier Coatings
The energy transport process in ceramic thermal barrier coatings (TBCs) has been measured until recently by an empirical parameter: thermal conductivity. This measure does not distinguish the relative contributions of radiation and true conduction. A role for radiative transport is raised by the transparency of some of the ceramics used for TBC applications in the infrared spectral region for wavelengths in the region of 1 to 6 µm (Thomas and Joseph, 1987; Thomas, 1989; Sova et al., 1992). This region also corresponds to the region of maximum black-body emission for the operating temperatures of present gas-turbine engines. Advanced engines under development in current NASA and U.S. Department of Energy programs are expected to reach even higher temperatures with correspondingly higher levels of infrared radiation incident on the coating in the 1- to 6-µm band from the interior of the engine. The combination of high infrared radiation density and low coating absorption suggests that radiation may compete with conduction for energy transport across the coating.
Radiative transport of energy across a uniform coating involves a number of factors:
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the intensity and spectral distribution of infrared radiation in the engine enclosure in the 1- to 6-µm region
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infrared reflection at the coating/engine and coating/blade interfaces
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scattering and absorption within the coating
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radiation trapping in the coating by internal reflection of radiation
Regarding the source energy distribution, the radiant energy that is incident on a coated blade or vane in the engine will have contributions from both the burning gas and the other engine surfaces. The relative contributions of these sources may change with position in the engine and blade number. Factors influencing infrared reflection at the coating/engine interface include a quasi-specular component associated with the difference in dielectric constants of the gas and coating as well as a diffuse reflection associated with the structure of the coating surface. For example, coatings applied using an electron-beam physical vapor deposition (EB-PVD) process have a polycrystalline columnar structure that leads to significant scattering in the visible spectral region. The same coatings are partially transparent in the infrared in the 1- to 6-µm region (Murphy et al., 1993), however, suggesting that scattering is size related via the parameter ka where a is a dimension of the crystallites in the coating and is the characteristic size of the scatterer, and ?is the wavelength. In the case of EB-PVD coatings the scatters are features such as the spacing and organization of columns in the coating (the coating has a columnar structure) and individual crystallites in a column. Both of these contribute to the scattering. This result further implies that the penetration of radiation from an external source will depend on the wavelength and angle of incidence.
Scattering has been shown to play an important role in determining the internal temperature distribution in layered specimens (Siegel and Spuckler, 1993b). For specimens that exhibit both scattering and absorption of radiation, the temperature distribution is affected by the albedo, which is a measure of the relative importance of scattering and absorption (Siegel and Spuckler, 1993a). Radiation trapping caused by internal reflection was also shown to play an important role in determining the temperature distribution (Siegel and Spuckler, 1993a). In light of the roles that scattering and radiative transport play in reducing the temperature gradient (i.e., creating more uniform temperatures along the blade) and since temperature gradient drives thermal conduction, any estimate of the relative importance of radiation and conduction requires that a treatment consider both mechanisms simultaneously.
TBCs fabricated from layers of oxides of varying optical thickness have been proposed to reduce radiative transport by selective reflection of infrared radiation in the 1- to 6-µm band (Soechting, 1994). These TBCs would form high-temperature interference filters in the near infrared. In addition, multilayered materials will affect the rate of conductive transport (Aamodt et al., 1990a,b). For example, multilayered structured TBCs, or more generally nanostructured TBCs, could reduce both conductive and radiative transport. The relative importance of the two processes should be determined through more extensive study.
REFERENCES
Aamodt, L.C., J.W.M. Spicer, and J.C. Murphy. 1990a. Analysis of characteristic thermal transit times for time-
resolved infrared radiometry studies of multilayered coatings. Journal of Applied Physics 68(12):6087-6098.
Aamodt, L.C., J.W.M. Spicer, and J.C. Murphy. 1990b. The effect of transverse heat flow and the use of characteristic times in studying multilayered-coatings in the time domain. Pp. 59-63 in Photoacoustic and Photothermal Phenomena II, J.C. Murphy, J.W.M. Spicer, L.C. Aamodt, and B.S.H. Royce, eds. Berlin, Germany: Springer-Verlag.
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Sova, R., M.J. Linevsky, M.E. Thomas, and F.F. Mark. 1992. High temperature optical properties of oxide ceramics. Johns Hopkins APL Technical Digest 13:369-378.
Thomas, M.E. 1989. A computer code for modeling optical properties of window materials. Proceedings of SPIE: Window and Dome Technologies and Materials 1112:260-267.
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