Analysis of Totally Translucent and Opaque Limiting Cases

The model was first applied to a baseline cooled iron engine. The simulation was carried out first with a single totally opaque iron layer of the same thickness as for the ceramic cases (2.5 mm). The coolant boundary condition was set up to provide a time average temperature on the surface of 650K. It was then repeated for the highly opaque and highly transparent insulated cases. The results obtained are summarized in Table I.

Insulation by the plasma sprayed ceramic substantially reduced the predicted time-averaged heat flux through the wall, from 0.458 MW/m2 down to 25-40% of this value (0.114-0.178 MW/m2), depending on whether the ceramic was translucent. When the ceramic was fully opaque, both the radiation and convection heat flux were deposited on the ceramic surface at the gas/ceramic interface. The mean heat flux through the wall was 0.114 MW/m2 or 75% lower than for the iron wall. A much higher temperature swing was observed, 113K vs. 27K for the iron. When the ceramic was fully transparent, the radiation was deposited on the ceramic/substrate interface rather than on the ceramic surface. This reduced the ceramic effectiveness as a heat barrier and the mean heat flux increased from 0.114 to 0.178 MW/m2, i.e., by 56%. The mean maximum wall temperature was decreased, and so was the surface temperature swing.

The results also showed the increased importance of radiation when the walls are insulated. While for the iron wall the radiation accounted for 21% of the total heat transfer, with insulation this proportion rose to 81% of the total for the opaque case.

Complete Parametric Study

The second part of the study was carried out by making perturbations of each parameter around the baseline ceramic case described above.

The most important radiative property was found to be the absorption

Table I. Comparison of Heat Fluxes and Temperatures for Three Different Wall Materials

Mean surface temperature (K) Surface temperature swing (K) Maximum surface temperature (K) Substrate interface temp. (K)

Total heat flux (mean) (MW/nr) Radiation flux (mean) (MW/m2) Convection flux (mean) (MW/m2) Radiation/total heat flux

Plasma Sprayed Zirconia

Iron Opaque Transparent

650 1007 936

27 113 92

670 1082 998

650 650

0.458 0.114 0.178

0.094 0.093 0.087

0.364 0.021 0.091

coefficient. Decreasing its value increased the total heat flux substantially. This increase was mainly due to an increase in the convective heat flux, although the radiative contribution is also seen to have increased by a small amount (Figure 17). The convective heat flux was increased in the transparent case because the radiation flux was not deposited in the ceramic, but passed right through it to the substrate. The ceramic was thus cooler (Figure 18) and this increased the convective heat transfer. The second most important parameter was the scattering coefficient, which also reduces the total heat flux (Figure 19). The back-scattering fraction and the refractive index had a much smaller effect on the time average heat flux through the ceramic.

The ceramic layer thickness has, of course, a major effect on the heat barrier effectiveness as a whole (Figure 20). The magnitude of the effects of translucence is accentuated with increasing thickness, and the ratio of heat flux for transparent case to that for an opaque case increases with increasing thickness. The thermal conductivity of the ceramic has an important effect: decreasing thermal conductivity (higher thermal barrier effectiveness) accentuates the sensitivity to translucence (Figure 21).

Figure 18. Effect of absorption coefficient on surface temperature, L — 2.5 mm.
Figure 19. Effect of scattering coefficient on heat flux, L = 2.5 mm.
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