10.07.2015   SonSolar

Suitable for the sky radiator surface among the calculated results. The spectral emissivity also strongly depends on the depth of gratings. The simulation result on a shallow grating structure is shown in Fig. 4. A sharp peak is observed at the periodicity of grating. This characteristic peak can be attributed to the resonant peak with surface plasmon polariton excited at the grating surface [10]. The high emissivity at the peak is suitable to the selective emitters. However, the strong angular dependence of emissivity as well as the narrow bandwidth of emission peak will be disadvantages for the application for sky radiators. On the other hand, the deep grating shows quite different spectral emissivity as shown in Fig. 5. In this case, instead of the sharp resonant peak as in Fig.4, a broadened emission band is observed at the long wavelength region comparing the periodicity. This broad band can be attributed to the cavity mode excited in the each micro cavity [11]. The spectral region of the broad band in Fig.5 corresponds to the atmospheric window, and the spectral emissivity shows little angular dependence. From these results, we have concluded that the deep grating with periodicity of 6pm and aperture ratio of 0.8 is a feasible structure for sky radiators. Figure 5 Spectral emissivity of a deep grating structure calculated with в =0 [deg]. Wavelength [gm] Figure 4 Spectral emissivity of a sharrow grating structure calculated with в =0 [deg]. . Estimation of the cooling power

The atmospheric radiation model proposed by Martin and Berdahl [12] is used in this study to estimate the cooling power. In this model the radiation is expressed by

F, (л, е) = 1 -(l — Ss Jt{X)/tav ]■ Exp[b(l.7 — 1/cos <?)]. (5)

Here, es is the averaged emissivity in clear sky, and is given by

= 0.711 + 0.5б(гф/100)+ 0.73(ГФ/100)2 . (6)

Here, 7dp is the dew point temperature [°C] (-13°C<Tdp<24°C) , b is a constant parameter, and t(X) is a shape function of the atmospheric window. tav is represented by

4 = £■ dXt {x)Eb (Л, Ta )/£ dAEb (Л, Ta) . (7)

Here, Ta is ambient temperature, and Eb(X, Ta) is the monochromatic thermal radiation power defined by Planck’s law. Using these formulations, the atmospheric radiation R is represented by

(8)

Rs (Л, в) = є, {x,0)Eb(Л, Ta)

Varying the zenithal angle the spectral emissive power shown in Fig.6 is calculated by using the above equations.

Figure 6 Spectral emissive power of the clear sky at temperature of 298 [K] and humidity of 80 [%].

The emissive power absorbed by the sky radiator surface is expressed by

4 (Л, в) = Е, (Л, в)кs (Л,0). (9)

Here, es(49) Is the spectral emissivity of sky radiator surface. On the other hand, the emissive power from sky radiator surface is represented by

Re M = e, (Л,0)Еь (Л, Te). (10)

Here, Te is the surface temperature of sky radiator. Using eq’s (9) and (10), the cooling power is expressed by

Ta-Te [K]

Figure 7 Calculated cooling power of the sky radiator with the spectral emissivity shown in Fig. 5.

Figure 7 shows the calculated cooling power of sky radiator with the spectral emissivity shown in Fig. 5 using equation (11). The ambient conditions used in the calculation are the typical values for summer season in Japan. As seen in this figure, high cooling power more than 100W/m2 can be obtained even at ДТ=10 K. This performance will be the level for practical application in Japan.

Ce = 2я% dX fj1 sin в cos 0d0{Re (X,0)~ Ae (Л, в)). (11)